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RocketAgent: A Long-Horizon Engineering Agent for Multidisciplinary Design of Liquid-Rocket Thrust Chambers
Junxiang He, Runze Mao, Kun He, Teng Zhang, Liming Zheng, Ke Xiao, Zhi X. Chen
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Abstract
Abstract:Liquid-rocket thrust-chamber design involves interdependent analyses in which downstream constraints can require earlier design decisions to be revisited. Managing these dependencies across heterogeneous tools requires consistent design information and coordinated updates throughout the workflow. We present RocketAgent, a long-horizon engineering agent for multidisciplinary preliminary design of liquid-rocket thrust chambers. A single plan-owning Coding Agent coordinates engineering skills for performance sizing, subsystem optimization, geometry generation, and multiphysics assessment. A provenance-aware knowledge graph supports method selection, while a typed Design Intermediate Representation maintains shared parameters, artifacts, and decisions. Revision-aware checks invalidate affected results and block superseded inputs, with consequential changes subject to engineering approval. In a representative simulation-based design, RocketAgent continued from an infeasible cooling search through an engineer-authorized operating-point revision, identified feasible subsystem designs, and coordinated subsequent geometry generation and multiphysics assessment to support final configuration selection. Separate module tests assessed surrogate predictions and nozzle adaptation. A two-configuration comparison across three controlled scenarios verified the expected dependency invalidations and superseded-input blocking before solver execution. The representative case demonstrates sustained coordination across a multidisciplinary design workflow, while the controlled tests establish the behavior of the revision mechanisms supporting that execution.
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- Source: https://arxiv.org/abs/2610.06044v1
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RocketAgent: A Long-Horizon Engineering Agent for Multidisciplinary Design of Liquid-Rocket Thrust Chambers Junxiang He a,b , Runze Mao a,c,d,∗ , Kun He c , Teng Zhang c , Liming Zheng c , Ke Xiao c , Zhi X. Chen a,c,d,∗ a State Key Laboratory of Turbulence and Complex Systems, School of Mechanics and Engineering Science, Peking University, Beijing, 100871, China b College of Engineering, Peking University, Beijing, 100871, China c Legendspace Intelligence Technology Co., Ltd., Beijing, 100080, China d AI for Science Institute (AISI), Beijing, 100084, China Abstract Liquid-rocket thrust-chamber design involves interdependent analyses in which downstream constraints can require earlier design decisions to be revisited. Managing these dependencies across heterogeneous tools requires consistent design information and coordinated updates throughout the workflow. We present Rock- etAgent, a long-horizon engineering agent for multidisciplinary preliminary design of liquid-rocket thrust chambers. A single plan-owning Coding Agent coordinates engineering skills for performance sizing, subsys- tem optimization, geometry generation, and multiphysics assessment. A provenance-aware knowledge graph supports method selection, while a typed Design Intermediate Representation maintains shared parameters, artifacts, and decisions. Revision-aware checks invalidate affected results and block superseded inputs, with consequential changes subject to engineering approval. In a representative simulation-based design, Rocke- tAgent continued from an infeasible cooling search through an engineer-authorized operating-point revision, identified feasible subsystem designs, and coordinated subsequent geometry generation and multiphysics as- sessment to support final configuration selection. Separate module tests assessed surrogate predictions and nozzle adaptation. A two-configuration comparison across three controlled scenarios verified the expected dependency invalidations and superseded-input blocking before solver execution. The representative case demonstrates sustained coordination across a multidisciplinary design workflow, while the controlled tests establish the behavior of the revision mechanisms supporting that execution. Keywords: Long-horizon engineering agents; Knowledge graph; Multidisciplinary design; Workflow orchestration; Design revision management; Liquid-rocket thrust chambers ∗ Corresponding authors. E-mail addresses: maorz1998@pku.edu.cn (R. Mao), chenzhi@pku.edu.cn (Z. X. Chen). arXiv:2610.06044v1 [cs.AI] 5 Oct 2026 1. Introduction The design of complex engineering products involves interdependent decisions across disciplines and com- putational tools. Requirements, model assumptions, and analysis results must remain consistent as a design develops, while findings from later stages can require earlier decisions to be revised [1, 2]. Managing these dependencies requires engineers to determine which tasks can proceed, which results remain applicable, and which analyses must be repeated after a change. Supporting this coordination is an engineering informatics problem that connects the representation of design knowledge with its use in an evolving workflow. Liquid-rocket thrust-chamber design provides a concrete setting for studying this problem. Propulsion performance, regenerative cooling, injector design, and structural response impose coupled requirements on the same design [3–5]. An operating point selected for high specific impulse may prove incompatible with cooling constraints, prompting a revision that changes propellant flows, subsystem designs, and inputs to subsequent analyses. These changes must be carried consistently through specialized calculation, geometry, and simulation tools. Completing the preliminary design therefore requires coordination across successive engineering decisions, including feedback that redirects work to an earlier stage [1, 3]. Established engineering approaches provide foundations for managing this process. Knowledge-based engineering (KBE) and knowledge graphs (KGs) formalize reusable knowledge and its relationships, sup- porting method selection and design decisions [6, 7]. Digital threads connect design information across stages [2], while multidisciplinary design optimization organizes coupled analyses around explicit variables, objec- tives, and constraints [8]. These approaches address complementary aspects of knowledge representation, information continuity, and computational design. Their integration into an executable workflow requires the represented knowledge and dependencies to inform what work is performed and how its results affect subsequent decisions. Large language model (LLM)-based agents offer an approach to this coordination through knowledge retrieval, planning, and tool use [9–11]. Engineering applications have connected agent decisions to deter- ministic calculations for code-compliant structural design, finite-element optimization, and traceable analysis workflows [12–14]. Such systems provide precedents for using computational feedback to guide further ac- tions. However, LLM outputs can contain unsupported content [15], making engineering knowledge, explicit interfaces, and numerical checks essential to their application. For an extended multidisciplinary workflow, these controls must operate across task boundaries: a locally valid calculation may still use an outdated operating point, depend on an unaccepted subsystem design, or produce results that become inapplicable after a revision. The problem addressed here is how to connect agent planning with the evolving engineering basis of a design. The agent needs access to applicable methods, accepted inputs, unresolved constraints, and the dependencies between computational results. When an assessment fails, the workflow must distinguish 2 an input error or numerical failure from physical infeasibility and determine the appropriate continuation. When a change is accepted, affected results must be identified before they are reused. These requirements motivate the integration of reusable engineering knowledge, persistent design state, and revision handling within the execution process. We present RocketAgent, a long-horizon engineering agent for multidisciplinary preliminary design of liquid-rocket thrust chambers. Here, long-horizon execution denotes continued progression through an ex- tended sequence of dependent engineering tasks, including feedback-driven revisions and expert decision points. A single Coding Agent maintains the global plan and coordinates engineering skills through de- clared inputs, outputs, and validation requirements. A provenance-aware KG supports method selection, while a typed Design Intermediate Representation (Design IR) links requirements, parameters, artifacts, evi- dence, and decisions. Accepted changes trigger dependency-scoped invalidation and an ordered re-execution plan; solver-entry checks block superseded inputs. Deterministic tools perform calculations and enforce numerical criteria, while engineers authorize consequential changes and review the final design. The study contributes an architecture that connects these mechanisms and evaluates their operation at complementary levels. A representative simulation-based case traces the workflow from accepted re- quirements through cooling-driven redesign, subsystem development, geometry generation, and multiphysics assessment. This record documents how the Agent carries work across stages and continues after engineer- ing feedback. Separate module tests assess surrogate predictions and geometry-interface reuse. A two- configuration comparison across three controlled scenarios tests dependency invalidation and superseded- input blocking, with execution stopping before solver launch. Together, these evaluations examine sustained workflow execution and the specific revision mechanisms that support it, within the scope of simulation-based preliminary design. Section 2 reviews related work, Section 3 presents the framework, and Section 4 reports the engineering and controlled-test results. Sections 5 and 6 discuss their implications and summarize the contributions. 2. Background and Related Work 2.1. Knowledge-Based, Knowledge-Graph, and Model-Based Engineering Design Knowledge-based engineering (KBE) formalizes product and process knowledge to automate recurring engineering tasks. Verhagen et al. [6] consolidated its foundations and identified challenges in traceability, interoperability, and implementation. Al-Ashaab et al. [16] connected automotive design changes to valida- tion plans through KBE-ProVal, linking physical tests, theoretical knowledge, and historical results within a product-lifecycle-management environment. These approaches establish knowledge reuse and change trace- ability as practical design capabilities. 3 Knowledge graphs extend these capabilities to decision support and design exploration. Hao et al. [7] structured decision knowledge for retrieval and navigation, using natural-language processing to transform compromise Decision Support Problem formulations into graph representations. Their evaluation covered 25 supply-chain decision problems. Liu et al. [17] used graph embeddings to predict functional-coupling relations in smart products. Huang et al. [18] combined a multi-source KG with graph matching, multi- objective optimization, decision making, and mechanism-based simulation for launch-vehicle stage-separation architectures. Their workflow illustrates how structured knowledge can support a design–evaluation loop with traceable feedback and confidence tagging. Model-based systems engineering and digital threads supply complementary information-management principles. Madni and Sievers [19] described an evolving system model supporting specification, design, vali- dation, and configuration management. Singh and Willcox [2] linked lifecycle information through stagewise updates for iterative design under uncertainty. Together, these foundations motivate a separation between reusable engineering knowledge and the evolving state of a particular design. RocketAgent implements this separation through a provenance-aware KG and a shared Design IR, then connects both to executable engineering skills. 2.2. LLM-Based Engineering Agents and Skill/Tool Use LLM-based workflows connect language interpretation to knowledge retrieval and executable actions. Retrieval-augmented generation conditions responses on external documents [9], while ReAct interleaves reasoning, actions, and observations [10]. Engineering applications adapt these patterns to product devel- opment: DesignGPT organizes role-based collaboration with human designers [20], natural-language CAD workflows connect requirements to calculations and editable geometry [21], and iDesignGPT combines agent clusters, design methods, and a knowledge base for concept development and evaluation [11]. The CAD study demonstrated parameter-consistent generation of a one-stage reduction-gear system. iDesignGPT evaluated conceptual-design support through design-space metrics, expert assessment across six public challenges, and controlled user studies. Physics-backed agents extend this interaction into computational design loops. Chen and Bao [12] used specialized agents and deterministic modules for code-compliant reinforced-concrete beam design. Their subsequent framework combined LLM supervision, genetic optimization, and finite-element evaluation of ultra-high-performance concrete beams [13]. StructureClaw connects governed skills, typed tools, shared ar- tifacts, and local analysis backends, evaluating execution traces across 150 controlled structural-engineering scenarios [14]. Its benchmark covers standard workflows, interactive robustness, and multimodal structural- model reconstruction. These studies demonstrate executable feedback and increasingly explicit workflow governance for bounded engineering tasks. They also establish useful precedents for separating agent plan- ning from deterministic calculation and for evaluating the resulting execution records. 4 For a thrust chamber, orchestration extends across thermochemistry, cooling, geometry, reacting flow, and structural assessment. RocketAgent focuses on driving this long task sequence through one plan-owning Coding Agent and contract-bound skills. A revision-aware Design IR carries inputs and artifacts between tasks, while source-linked execution and deterministic checks address the risk of unsupported LLM output [15]. 2.3. Computational Methods for Thrust-Chamber Design Thrust-chamber analysis combines specialized models with different inputs and assumptions. NASA CEA computes chemical-equilibrium compositions, thermodynamic properties, and theoretical rocket performance [22]; RocketCEA exposes these calculations through Python [23]. RPA supports liquid-rocket performance analysis and thermal analysis of cooled chambers and nozzles [24, 25]. Their outputs inform geometry and cooling design, provided that units, equilibrium assumptions, and nozzle conventions remain aligned. Established geometry and design methods include Rao’s optimum-thrust nozzle contour [26], the para- metric thrust-chamber model of Rezende et al. [27], liquid-propellant engine design procedures [3], and fluid-cooled chamber criteria [28]. PicoGK supplies programmable voxel, mesh, and lattice operations for computational geometry [29]. Coupled analyses resolve interactions within such geometries: Kim et al. [5] linked compressible reacting-flow calculations to regenerative cooling and compared performance predictions with hot-firing measurements, while Liu et al. [30] transferred thermal and pressure fields into a combustion- chamber structural model. These studies establish the physical links that a cross-tool design workflow must preserve during redesign. Optimization methods search the resulting trade spaces. Martins and Lambe [8] organized multidisciplinary- design-optimization architectures around unified formulations and process flows. NSGA-I provides elitist multi-objective search [31], while efficient global optimization and surrogate-based methods reduce reliance on expensive function evaluations [32, 33]. These methods assume that variables, objectives, constraints, and analysis interfaces have been defined. In requirement-driven design, this formulation must remain consis- tent as operating conditions and geometry evolve. RocketAgent uses a GA for regenerative-cooling-channel search and NSGA-I for surrogate-assisted centrifugal-injector screening, with each search connected to the shared design state. Higher-fidelity methods provide flow-field evidence and numerical-credibility procedures. DeepFlame extends the OpenFOAM finite-volume framework for reacting-flow computation through Cantera, PyTorch, and additional computational utilities [34]. Assessments of OpenFOAM and EBIdnsFoam examine nu- merical accuracy and parallel performance [35]. The VOF method resolves free-boundary dynamics [36]. Discretization-uncertainty estimation [37], verification and validation principles [38], ASME V&V 20 [39], and NASA-STD-7009B [40] guide interpretation of computational evidence. These methods supply the numerical capabilities and credibility practices on which the integrated workflow builds. 5 2.4. Summary of Research Gap Existing research provides mature design methods and task-bounded closed loops in which computational evaluation guides design revision [12–14, 18]. The remaining gap concerns their joint execution for a complex industrial product such as a liquid-rocket thrust chamber. Its preliminary design requires knowledge, mutable parameters, heterogeneous models, and revision feedback to remain connected from requirements to the expert-reviewed design package. The reviewed digital-thread, artifact-centered agent, and model-credibility approaches provide complementary foundations [2, 14, 40], but do not jointly address this coupled thrust- chamber workflow. Driving this extended workflow requires three supporting capabilities: state continuity, linking require- ments and parameters to their sources and artifacts; evidence-closed execution, connecting tool results to design checks and selection decisions; and feedback and governance continuity, identifying affected depen- dencies and coordinating re-execution after changes. These capabilities allow the Agent to carry work across stage boundaries and continue after a design revision. For example, a mixture-ratio change affects thermal loads, cooling feasibility, and downstream geometry, requiring the plan and dependent results to be updated together. These challenges motivate an Agent-driven workflow that connects multidisciplinary tasks from requirements to design evaluation, supported by consistent information transfer and revision handling. 3. Proposed Methodology and System Realization RocketAgent drives thrust-chamber design through three connected stages: translating requirements into a design concept, developing its coupled subsystems, and verifying the resulting configurations. The following sections explain the engineering decisions at each stage and the shared-state mechanism that supports continuation when a design must change. 3.1. Problem Formulation The problem concerns steady, simulation-supported preliminary design of hundred-newton-class liquid- rocket thrust chambers. Given thrust and operating requirements, the design process must determine a consistent performance state, chamber/nozzle contour, regenerative-cooling layout, and preliminary swirl- injector configuration, then assess their integrated multiphysics response. Propellants, wall materials, nozzle families and angles, and subsystem configurations are replaceable inputs supported by the corresponding backend models. The design space combines architectural choices with continuous operating and geometric parameters. Hard constraints enforce geometric consistency, thermal-hydraulic limits, structural margins, and model applicability; soft objectives compare performance and distance from active constraints. Some quantities remain open to optimization, and their eventual values become accepted design decisions. Because these 6 c. Result a. Natural Language Intent “Design a 500 N sea-level LOX/RP-1 rocket engine with regenerative cooling, and a conical nozzle.” b. RocketAgent Framework Improve Observe Act Think Knowledge Sources Domain Ontology Requirements Functions Constraints Reviewed Literature Fact Cards Engineering Rules Tool Cards Case Experience Design IR Tool Artifacts Validation Events Semantic Property Graph d. KnowledgeGraph Constraint Parameter Requirement Component Function Tool Design Case maps_to constrains generated_bysupported_by part_of maps_to e. Engineering Tools Engineering Solvers RPA Cooling Channel Thermal Analysis ABAQUS Injector strength verification FLUENT Combustion simulation Optimization & Surrogate Alogrithms Gaussian Process Regression(GPR) Surrogate prediction Injector response Genetic Alogrithm(GA) Candidate generation Cooling-design search CEA Specific Impulse Analysis PicoGK STL generation DeepFlame Nozzle VOF simulation RocketAgent Figure 1: RocketAgent architecture: (a) natural-language design intent; (b) the plan-owning Coding Agent and its Think–Act– Observe–Improve cycle; (c) an illustrative thrust-chamber representation; (d) the engineering KG; and (e) specialist calculation, geometry, simulation, and optimization capabilities. decisions couple successive analyses, completing the task requires coordination across engineering knowledge, numerical tools, and design revisions. Fig. 1 translates this coordination problem into an architecture. Its central sequence, (a)–(c), connects natural-language intent to a preliminary-design output through a plan-owning Coding Agent. Within the cycle in (b), the Agent interprets the current task, invokes an engineering skill, examines the returned result, and updates the plan. The two supporting branches provide different inputs to this cycle: the KG in (d) supplies applicable knowledge and prior experience, while the calculation, geometry, simulation, and optimization tools in (e) evaluate the evolving design. The architecture therefore links reasoning about the next task to execution of that task. Section 3.2 develops this component-level view into the extended engineering workflow. 3.2. Design-State Governance and Execution Architecture Fig. 2 organizes the workflow into Conceptual Design, Embodiment Design, and Verification. The plan- owning Coding Agent spans all three stages: it maintains the task plan, selects eligible skills, inspects their outputs, and determines whether to advance or revisit earlier work. Long-horizon execution means 7 Reqirements Accepted concept and constraints KG-grounded concept Knowledge Graph (KG) Human approval Conceptual Design Embodiment Design Capability Skill Adapter Dependency graph Engineering backends Performance Geometry Optimization Subsystem gates Geometry realization Accepted design state Verification Simulation evidence Structural evidence Validation and gates State commit new accepted revision Plan-owning Coding Agent revision-aware invalidation and replanning Figure 2: Conceptual workflow of RocketAgent across Conceptual Design, Embodiment Design, and Verification, coordinated by a plan-owning Coding Agent with revision-aware feedback. driving this extended sequence from requirements to an accepted design state, including continuation after engineering feedback. Conceptual Design combines requirements with reusable KG knowledge and human approval to establish the accepted concept and constraints (Section 3.3). Embodiment Design translates this basis into perfor- mance, geometry, and optimization tasks through the capability–skill–adapter interface. The dependency graph identifies the prerequisites for these tasks, and subsystem gates check the resulting designs before geometry realization (Section 3.4). Verification brings simulation and structural evidence to the validation gates, then commits accepted results to the design state (Section 3.5). The orange return connects feedback to revision-aware invalidation and Agent replanning. When a change is approved, the Agent revisits the affected tasks and carries the accepted revision into subsequent work, represented by the lower blue return. Knowledge reuse remains subject to the provenance and review requirements in Section 3.3. These cross-stage handoffs use the Design IR as the active preliminary-design digital thread [2]. Whereas the KG supplies reusable methods and experience, the Design IR links the current requirements, parameters, artifacts, and decisions through units, provenance, dependencies, and revisions. For workflow step k, the state and its checked update are S k =⟨Q k ,X k ,A k ,E k ,D k ⟩, S k+1 =C i [T i (S k )],(1) where Q k denotes accepted requirements and assumptions, X k typed parameters, A k artifact references, E k evidence, and D k recorded decisions. A skill transformationT i proposes a successor, andC i checks its inputs, engineering criteria, and required approval before commitment. Failed checks retain the previous state and return feedback. Acceptance permits downstream use, feasibility denotes satisfaction of the applicable hard constraints, and selection chooses among feasible alternatives. 8 Revision-aware automatic invalidation is integrated into the main state-update path. An accepted change identifies direct consumers, propagates through downstream dependencies, marks affected results stale, and generates an ordered re-execution plan. Unaffected outputs retain their valid bindings. Solver-entry checks additionally compare submitted artifacts with the active registry, blocking superseded files even when their existence and checksums are valid. Separate consumers for structural-only material fields permit local revisions without invalidating unrelated cooling or geometry results. Section 4.3.5 evaluates these paths. The capability–skill–adapter separation connects planning to execution: capabilities identify engineering tasks, skills define procedures and checks, and adapters translate the accepted state into backend inputs. Deterministic programs calculate responses and apply numerical gates; externally coordinated Fluent runs enter through the same evidence interface. Human approval governs consequential changes and final selec- tion. Record and interface details are retained in Appendix D, and the Agent’s runtime and execution records in Appendix B. 3.3. KG-Grounded Conceptual Design Conceptual design converts the initial request into a numerical design problem through the relations in Fig. 3. Region A traces a requirement through its design function and engineering constraint to a tool input; parameter and IR-path links identify where that input belongs in the shared state. Region B connects these requirements to the thrust-chamber assembly, its subsystems, and their interfaces. Together, these paths turn a requested capability into the objects, parameters, and constraints that embodiment design must resolve. The lower half of the schema explains how this translation is supported. Region C links design records, literature facts, and experience to evidence references; region D connects design methods to workflow stages and conflict-resolution steps. Retrieval follows these links using the active stage and operating requirements, returning compatible prior designs, RPA examples, method cards, and reviewed facts with their provenance. These historical records can seed initial mixture-ratio ranges, nozzle and cooling alternatives, injector fam- ilies, and conflict priorities before numerical evaluation. The Agent proposes an applicable method, and deterministic checks test its units, input ranges, and prerequisites. Missing mandatory information prompts focused clarification. Retrieval weights and budgets are retained in Appendix A. The conflict links also explain why a locally attractive choice may require revision elsewhere. For example, maximizing specific impulse can select an operating point that cooling cannot accommodate, while increasing channel count changes the hydraulic trade-off. The accepted targets, configuration choices, assumptions, and screening rules initialize the shared state. Subsequent tool results refine that state and enter the knowledge-review process in Section 3.5.5. 9 m e t h o d s o b j e c t s r e q u i r e m e n t s e v i d e n c e Design Case Requirement mapping Tool-gated design Evidence trace Constraint checking A. Requirement Semantics B. Engineering Objects D. Methods & Agents C. Cases & Evidence User Reqirement Key Parameter Interface Design Function Engineering Constraint Tool Input Tool IR Path Parameter maps to constraints feeds uses Design Case Requirements PerformanceCooling ResultGeometry Artifacts Case Record Evidence Reference Literature Source Fact Card Experience Event Experience Channel Thrust Chamber Assembly Nozzle Combustion Chamber Cooling Channel Swirl Injector Validation Artifacts Design Method Agent Role Workflow Method Artifact Resolution Setup Design Conflict Design Stage Unified Semantic Schema Figure 3: KG semantic schema: (A) requirement semantics, (B) engineering objects, (C) cases and source-linked evidence, and (D) methods and agents. The four relation groups connect design intent to an accepted concept and numerical inputs. 3.4. Skill-Coordinated Embodiment Design Fig. 4 organizes embodiment design into three connected task families, linked to their physical regions in the chamber schematic. The left panel follows design inputs through performance analysis, geometry generation, and thermal assessment; its return arrow indicates refinement when the geometry requires ad- justment. The central panel illustrates how GA-generated cooling candidates expose the trade-off between wall temperature and pressure loss. The right panel combines GPR response prediction with NSGA-I search for injector alternatives at fixed propellant flows. The three tasks share an operating state and must yield a compatible contour, hard-feasible cooling layout, and admissible injector before PicoGK realizes the assembled geometry. 3.4.1. Thrust-Chamber Performance and Contour Determination The accepted propellant pair, chamber pressure, ambient condition, and target thrust define the per- formance calculation. RocketCEA evaluates equilibrium specific impulse over the prescribed mixture-ratio interval and identifies the maximum-performance operating point [22, 23]. When nozzle expansion is not prescribed, the exit pressure is matched to the ambient pressure. An optional, source-supported upper bound 10 Nozzle GPR Surrogate Model Design Variabl e x Obj ective f NSGA-I Alogrithm Pareto Front ... Gen. 2t+ Gen. t Gen. 1t+ Cooling Channel GA Algorithm P ∆ w T () () (1)( 2) 2 (1) 0, 0.12 c j j x xxNul α =+ − ′ = +− Thrust Chamber Design Inputs Propellants Thrust F Chamber Pressure c P Performance Analysis O/F Optimization sp I Mass Flow m Geometry Generation Chamber & Nozzle cctee RLRRL⋅ ⋅ ⋅ ⋅ Pareto Front Pareto front Candidate designs Selected design Thermal Analysis Wall Temperature w T Pressure Drop P∆ Figure 4: Embodiment-design tasks linked to the thrust-chamber regions: performance, geometry, and thermal refinement (left); GA-based cooling-channel search and trade-off selection (center); and GPR-assisted NSGA-I injector optimization (right). The Pareto and surrogate plots are schematic. may reduce the specific impulse used for conservative flow sizing when comparable prior-design evidence is available. The raw calculation and the resulting design value are retained separately. The design specific impulse I sp determines total propellant flow, while the oxidizer-to-fuel ratio r Ox/Fuel determines its allocation: ̇m = F I sp g 0 , ̇m Ox = r Ox/Fuel 1 + r Ox/Fuel ̇m, ̇m Fuel = 1 1 + r Ox/Fuel ̇m.(2) Here, F is the target thrust, g 0 is standard gravitational acceleration, and the subscripts Ox and Fuel denote oxidizer and fuel. Eq. 2 supplies the physical flow budget used by cooling and injector design. RPA-reported flow provides a cross-tool consistency check. RPA sizes the chamber and nozzle from this operating point, the contraction ratio, characteristic length, and selected nozzle family [24, 26, 27]. Supported contours include axisymmetric TOC, conical, and parabolic-bell profiles. The resulting chamber, throat, and exit dimensions are accompanied by an axi- ally ordered contour shared by thermal analysis and geometry realization. Positive dimensions, increasing axial coordinates, and consistent geometric anchors are checked again after dimensional quantization. If cooling cannot accommodate the maximum-performance operating point, an engineer-authorized off-peak 11 mixture ratio initiates a new performance, contour, and thermal evaluation. Thus, the performance optimum remains subject to subsystem feasibility. 3.4.2. Regenerative-Cooling Design under Coupled Constraints Cooling design seeks thermally effective channel layouts without excessive pressure loss or inadequate wall strength. A bounded search varies channel count, inlet and outlet widths and depths, hot-wall thick- ness, channel angle, and coolant-flow factor. The genetic algorithm generates candidates through selection, crossover, and mutation; geometric checks eliminate unrealizable channel arrangements before thermal eval- uation. Selection prioritizes feasibility and then the configured scalar score. Separate nondominated post- processing minimizes four normalized responses: maximum wall temperature, coolant outlet temperature, pressure loss, and structural risk. The first three are normalized by their respective limits; structural risk is SF req /SF min , where SF req is the required safety factor. Each admitted candidate is evaluated using a single full-contour RPA channel-wall model, with fuel flow- ing from the nozzle exit toward the chamber head. RPA provides stationwise heat flux, wall temperatures, coolant states, and pressure loss. A low-order structural screen combines pressure loading, the through-wall thermal gradient, and local channel-span bending [5, 28]. At axial position x, its scalar stress is σ scr (x) = σ vm,p (x) + σ th (x) + σ bend (x) + σ r (x),(3) where σ vm,p combines rib-ligament-corrected hoop pressure and closed-end axial pressure, σ th = αE|T wi − T wc |/[2(1−ν)], σ bend =|P cool −P g |w 2 ch /(2t 2 w ), and σ r is an optional mean thermal-restraint term. Here, T wi and T wc are the hot-side and coolant-side wall temperatures; P g and P cool are the gas and coolant pressures; w ch and t w are the channel span and hot-wall thickness; and α, E, and ν are the thermal-expansion coefficient, Young’s modulus, and Poisson’s ratio. The minimum screening safety factor is SF min = min x∈Ω tc σ allow (T w (x)) σ scr (x) ,(4) where Ω tc contains the sampled chamber/nozzle wall stations and σ allow is the configured allowable stress. The screen supports preliminary chamber and nozzle wall-strength assessment. The representative design uses CuCrZr with the common material definition and component-specific limits listed in Appendix A. Downstream admission requires a valid channel-wall thermal solution and simultaneous satisfaction of wall-temperature, coolant-state, pressure-loss, manufacturing, and safety-factor limits. Fuel-specific coolant- temperature and coking screens are included where applicable. Nondominated ranking reveals trade-offs among evaluated candidates, but only a candidate passing the complete hard-constraint set can be selected for geometry realization. A favorable ranking alone cannot promote an infeasible design. Search bounds and numerical settings are retained in Appendix D.2. 12 3.4.3. Fixed-Flow Surrogate-Assisted Injector Screening Injector design allocates the accepted Ox and Fuel flows among a chosen number of coaxial swirl el- ements within the injector-face envelope and igniter-clearance requirement. Changing the element count changes the single-element flow, so each layout receives a separate geometry search. The externally trained GPR model uses ten geometric or derived features and two original-propellant single-element flow features. RocketAgent keeps these flow features fixed during optimization and does not retrain the model during the design execution. The model-development VOF calculations use water in both liquid circuits. Their inlet flows are related to the original-propellant flows by ̇m (e) w,j = ̇m j N e r ρ w ρ j , j ∈Ox, Fuel,(5) where N e is the element count and w denotes water. This mapping follows ̇m = C d A √ 2ρ∆p and ap- proximately preserves pressure drop for unchanged geometry and approximately equal discharge coefficients C d . Training features retain the original-propellant flows, whereas training responses correspond to the mapped water conditions. Consequently, RocketAgent supplies the original-propellant flows directly at in- ference without applying the conversion again. GPR predicts the water-reference spray-cone angle, Fuel- and Ox-side pressure drops, and their standard deviations. NSGA-I varies the injector geometry to minimize normalized deviations from the prescribed spray-angle and pressure-drop targets [31]. Admission checks the model domain, geometric constraints, configured mean spray-angle interval, and both mean water-reference pressure drops, which must exceed 0.20P c . The μ− 2σ values are retained as diagnostics because nominal GPR intervals need not be calibrated [41]. Dimensional and angular variables are quantized and freshly evaluated before admission. Each approved layout then proceeds to its own geometry realization and configuration-level verification. Held-out prediction errors and independent post-selection VOF comparisons are reported in Section 4.2. Common geometry-realization handoff. The three design families converge on a shared geometry-realization step. PicoGK combines the accepted chamber/nozzle contour, hard-feasible cooling layout, and admissible count-specific injector geometry into solid and fluid assemblies [29]. The RPA injector-face-to-exit coordi- nate convention is retained. Each layout produces its own STL assemblies and linked generation record. Coordinate consistency and artifact checks establish the handoff, while topology and mesh suitability require their own validation records. The resulting analysis-specific domains support the multiphysics verification described next. Appendix D.2 records the numerical settings and geometry-handoff checks. 3.5. Verification-Driven Refinement Verification-driven refinement separates four questions: injector-scale spray and hydraulic response, chamber-scale reacting flow, thermal–structural strength, and configuration-level flow acceptance. The 13 software stack is therefore selected by physical role. DeepFlame provides transient interface-resolving VOF evidence for the injector; Fluent provides the three-dimensional reacting-flow assessment; Abaqus provides finite-element thermal–structural assessment; and deterministic flow and state checks compare the result- ing configurations. This separation keeps each tool responsible for the quantities it can resolve and gives the Agent a typed evidence record for downstream decisions. Case-specific meshes, boundary conditions, material cards, solver controls, and numerical outputs are reported in Appendix A, Appendix C and in Section 4. 3.5.1. Injector Spray and Hydraulic Response DeepFlame is selected for injector-scale evidence because its OpenFOAM-derived finite-volume infras- tructure supports transient volume-of-fluid (VOF) interface transport and the resolution of liquid-sheet development and primary breakup [34, 36, 42, 43]. The resulting phase-fraction and velocity fields comple- ment scalar spray-angle and pressure-drop responses, while the solver’s fluxes provide a direct conservation check. Turbulence and pressure–velocity coupling are configured through the declared backend interface. 3.5.2. Chamber Combustion Performance A chamber-scale reacting-flow solver is required after geometry realization because injector-level inter- face dynamics do not determine the coupled temperature and pressure fields in the chamber and nozzle. Fluent is used for this role because it supports three-dimensional finite-volume reacting-flow calculations, turbulence and spray closures, combustion-chemistry models, and field or integral post-processing on the realized geometry. The resulting temperature, pressure, and integral responses provide the combustion- side evidence used in the preliminary-design screen. For each integral response y j , the relative deviation is defined as δ j = (y j − y ref j )/y ref j , where y ref j is the corresponding accepted-design or RocketCEA reference; the combustion gate requires |δ j | < 10% for chamber pressure, thrust, specific impulse, and characteristic velocity. This threshold is an engineering consistency criterion for preliminary configuration screening. Its configuration, chemistry, and discretization details are retained in Appendix C. 3.5.3. Coupled Thermal–Structural Strength Abaqus is selected for the structural branch because it provides finite-element thermal analysis, pres- sure loading, support conditions, and transfer of temperatures into a mechanical step within one solver environment. The injector top plate is treated as the focal structural region because it carries the coupled loads around the injector and igniter openings; this makes a declared stress path more interpretable than an unqualified maximum over all constrained edges. The assessment records temperature, displacement, stress, and reaction-force evidence, with the material definition and admission criteria kept in Appendix A. 14 3.5.4. Oxidizer Distribution and Configuration Selection Configuration selection requires a flow check in addition to local thermal, combustion, and structural checks. The flow ledger first tests whether integrated outlet flow is consistent with the prescribed inlet; only then does it rank the within-layout distribution. For a resolved Oxidizer feed, let ̇m Ox,i be the integrated outlet flow of element i, and let ̇m Ox be the layout mean. The coefficient of variation and maximum relative deviation are CV Ox = q N −1 e P N e i=1 ( ̇m Ox,i − ̇m Ox ) 2 ̇m Ox × 100%, δ Ox,max = max i | ̇m Ox,i − ̇m Ox | ̇m Ox × 100%. (6) These measures quantify distribution among resolved branches. The flow-admission definitions and the configuration-specific values are retained in Appendix A and Section 4.3. 3.5.5. Feedback, Approval, and Design Continuation A failed check returns its violated criterion, affected artifacts, and permitted change scope to the Agent. The response is selected by failure class: an input or binding error requires correction, a numerical failure requires execution or discretization review, and physical infeasibility requires redesign. Once a change is approved, dependency-scoped invalidation marks stale results and schedules the affected analyses for re- execution; ambiguous or out-of-scope changes return to the engineer. The same Agent also drives the simulation stages through the declared skills and tool adapters: it se- lects the eligible solver task, binds the accepted Design IR to solver inputs, launches or coordinates the backend run, inspects the returned evidence, and routes the workflow either to the next gate or to revi- sion. The Agent-mediated CFD procedure follows the method developed in our team’s previous FlamePilot work, which uses an LLM-based research assistant to configure, execute, post-process, and iteratively refine DeepFlame/OpenFOAM simulations [44]. RocketAgent adopts this procedure directly and extends it across injector, combustion, thermal–structural, and flow checks within a shared design state. Human approval governs requirements, consequential model or safety-limit changes, expensive simulation commitments, and final selection. Verified, failed, and unresolved outcomes are retained as separate evidence states, while promotion of a result into reusable engineering knowledge additionally requires provenance, applicability, and expert review. This governance layer connects solver outputs to design continuation. Execution traces and numerical settings are provided in Appendix B and Appendix C; the representative outcomes and revision-governance checks are reported in Section 4. 4. Performance Evaluation and Results Result at a glance. RocketAgent drove a long-horizon engineering chain from requirements and knowledge- grounded concept selection to an AI-assisted, multiphysics-evaluated liquid-rocket thrust chamber. In this 15 ab c Fuel Inlet Oxidizer Inlet Regenerative Cooling Channels Combustion Chamber Injectors Liquid Collection Chambers Igniter Port Figure 5: Selected four-element thrust-chamber geometry: (a) exterior view showing the igniter port and separate oxidizer and fuel inlets; (b) longitudinal section showing the injectors, combustion chamber, nozzle, and regenerative-cooling channels; (c) enlarged injector-head cutaway showing the liquid collection chambers and internal injector passages. sense, the engine was not merely analyzed by an AI tool: an AI Coding Agent carried the accepted de- sign state through performance calculation, cooling redesign, injector search, geometry realization, and independent verification, returning a selected chamber configuration. Applying the workflow in Section 3 to a representative 500 N LOX/RP-1 task produced the four-element design shown in Fig. 5. The result is an integrated engineering artifact: a cooling-feasible operating point, an embodied injector and nozzle, solver-ready solid and fluid geometry, and independent VOF, reacting-flow, thermal–structural, and flow- acceptance evidence are connected by one shared design state. The delivered assembly connects the external interfaces to the internal geometry developed across the workflow. Panel (a) locates the central igniter port, head-end Ox inlet, and nozzle-end Fuel inlet. The section in (b) exposes the injector head, chamber/nozzle contour, and regenerative-cooling passages, while the cutaway in (c) reveals the collection chambers and internal injector passages. The following results explain how this integrated design was obtained and why it was selected. 16 4.1. Conceptual Design: Requirements and Design Basis The representative task requires a 500 N thrust chamber at sea level and P c = 1.0 MPa, using LOX/RP- 1, a 15 ◦ conical nozzle, regenerative cooling, and CuCrZr. These accepted inputs instantiate the problem formulation in Section 3.1; mixture ratio, cooling geometry, and injector geometry remain design decisions. At this point, the KG supplies historical priors, guiding the initial performance, cooling, and injector choices while exposing known trade-offs. For example, prior experience can flag the tension between a maximum-I sp operating point and cooling feasibility before the expensive embodiment searches begin. The conceptual stage therefore establishes the requirements, KG-informed starting hypotheses, and admissibility logic for the coupled calculations and subsystem searches in embodiment design. The assessment follows the admission and selection logic of Sections 3.4 and 3.5. Subsystem candidates must satisfy their complete hard-constraint sets before preference-based selection. Realized layouts must then pass the configuration-level checks before Ox-side flow uniformity determines the preferred arrangement. The < 1% flow-admission limits apply separately to Ox, Fuel, and total propellant flow, with inlet-normalized and pairwise definitions retained in Appendix A. They do not limit individual branch dispersion. Fig. 6 maps the representative task onto the physical design objects and assessments reported below. Requirements and a KG-grounded chamber concept lead to the chamber contour, cooling channels, and four- and five-element injector alternatives. After geometry realization, the assembly is routed through injector VOF, chamber-combustion, and coupled thermal–structural assessments. The evidence column records the corresponding spray-angle/pressure-drop, thrust/chamber-pressure, and stress/margin checks before the selected design is advanced. These cards summarize the primary multiphysics gates; the Ox- side flow-admission and layout-selection comparison is reported separately in Section 4.3. The cooling- driven operating-point revision is detailed in Section 4.2.1, while task plans, tool records, and independent validation populations retain their own assessment traces. This design basis supplies the inputs to RocketCEA/RPA performance and contour calculations and the coupled subsystem searches. The resulting operating-point revision and geometry realization are reported next as one connected embodiment sequence. 4.2. Embodiment Design: From Accepted State to Realized Hardware The conceptual state now enters embodiment. Its first question is whether the performance point can be realized thermally and hydraulically; only after that question is answered are injector sizing and geometry generation allowed to proceed. RocketAgent therefore carried the accepted state into a coupled cooling and injector design. The same Ox and Fuel totals were passed to both injector layouts, while the eventual cooling layout supplied the wall and flow context for geometry realization. 17 Embodiment Design Chamber contour Cooling channel Conceptual Design • Mission • Conditions • Thrust • Fuel • Oxidizer • Materials • Cooling • Nozzle Type • ...... Requirements KG-grounded concept Thrust Chamber Cooling Channel Injector Verification Combustion assess. Thermal-structural assess. VOF assess. Geometry realization Selected Design Injector 4 elements5 elements Evidence Margin Stress σ PASS Thrust F Chamber pressure c p PASS Spray angle Pressure drop p∆ PASS Figure 6: Representative engineering workflow for the 500 N LOX/RP-1 thrust chamber. Conceptual Design defines the re- quirements and KG-grounded concept. Embodiment Design realizes the chamber contour, cooling-channel layout, and four- and five-element injector alternatives. Geometry realization then feeds injector VOF, chamber-combustion, and coupled thermal– structural assessments. The evidence cards summarize spray angle/pressure drop, thrust/chamber pressure, and stress/margin checks; passing evidence advances to the selected design shown at right. 18 4.2.1. Feasibility-Driven Operating-Point Revision The first embodiment output was a cooling-feasible operating state. The question was whether the maximum-performance point could support a feasible cooling design. Following the KG-grounded require- ment clarification in Section 3.3, the accepted concept supplied the propellants, operating conditions, nozzle family, and cooling requirement to RocketCEA and RPA. The Agent’s recorded plan retained geometry generation as pending until the subsystem checks were resolved. Conditional human authorization allowed a richer mixture at fixed chamber pressure if cooling proved infeasible ( Appendix B). At the maximum-I sp operating point, none of 74 recorded cooling-candidate evaluations satisfied the complete thermal-hydraulic, manufacturing, and low-order structural criteria. This result activated the authorized return from cooling assessment to performance and contour determination. The Agent invoked the rich-side search and recalculated the dependent performance, flow, geometry, and cooling responses. At r Ox/Fuel = 1.09, eight of 70 recorded candidate evaluations were hard-feasible. The revised operating point established the common flow budget for the remainder of embodiment and verification. Eq. 2 gives ̇m = 0.282944 kg/s, comprising 0.147564 kg/s Ox and 0.135380 kg/s Fuel. Thus, the mixture-ratio decision changed the inputs to cooling and injector design together, implementing the cross-stage dependency described in Section 3.2. Fig. 7 shows the trade-off remaining after this operating-point revision. Lower maximum wall tempera- ture generally comes at greater coolant pressure loss along the projected envelope. The hollow orange points lie within the two displayed limits but fail another hard constraint, so these axes alone cannot determine admission. Among the hard-feasible alternatives, the blue square marks the selected balanced design and the red triangle a temperature-priority alternative. The selected balanced design uses a pressure loss of 0.221 MPa, a maximum wall temperature of 725.3 K, and a minimum low-order safety factor of 1.81 under the common CuCrZr definition. This balanced point was preferred because it retains substantial thermal and structural margin without the large pressure-loss penalty of the temperature-priority alternative, and it fixed the cooling state inherited by the injector and geometry branches. With the operating point and cooling state fixed, the remaining embodiment task is to generate injector alternatives and realize their common geometry interfaces. 4.2.2. Surrogate-Assisted Injector Embodiment Fig. 8 summarizes the prediction evidence supporting the count-specific searches. The upper panels com- pare held-out point predictions with VOF responses; the lower panels examine post-selection residuals and an optimization trade-off. These evaluations define the injector embodiment search and its uncertainty con- text; the independent endpoint VOF verification of the realized configuration is reported in the verification subsection. Injector-module validation used 549 training samples, 118 validation samples, and 118 non-overlapping 19 0.00.20.40.60.81.0 Coolant pressure loss, Δp (MPa) 650 675 700 725 750 775 800 825 850 Maximum wall temperature, T w, max (K) Wall-temperature limit Δp= 1.0 MPa Preferred direction 2D projected envelope Gate-infeasible candidate Hard-feasible candidate Selected balanced design Temperature-priority alternative Figure 7: Cooling-channel trade-off after the governed rich-side redesign. The axes show coolant pressure loss ∆p and maximum wall temperature T w,max . Hollow markers fail at least one hard gate, whereas green markers are fully feasible. The blue square marks the selected balanced design and the red triangle a temperature-priority alternative. held-out VOF samples, all based on water-substitute calculations. In Fig. 8(a), distance from the diagonal measures spray-angle prediction error; the complete held-out set achieved R 2 = 0.926, MAE = 3.746 ◦ , RMSE = 4.881 ◦ , and NRMSE = 4.314%. Panel (b) compares the two pressure drops on logarithmic axes, accommodating their different response ranges. Fuel-side pressure drop achieved MAE = 42.043 kPa, RMSE = 89.123 kPa, and NRMSE = 3.247%; Ox-side pressure drop achieved MAE = 10.133 kPa, RMSE = 16.234 kPa, and NRMSE = 4.106%. These statistics retain all 118 held-out samples and quantify the point-prediction evidence behind the upper panels. Seven target-conditioned NSGA-I searches used a population of 160 for 100 generations and recorded 16,160 surrogate evaluations per target, or 113,120 in total. They produced 1,079 feasible first-front can- didates and 140 exported representatives. After the candidate list and search decisions were frozen, these 140 representatives were evaluated in separate VOF runs. The resulting labels were not used for GPR fitting, calibration, ranking, or selection; they therefore form an independent post-selection verification set for this search. The surrogate-to-VOF spray-angle MAE/RMSE was 5.895 ◦ /7.476 ◦ , the Fuel-pressure-drop MAE/RMSE was 17.905/24.485 kPa, and the Ox-pressure-drop MAE/RMSE was 8.506/10.691 kPa. The 140 labels are independent of model fitting and search decisions, but they are search-conditioned because the evaluated geometries were exported by the surrogate-assisted procedure rather than sampled randomly from the full design domain. Fig. 8(c) uses the predictions recorded before those VOF runs to separate target matching from uncertainty: its horizontal coordinate is prediction divided by target, whereas its vertical coordinate is the standardized VOF residual. A prediction near the target therefore need not have a small residual. For response j, z ij = (y ij − μ ij )/σ ij and empirical coverage is C j (k) = n −1 P i 1(|z ij | ≤ k), with n = 140. Here, σ ij is the GPR predictive standard deviation, including its fitted noise-kernel 20 406080100120 VOF spray angle, θ (deg) 40 60 80 100 120 Predicted spray angle, μ θ (deg) n= 118 MAE = 3.75 deg RMSE = 4.88 deg R 2 = 0.926 a Held-out test 10 2 10 3 VOF pressure drop, Δp w (kPa) 10 2 10 3 Predicted pressure drop, μ Δ p w (kPa) b Fuel, Δp w, Fuel (kPa) Ox, Δp w, Ox (kPa) 0.61234 Normalized prediction, μ/y target (-) −3 −2 −1 0 1 2 3 Standardized residual, z (-) c Within ±2σ (n= 140) Fuel Δp: 100.0% Spray angle θ: 80.7% Ox Δp: 93.6% Fuel objective, 10 3 J Δp, Fuel (-) Spray-angle objective, 10 3 J θ (-) Ox objective, 10 3 J Δ p , Ox (-) d Active: FuelRIn-OxRIn 1.00 m (limit 1.00 m) zero violations; in domain Figure 8: Water-reference injector-module surrogate and search evidence. (a) Held-out VOF–surrogate parity for spray-cone angle (n = 118). (b) Held-out parity for Fuel- and Ox-side pressure drops. (c) Standardized residuals z = (y− μ)/σ for 140 independent, search-conditioned post-selection VOF evaluations; dashed lines at z =±2 mark nominal two-standard-deviation limits, whose empirical coverage is reported in Table 1. (d) NSGA-I nondominated objective set, colored by the Ox-pressure- drop objective, with the selected module-validation knee point highlighted. Table 1: Uncertainty assessment on 140 independent, search-conditioned post-selection water-reference VOF evaluations. Gaus- sian reference coverage is 68.27% at ±1σ and 95.45% at ±2σ. NLPD uses degrees for angle and Pa for pressure; its values are unit-dependent and are not compared across outputs. ResponseC(1) (%) C(2) (%) Mean z SD z NLPD Spray-cone angle50.7180.710.750 1.1753.565 ∆p w,Fuel 92.86100.00 −0.007 0.540 11.762 ∆p w,Ox 64.2993.57 −0.430 0.945 10.680 contribution. Table 1 reports the resulting search-conditioned uncertainty statistics, and Fig. A.14 provides the calibration curves. The spray-angle markers in panel (c) extend beyond the nominal ±2σ band more frequently than the 21 pressure-drop markers, consistent with their 80.71% coverage and positive residual bias. Fuel-pressure inter- vals are conservative, while Ox-pressure intervals are closer to nominal coverage. This response-dependent calibration explains why the protocol retains μ− 2σ as a diagnostic alongside its deterministic mean-value admission rule. Fig. 8(d) shows how a module-validation candidate was selected: the axes express Fuel-pressure and spray-angle target errors, color encodes the Ox-pressure objective, and the star marks the knee compromise. Against targets of 320 kPa, 80 ◦ , and 120 kPa, its independent VOF evaluation returned 317.06 kPa, 82.48 ◦ , and 127.11 kPa, respectively. The target-normalized RMSE of its three surrogate-to-VOF deviations was 3.93%, and the maximum relative discrepancy between measured and prescribed water-circuit flow at t = 0.1 s was 1.212 ppm. This module-level selection is separate from the representative-design P c = 1.0 MPa dual-pressure-drop admission test. 4.2.3. Count-Specific Design Alternatives Once the surrogate evidence established the admissible prediction domain, the model was used to gener- ate separate count-specific embodiment candidates. Each candidate was then quantized and checked again before it could enter the realized-geometry stage. For the representative chamber, both sets of prescribed single-element propellant flows lay within the surrogate’s declared applicability domain. Fixed-flow searches produced nondominated alternatives, which were quantized and freshly evaluated against the complete injec- tor admission criteria. At the four-element allocation, the retained geometry had a predicted water-reference spray angle of 87.25 ◦ and Fuel- and Ox-side mean pressure drops of 306.8 and 251.7 kPa, respectively. It satisfied the applicability, configured spray-angle, and dual-pressure-drop screens. Predictive standard de- viations were 6.52 ◦ , 48.24 kPa, and 10.94 kPa for these three responses. The corresponding pressure-drop μ− 2σ values were 210.35 and 229.80 kPa, both above the 200-kPa screening threshold. The five-element alternative was optimized at its own single-element flows rather than reusing the four- element geometry. Its predicted water-reference spray angle was 88.01 ◦ , and its Fuel- and Ox-side mean pressure drops were 375.08 and 223.17 kPa. The corresponding μ−2σ diagnostics were 280.01 and 200.90 kPa. Both count-specific designs therefore passed the mean pressure-drop screen. This admitted two candidates for geometry realization, but did not yet determine which layout should be selected. 4.3. Verification and Refinement: Multiphysics Evidence and Final Selection The two admitted injector designs mark the end of embodiment search: both have passed their module- level admission criteria, but neither is selected yet. They were combined with the accepted contour and cooling layout to produce separate PicoGK solid and fluid assemblies. This handoff implements the joint subsystem prerequisite in Section 3.4. Verification then asks whether the realized assemblies satisfy inde- pendent evidence contracts: injector-scale VOF, chamber-scale reacting flow, top-plate thermal–structural 22 Figure 9: Injector-scale VOF verification. (a) Water volume fraction α water and (b) velocity magnitude |U| in m/s on the centerline x–z plane at t = 0.1 s. response, and configuration-level flow acceptance. The order below follows that evidence chain and ends with the selection decision. 4.3.1. Injector VOF Endpoint Verification The surrogate and count-specific searches provide the embodiment candidates; the final injector check compares a representative realized geometry and flow condition directly with an independent DeepFlame VOF calculation. The response-level comparison is summarized in Table 2. All three VOF means lie within approximately one predictive standard deviation of the GPR estimates. Pressure-drop agreement is especially close, while the spray-angle prediction is slightly high but remains consistent with its stated uncertainty. The endpoint check confirmed the water-equivalent flow mapping, with relative errors of 2.6× 10 −7 and −4.1×10 −8 for the Fuel and Ox circuits, respectively. Three of the ten temporal frames carried a quality flag; excluding them reduced the mean spray-cone angle from 84.7 ◦ to approximately 83.4 ◦ , without changing the overall verification conclusion. The frame-quality screening and seven-frame sensitivity are summarized in Appendix C. Fig. 9 retains the spatial evidence for the realized injector. Panel (a) shows the centerline water-volume- fraction field and panel (b) the velocity magnitude at t = 0.1 s, with the injector passages above the discharge plane and the spray region below. The scalar comparison is reported separately in Table 2. This injector- scale VOF evidence is the first verification layer before the chamber-scale Fluent and Abaqus assessments. The three surrogate-to-VOF relative deviations are all below 5% (0.65–3.48%). This agreement is ac- ceptable for the declared injector-screening task and indicates that the surrogate predictions are sufficiently reliable to support geometry ranking and embodiment decisions, while the independent VOF calculation remains the endpoint verification of the realized design. 23 Table 2: Independent endpoint comparison between the GPR prediction and the DeepFlame VOF window mean. Deviations are VOF minus GPR; the relative deviation uses the GPR mean, and z is the standardized residual. ResponseGPR μ± σVOF mean VOF–GPR Relative deviation z Spray angle87.621± 5.523 ◦ 84.674 ◦ −2.947 ◦ 3.48%−0.53 Fuel ∆p311.266± 44.963 kPa313.295 kPa+2.029 kPa0.65%+0.05 Ox ∆p253.004± 11.646 kPa246.505 kPa −6.498 kPa2.64%−0.56 4.3.2. Combustion-Field Assessment After the injector endpoint check establishes the first physical evidence for the realized head, the verifi- cation moves to the chamber scale. Fig. 10 shows the representative reacting-flow fields for the four-element configuration. Panel (a) displays the three-dimensional static-temperature field on a 0–3400 K scale, whereas panel (b) shows the corresponding velocity magnitude on a 0–2200 m s −1 scale. Both panels expose the injector-side entry, chamber, convergent section, and nozzle and use sections at z = 20, 60, 100, and 140 m to show the axial evolution. The integral comparison for both layouts is reported in Table 3. The registered Fluent calculations use the reacting-flow setup in Section 3.5. The computed fields show a continuous and approximately axisymmetric reacting flow through the realized chamber. The temperature field develops a centered high-temperature core with smooth radial and axial transitions from the injector face to the throat and exit, without isolated hot spots or abrupt discontinuities dominating the solution. The velocity field shows the complementary expected pattern: lower velocities in the head-end mixing region, progressive acceleration through the convergent section, and the largest magnitudes near the throat and in the divergent nozzle. The coherent temperature and velocity distributions indicate adequate mixing and orderly expansion, consistent with reported numerical assessments of regeneratively cooled rocket thrust chambers [5, 45]. For this preliminary-design study, these field patterns provide the qualitative flow-organization evidence, while the integral quantities in Table 3 provide the quantitative screening check. The ideal-gas oxidizer closure and the effective Fuel spray boundary condition are retained as declared preliminary-model assumptions; their detailed definitions are documented in Appendix C. An independent performance-summary workbook was used to compare the reacting-flow outputs with the accepted design state. Both layouts retained r Ox/Fuel = 1.0901, a total flow of 0.283 kg s −1 , a throat diameter of 22.8 m, and the same throat area of 4.08281× 10 −4 m 2 , corresponding to deviations of only 0.01% in mixture ratio and 0.02% in total flow from the design ledger. Table 3 reports the absolute responses and their deviations from the corresponding design or RocketCEA references. All four integral responses for both layouts remain within the declared |δ| < 10% preliminary-design criterion; the largest listed deviation is 7.91%. The four-element layout is consistently closer to the target state, while the five-element snapshot is retained as lower-confidence evidence because of its approximately 2.5% mass imbalance. With the imposed 24 z = 20 mmz = 60 mmz = 100 mmz = 140 m x y z 05001000150020002200 Velocity magnitude (m/s) z = 20 mmz = 60 mmz = 100 mmz = 140 m x y z 0500100015002000250030003400 Static temperature (K) b a Figure 10: Chamber-scale Fluent verification for the four-element configuration. (a) Three-dimensional static-temperature field on a 0–3400 K scale. (b) Corresponding velocity-magnitude field on a 0–2200 m s −1 scale. Both panels show sections at z = 20, 60, 100, and 140 m and expose the injector-side entry, chamber, convergent section, and nozzle. flow and throat area matched, these comparisons provide a consistent basis for preliminary configuration selection. 4.3.3. Top-Plate Thermal–Structural Assessment The Fluent branch establishes the chamber-scale thermal and pressure environment; the next question is whether the realized head can carry its coupled loads. The injector top plate transfers combined pressure and thermal loads around the injector and igniter openings, making it a critical region for structural verification. Fig. 11 connects this loading to the four-element candidate assembly’s response. The nodal-temperature field in (a), spanning 140.18–396.38 K, supplies the thermal load for the structural calculation in (b), together 25 Table 3: Integral chamber-performance comparison from the Fluent reacting-flow calculations. Relative errors are measured against the corresponding design or RocketCEA reference; the preliminary-design screening criterion is|δ| < 10% for each listed response. Metric Design reference Four elements Relative error Five elements Relative error p c 1.000 MPa0.9441 MPa −5.59%0.9303 MPa −6.97% F500 N471.63 N−5.67%460.53 N−7.89% I sp 180.197 s169.939 s−5.69%165.940 s−7.91% c ∗ 1403.5 m s −1 1362.1 m s −1 −2.95%1342.2 m s −1 −4.37% with the pressure loads. These views locate the coupled response around the openings and surrounding housing. Panel (c) supplies the quantitative stress assessment. Along the declared top-plate path in Fig. 11(c), the von Mises stress ranges from 0.96 to 254.00 MPa, peaking at X = 18.175 m. Relative to the approximately 350 MPa aged-state CuCrZr yield reference, this gives a path-based stress margin of 1.38, defined as the ratio of the yield reference to the maximum path stress, and satisfies the minimum criterion of 1.2. The stress distribution along the declared top-plate path and around the injector–igniter load-transfer region remains spatially coherent and physically reasonable for the preliminary structural assessment. Both layouts passed the prescribed top-plate check, permitting the subsequent flow-uniformity comparison. 4.3.4. Flow Acceptance and Injector-Layout Selection With both layouts satisfying the injector, geometry, preliminary-design combustion, and top-plate gates, the final configuration-level check compares their Ox outlet distributions. The distribution plot is intention- ally limited to Ox: the CFD model resolves the Ox feed passages and obtains each branch flow by outlet integration, whereas the Fuel total flow is imposed directly through the spray-injection boundary condition rather than being solved as a separate branching network. Fuel and total-flow balances are still checked against their prescribed values, but they do not provide an analogous resolved Fuel branch distribution. Fig. 12 compares the two layouts. Circles in (a) represent four elements and squares in (b) five elements; each marker is measured relative to its own layout’s mean, indicated by the dashed zero line. The narrower spread in (a) therefore shows more uniform allocation. The integrated Ox outlet totals, shown rounded in Fig. 12(a) and (b), are 0.14736 and 0.14664 kg/s. Relative to the common prescribed Ox inlet of 0.14756 kg/s, their absolute flow-balance deviations are 0.139% and 0.624%, both below 1%. Their mean-normalized pairwise difference is 0.487%, also below 1% but distinct from either inlet-to-outlet deviation. These reported balances concern the Ox circuit; the prescribed Fuel flow remains 0.13538 kg/s. They are separate from the approximately 2.5% total mass imbalance reported for the five-element reacting-flow performance snapshot. With Ox total-flow acceptance established, the tighter distribution in (a) gives a lower coefficient of variation (1.92% versus 5.08%) and 26 Figure 11: Coupled thermal–structural response of the selected four-element injector assembly: (a) steady nodal-temperature field obtained from the kerosene- and LOX-side film conditions; (b) von Mises stress field after transfer of the temperature field and application of the pressure loads; and (c) averaged nodal von Mises stress along the declared top-plate path. The path maximum is 254.00 MPa at X = 18.175 m, corresponding to a margin of 1.38 relative to the approximately 350 MPa aged-state yield reference and satisfying the minimum criterion of 1.2. The connecting line in panel (c) is for visualization only. worst-branch deviation (3.11% versus 6.51%). Four elements were therefore selected, while five remained feasible but with lower-confidence integral CFD performance. The flow comparison converts verification into a selection decision. The selected assembly combines an operating point of r Ox/Fuel = 1.09 and I sp = 180.20 s with chamber, throat, and exit radii of 28.0, 11.4, and 17.1 m, respectively; L c = 142.2 m and L e = 21.8 m. Its 32-channel balanced cooling layout gives T w,max = 725.3 K, T out = 379.8 K, a pressure loss of 0.221 MPa, and a low-order safety factor of 1.81. Combined with the admitted four-element injector, these outputs form the geometry shown at the start of this section. The progression from the revised operating point to this verified and selected configuration realizes the shared-state continuity described in Section 3.2. 27 1234 Element index, i (-) −8 −6 −4 −2 0 2 4 6 8 Ox-flow deviation, d Ox, i (%) Total Ox flow, ∑ ̇ m Ox, i = 0.147359 (kg/s) CV Ox = 1.92 (%), δ Ox, max = 3.11 (%) a 0.037985 0.036570 0.036741 0.036064 12345 Element index, i (-) Total Ox flow, ∑ ̇ m Ox, i = 0.146644 (kg/s) CV Ox = 5.08 (%), δ Ox, max = 6.51 (%) b 0.027917 0.027419 0.029383 0.030716 0.031208 Figure 12: Oxidizer-side branch mass-flow distributions from CFD under the same prescribed Ox inlet flow. Each marker gives the percentage deviation d Ox,i = 100( ̇m Ox,i / ̇m Ox − 1); labels report the integrated Ox outlet flow in kg/s. (a) Four elements: total 0.14736 kg/s, CV Ox = 1.92%, and δ Ox,max = 3.11%. (b) Five elements: total 0.14664 kg/s, CV Ox = 5.08%, and δ Ox,max = 6.51%. Both layouts satisfy the flow-acceptance checks for the Ox circuit; the lower within-layout dispersion favors four elements. 4.3.5. Workflow-Level Refinement and Configuration Reuse The physical checks above end with a selected configuration; the workflow must then show that this state can be revised without silently reusing superseded evidence. The engineering sequence also includes correction of a thermal-profile/selected-geometry binding followed by repeated low-order structural analysis ( Appendix B). These actions illustrate continuation through both physical infeasibility and an input-binding correction. The following controlled tests therefore move from physics-level verification to workflow-level refinement: dependency-aware revision handling and reuse of the geometry interface across nozzle families. Revision-Aware Workflow Validation.. Two configurations are compared on three controlled scenarios from the same frozen design snapshot. The full configuration enables automatic invalidation and revision-aware admission; the comparison disables only these checks while retaining the same baseline, invocation parame- ters, snapshot-integrity checks, and file-existence and checksum checks. An upstream mixture-ratio change and a structural-only material change exercise the main state-update path; submission of a superseded STL exercises the actual Abaqus adapter’s entry checks. Each scenario starts from the same baseline in both configurations, giving six deterministic executions that stop before solver launch. Expected affected sets were registered before execution, and the replay records missed and excess in- validations, additions to the re-execution plan, and stale-file admission outcomes ( Appendix A). The full configuration reproduced both expected invalidation sets and blocked the superseded STL. The upstream 28 mixture-ratio change invalidated 24 artifacts across 11 stages and added seven stages to the dependency- ordered re-execution plan, whereas the configuration with revision checks disabled detected none of these newly affected records. The structural-only material change invalidated five artifacts across four stages in the full configuration; the affected stages were already pending when checks were disabled, so newly invali- dated records rather than plan differences establish detection. For the superseded STL, the full configuration rejected the inactive file at the Abaqus entry while the comparison configuration accepted it at preflight. Nozzle-Configuration Reuse.. Configuration reuse was tested by changing only the nozzle-shape branch while holding thrust (500 N), chamber pressure (1.0 MPa), propellants (LOX/RP-1), mixture ratio (1.05), contraction ratio (6), 0.1-m parameter quantization, and a common cooling/wall configuration fixed. The TOC, 15 ◦ conical, and 30 ◦ /10 ◦ parabolic-bell profiles all retained the injector-face, chamber-end, throat, and exit anchors with strictly increasing axial coordinates. Maximum radial reconstruction error was at most 0.1 m. All six solid/fluid STLs passed binary-format validation, the expected log markers were present, and 15 generator regression tests passed. Profile discretization and triangle counts are retained in Appendix D.2. Fig. 13 separates the contour comparison at the throat. Panel (a) shows the nearly coincident chamber and convergent profiles from the injector face to the throat, using the axial coordinate x. Panel (b) shows only the divergent sections, with each throat reset to x− x t = 0. The insets illustrate these coordinate definitions on a schematic thrust chamber. The parabolic bell reaches its exit over the shortest downstream distance, followed by the conical contour and TOC. Including the upstream sections, their complete profile lengths are 158.5, 164.8, and 177.7 m, respectively. Open markers identify the retained sparse coordinates. Together with the common validation results, the profiles demonstrate reuse of the geometry interface across nozzle families at the declared tolerance. Together, the controlled tests show how the shared-state and geometry interfaces support the executed engineering sequence: revision checks identify dependent work and reject inactive inputs, while the same geometry contract accommodates different contour families. These mechanism-level results complement the representative design’s physical assessments and selection outcome. 5. Discussion 5.1. Long-Horizon Workflow Execution Long-horizon execution here means that the Agent drives an extended sequence of dependent engineering tasks from requirements to a reviewed preliminary design. The recorded plan retained unresolved work across stages and kept geometry generation pending until subsystem admission was resolved ( Appendix B). This makes progression an engineering decision: a completed calculation enables further work only when its outputs satisfy the relevant conditions. Conditional human approval also supports continuation. The 29 t x− x Figure 13: Contour comparison after strict 0.1-m simplification. (a) Chamber and convergent profiles from the injector face to the throat, plotted against x. (b) Divergent profiles from the throat to the exit, plotted against x− x t . Insets illustrate the coordinate definitions and are not to scale. Open markers denote retained profile points; maximum interpolation errors against the quantized source profiles are 0.1000 m for TOC, 0.09828 m for the 15 ◦ conical contour, and 0.1000 m for the 30 ◦ /10 ◦ parabolic bell. cooling failure activated a previously authorized rich-side search without granting unrestricted changes to chamber pressure or safety limits. Different failures require different continuations. Cooling infeasibility prompted a physical redesign, whereas the thermal-profile/selected-geometry mismatch required correcting the input binding and repeating structural analysis. The controlled revision tests in Section 4.3.5 address a third problem: preventing downstream use of evidence superseded by a design change. These tests support the invalidation and solver- entry mechanism separately from the historical execution record. Across these forms of continuation, one coordinator retains the global plan and decision ownership, deterministic programs evaluate candidates and enforce numerical gates, and engineers authorize consequential changes and review the outcome. 5.2. Comparative Engineering Value Fixed scripts and multidisciplinary optimization support reproducible calculations once the formulation and execution order are known [8]. RocketAgent adds a policy-bounded, non-manual self-repair loop be- tween those calculations: the plan-owning Agent observes a failed or inconsistent result, selects an already authorized continuation, updates the shared Design IR, invalidates dependent artifacts, and resumes the affected stages without requiring an engineer to hand-edit every downstream input. In the representative workflow, the infeasible maximum-I sp cooling point activated the pre-authorized rich-side search, which 30 changed the operating point to r Ox/Fuel = 1.09 and propagated the new flow state through performance, cooling, injector, and geometry tasks; the resulting search recovered hard-feasible cooling candidates. A separate thermal-profile/selected-geometry mismatch was corrected through input rebinding and a repeated structural calculation. The controlled revision tests provide a complementary mechanism-level example: an upstream change automatically invalidated dependent records and a superseded STL was rejected at solver entry, while the comparison configuration left those records admissible. These examples demonstrate self- repair as governed continuation rather than unrestricted autonomy: human approval defines the allowable change envelope and reviews the result, whereas the Agent performs the intermediate diagnosis, propagation, and recovery actions. This gives RocketAgent advantages in handoff clarity, state continuity, provenance, and feedback-to-redesign traceability when a long engineering task chain crosses heterogeneous tools. 5.3. Framework Evolvability RocketAgent supports extension at the configuration, computational-capability, and knowledge levels. Alternative injector counts and nozzle contours demonstrate reuse of common interfaces with configuration- specific outputs. Materials, propellants, operating conditions, and cooling architectures can likewise be represented through backend definitions, applicability conditions, and engineering gates. Extending these definitions requires evidence appropriate to the new configuration, rather than transferring acceptance from an existing design. The capability–skill–adapter separation in Section 3.2 extends this reuse to replacement solvers or higher-fidelity analyses through declared inputs, outputs, units, validators, and dependency effects. Knowledge evolves through the review process in Section 3.5: completed revisions and feedback provide provenance-linked experience, from which reviewed, applicable guidance can be reused. This preserves a distinction between recording an outcome and accepting it as a general engineering rule. Together, these extension paths provide a basis for broader product coverage without requiring every computational backend to share an implementation. 5.4. Limitations and Future Work The representative workflow and module tests support simulation-based preliminary design. They do not establish ignition/shutdown behavior, combustion stability, cyclic life, feed-system dynamics, or manufac- turing qualification. Material characterization, cold-flow testing, and hot-fire evidence remain necessary for component qualification. Future work will connect experimental evidence, extend configuration and anal- ysis coverage, and examine whether reviewed experience improves subsequent design work across repeated workflows. 31 6. Conclusions RocketAgent enables a Coding Agent to drive an extended multidisciplinary workflow for preliminary thrust-chamber design. To the best of the authors’ knowledge, it is the first knowledge-constrained single- coordinator, multi-skill architecture explicitly directed at preliminary design of a complex industrial product such as a liquid-rocket thrust chamber. The Agent maintains the overall plan and coordinates skills from requirements through subsystem design, geometry realization, and multiphysics evaluation. The KG and De- sign IR support cross-stage execution, while revision-aware invalidation and solver-entry admission manage dependent work when the design changes. The representative design demonstrates closed-loop refinement and configuration selection. Changing to r Ox/Fuel = 1.09 moved the cooling search from 0/74 to 8/70 hard-feasible candidates. Injector screening linked physical-flow allocations to water-reference surrogate predictions, assessed using 118 held-out and 140 independent post-selection VOF evaluations. Four- and five-element configurations passed the reported engineering gates and Ox total-flow criterion. Their Ox-flow coefficients of variation were 1.92% and 5.08%, respectively, supporting selection of four elements while retaining five as feasible. Two configurations and three controlled scenarios tested revision handling in the main workflow. The full configuration reproduced the expected upstream and local invalidation sets and rejected a superseded STL at solver entry. Disabling revision checks removed these responses. The contribution to engineering informatics is Agent-driven execution across a long engineering task chain, supported by auditable state management and extensible configurations, capabilities, and knowledge. The simulation-based results establish a foundation for subsequent experimental qualification. Appendix A. Evaluation Scope and Reproducibility The representative evaluation uses 500 N, sea-level static operation (P amb = 1 atm), P c = 1.0 MPa, LOX/RP-1 at the accepted r Ox/Fuel = 1.09, a 15 ◦ conical nozzle, regenerative cooling, and four- and five- element injector layouts. Configured search bounds are P c = 0.4–1.20 MPa and RocketCEA r Ox/Fuel = 0.4– 4.0. By comparison, realized RPA artifacts span r Ox/Fuel = 0.9–2.6596, with thermally feasible recorded samples at approximately 1.0–1.81. These configured and sampled ranges are not universal feasibility or qualification limits. LOX enters at 90.18 K and the fuel coolant at 293 K and 2.5 MPa. Both the cooling structural screen and Abaqus use the input card’s constant isotropic CuCrZr properties: k = 320 W/(m K), E = 128 GPa, ν = 0.34, α = 1.70× 10 −5 K −1 , and stress-free T ref = 293.15 K, without a temperature-dependent property table or plasticity model. Component strength criteria remain distinct. Cooling admission requires SF ≥ 1.5 relative to a conservative 120-MPa screening allowable, which is a component-level policy rather than a CuCrZr yield property. Recomputing the screen on the retained thermal fields gives a maximum combined stress of 61.63 MPa and a minimum safety factor of 1.947, 32 retaining eight hard-feasible candidates and the same selected geometry. The Abaqus calculation uses an approximately 350-MPa aged-state yield reference and the same nominal top-plate path metric. Its path maximum of 254.00 MPa gives a path-based stress margin of 1.38, defined as the ratio of the yield reference to the maximum path stress, exceeding the minimum criterion of 1.2. Local contour extrema remain diagnostic and do not replace the declared path metric. The remaining cooling hard gates require T w ≤ 850 K, single-phase coolant, compliance with the pressure- loss budget, RP-1 bulk temperature ≤ 399 K, cooling-side wall temperature ≤ 728 K, and channel width and depth each ≥ 1.0 m after 0.1-m quantization. Auxiliary robust targets of T w ≤ 820 K, pressure loss ≤ 0.8 MPa, and SF ≥ 1.7 are assessed separately from hard admission. At configuration level, the < 1% flow criterion applies separately to Ox, Fuel, and total propellant flow: each layout’s absolute inlet-to-outlet deviation is normalized by its prescribed inlet flow, and the absolute difference between layout outlet flows is normalized by their arithmetic mean. Both must be below 1%. Within-layout flow uniformity remains a separate ranking metric. The reacting-flow combustion screen uses the same relative-deviation definition as the main text and requires |δ| < 10% for chamber pressure, thrust, specific impulse, and c ∗ relative to their accepted-design or RocketCEA references. This is a preliminary-design consistency criterion for comparing realized configura- tions; it does not establish high-fidelity solver accuracy, real-fluid model validity, or hardware qualification. Predictive uncertainty.. Fig. A.14 compares empirical central-interval coverage with Gaussian nominal cov- erage 2Φ(k)− 1 for the 140 post-selection evaluations. Relative to the equality diagonal, the spray-angle curve lies below nominal coverage across most levels, whereas the Fuel-pressure curve lies above it; the Ox-pressure curve follows the diagonal more closely. The three curves therefore distinguish underestimated spray-angle uncertainty from conservative Fuel-pressure intervals, extending the two coverage levels in Ta- ble 1. The Gaussian negative log predictive density in that table is NLPD j = (2n) −1 P i [log(2πσ 2 ij ) + z 2 ij ]. No recalibration is fitted on these labels, and the resulting coverage applies to the evaluated benchmark rather than configuration-specific inference. KG retrieval settings.. Stage and the internal design-record identifier set the retrieval context. Prior-design scores weight thrust, chamber pressure, Ox, and Fuel by 0.20 each, and nozzle configuration and cooling requirement by 0.10 each. Thrust and pressure use N and MPa. Positive numerical fields use s num (a,b) = max0, 1−| ln(a/b)|/ ln(10). Categorical fields use lowercase exact or substring matching after removing hyphens and underscores. Missing or nonpositive numeric values and missing categories contribute zero without weight renormalization; ties preserve index order. Default retrieval returns up to three positive-scoring prior designs, four positively ranked RPA examples, and six stage-compatible method cards. RPA ranking uses required analysis features, ChannelWallSeg- ment/thermal capability, propellant compatibility, pressure proximity, nozzle features, and example class. 33 020406080100 Nominal coverage, C nom (%) 0 20 40 60 80 100 Empirical coverage, C emp (%) Post-selection VOF (n= 140) Nominal coverage Spray-cone angle, θ (deg) Fuel pressure drop, Δp w, Fuel (Pa) Ox pressure drop, Δp w, Ox (Pa) Figure A.14: Calibration diagnostic for the 140 independent post-selection water-reference VOF evaluations. The diagonal denotes equality between empirical and nominal central-interval coverage. Curves below it indicate under-coverage and curves above it indicate conservative intervals. The candidates are selected by optimization; the curves describe this search-conditioned population, not a random held-out test or a guarantee for real-propellant operation. Reviewed facts are filtered by stage and topic aliases: all matches remain in the linked response, with at most five displayed in the compact trace. Subgraph expansion retains up to 20 edges from each of six relation families: design record, stage, method, requirement–function, conflict, and experience. The 120-assignment limit permits repeated edges across families. Rule-card JSON pointers specify the scope, unit, range, state, and artifact predicates used for applicability checks. Code and artifact availability.. The frozen evidence package contains the Design-IR and workflow schemas, solver inputs and configuration files, scripts, geometry and mesh artifacts, native and processed outputs, validation reports, decision records, manifests, and checksums supporting the reported results. The code and data supporting the findings of this study are available from the corresponding author upon reasonable request. Revision-governance replay records.. The replay package retains the frozen baseline, two configuration files differing only in the revision-check switch, preregistered expected sets, six execution traces, and set-by-set comparisons. Expected sets are specified in a separate protocol file, hashed before execution and loaded for comparison only after all traces are closed. They are protocol-preregistered without a claim of independent human sign-off. The upstream perturbation changes the selected mixture ratio from 1.09 to 1.095. The 34 structural perturbation changes an isolated analysis card from 120 to 125 GPa; these workflow-test values do not replace the shared 128-GPa CuCrZr definition used in the physical analyses. The superseded-file check uses a five-element geometry branch in a benchmark-local copy of the ledger without altering the selected four-element design. The actual Abaqus adapter returns exit code 3 for the full configuration and 0 for the comparison configuration, with neither invocation creating a solver deck or launching a solve. The baseline already contains pending Abaqus, final-decision, validation, and knowledge-synchronization stages because required outputs are absent. This common backlog explains why the local-change plans are identical despite different invalidation records. The six executions are deterministic governance replays, not independent LLM trials, and report no avoided-solver cost. Appendix B. Agent Configuration and Execution Records Runtime and session context.. The representative design was developed in Codex Desktop on a local Win- dows workspace. The retained task log records client identifier 0.147.0-alpha.6.6, OpenAI model gpt-5.6-sol, and low reasoning-effort settings across turns. Work continued in the same persistent task across multiple dates, including context-compaction events. Engineering stages were therefore not independent LLM trials. The log records neither temperature nor an immutable backend model release, and these settings are not inferred from application defaults. Instructions and decision ownership.. Author-controlled instructions comprise the engineering request, project operating rules, the staged workflow, and task-specific skill documents. The Agent loads the relevant skill before invoking its scripts and maintains an ordered task plan with pending, in-progress, and completed states. It selects eligible actions, binds Design IR inputs, interprets returned evidence, and proposes revi- sions within the approved scope. Deterministic programs implement numerical search, objective evaluation, engineering thresholds, and revision propagation. One lead Agent owns the global plan, with bounded aux- iliary agents recorded for initial retrieval and readiness checks. Code and configuration editing are available, and requested adapter changes are logged with their checks. Human authorization governs changes to re- quirements, accepted models, and safety limits. The single-coordinator description thus refers to plan and decision ownership. Observed planning and execution.. The initial request specified a 500-N LOX/RP-1 design. Before com- putation, the Agent proposed operating conditions and obtained user confirmation, including conditional permission for a rich-side search at fixed chamber pressure if thermal screening failed. The recorded seven- step plan covered conceptual acceptance, performance, geometry, injector screening, cooling and low-order structure, STL generation, and final checking and reporting. Plan updates recorded progression and kept geometry generation pending when subsystem admission was unresolved. The performance call used the 35 accepted 500 N thrust and 1.0 MPa chamber pressure, with sea-level ambient pressure converted to the backend unit. After the maximum-specific-impulse cooling search returned no hard-feasible candidate, the Agent in- voked the authorized rich-side search and refined the feasible region. The confirmation run at r Ox/Fuel = 1.09 used the RocketCEA-derived physical Fuel flow of 0.135380 kg/s and retained eight hard-feasible candidates. The Agent sequenced these calls, while deterministic scripts calculated responses and enforced the thresh- olds. The log also records correction of a thermal-profile/selected-geometry binding followed by a repeated low-order structural calculation. User confirmations, skill-loading calls, plan updates, tool invocations, and file-change records provide the observable execution evidence. These historical actions are distinct from the subsequent controlled revision-governance evaluation in Section 4.3.5. Appendix C. Numerical Simulation Settings Injector cold-flow VOF.. The snappyHexMesh grid used a 0.5-m global cell size and 0.125-m local re- finement in the swirl chamber and downstream atomization region, giving approximately 5.5× 10 6 cells per configuration. Inlet mass flow, outlet pressure, and no-slip walls defined the boundaries. DeepFlame’s OpenFOAM-derived interFoam workflow used SST k–ω, PIMPLE coupling, and a fixed 10 −5 -s time step. Both circuits used water at the mapped flows in Eq. 5. Extracted quantities comprised spray angle, circuit pressure drops, phase/velocity fields, and water-flow conservation checks. The independent endpoint com- parison in Section 4.3 retained all ten temporal frames together with their quality flags and reported the seven-frame quality-screened sensitivity separately. Three frames were flagged as MULTIPLE_INTERSECTIONS; the remaining seven frames gave a mean spray angle of approximately 83.4 ◦ , compared with 84.7 ◦ over the full ten-frame window, while the flow-mapping errors remained below 5× 10 −7 in magnitude. Reacting chamber flow.. The Fluent mesh was generated with snappyHexMesh at 0.5-m background res- olution and 0.25-m refinement in the chamber head, totaling approximately 7.9× 10 6 cells. The steady RANS calculation used SST k–ω and a partially premixed FGM model with compressibility correction. Kerosene was represented by n-decane with the ten-step reduced Choi mechanism. Hollow-cone fuel injec- tion used 10 m s −1 velocity, 400 K initial droplet temperature, a 30 ◦ half-cone angle, and a Rosin–Rammler size distribution. The 400 K value is a combustor-model initialization condition, not the calculated cooling outlet temperature. Pressure–velocity coupling used the Coupled algorithm; final spatial discretization was second-order upwind. The Ox feed passages were resolved and their outlet fluxes were integrated branch by branch, whereas the Fuel total flow and spray distribution were prescribed through the injection boundary condition; consequently, only Ox has a resolved branch-uniformity result in the main text. The injector-angle conventions are distinct. The approximately 80 ◦ quantity reported by the water- reference GPR/DeepFlame analysis is a full spray-cone angle obtained from the two fitted liquid-sheet 36 half-angles, whereas the Fluent model prescribes a 30 ◦ Fuel hollow-cone half-angle. The latter is an effective numerical boundary condition selected to maintain a representative Fuel–Ox overlap under the ideal-gas Ox closure; it is not a conversion of, or a quantitative prediction of, the GPR/VOF angle. Spray geometry also depends on momentum-flux ratio, chamber pressure, and thermodynamic state, so water-reference angles are not transferred directly to the reacting LOX/RP-1 calculation [46]. Coupled top-plate analysis.. The selected Abaqus assembly includes the top plate, four peripheral injec- tor passages, central igniter passage, housing transitions, and side port. Its common thermal/structural quadratic-tetrahedral mesh contains 266,393 nodes and 161,274 elements. The steady thermal stage used DC3D10 elements, with film conditions on the actual Fuel- and Ox-wetted surfaces at bulk temperatures of 400 and 90 K, respectively; both heat-transfer coefficients were 5000 W m −2 K −1 . The thermal solution completed in six increments. Final nodal temperatures were transferred to the matching C3D10 structural mesh; 1.2 MPa pressure was applied to both wetted-surface groups. In the structural calculation, global U 3 was constrained on the lower Set-1 interface, the upper Set-2 interface was left unconstrained, and two minimal in-plane constraints were introduced to suppress rigid-body motion. A geometrically linear Abaqus/Standard step combined pressure and thermal strain using the common isotropic CuCrZr card in Appendix A. The analysis considered the selected four-element assembly; the alternative layout was not included in the structural calculation. Integration-point stresses were extrapolated to element nodes and arithmetically averaged over adjoining elements, with a 75% nodal-averaging threshold for contour display. The quantitative top-plate path retained 68 physical nodes in Y = 0± 0.05 m at Z = −0.2 m, over −29.5 ≤ X ≤ 29.5 m. The reported maximum and margin use those nodal values; connecting lines are only visual guides. Temperature, heat flux, temperature gradient, stress, displacement, and reaction-force outputs were retained as applicable. Evidence checks.. Each analysis retains its geometry and operating-state bindings, native outputs, extracted quantities, and disposition. Applicable numerical checks cover residuals, conservation, discretization and iteration stability, mesh quality, and physical consistency. Preparation-only, incomplete, diverged, and failed runs do not receive accepted status. Appendix D. Implementation and Search Details Appendix D.1. Shared Records and Execution Interfaces Fig. D.15 expands the shared state introduced in Section 3.2. Across the upper row, requirements constrain parameters, which in turn supply inputs to artifacts. The lower return path connects an artifact to its evidence and then to a decision; the dashed arrow authorizes a parameter revision, closing the recorded design loop. Assumptions separately qualify parameter use. This arrangement retains both the engineering 37 Shared Design IR | Typed records, provenance and revision links Requirement Recorded fields Statement; type; priority Source; criterion; owner Checks Completeness Conflict; ambiguity Parameter Recorded fields Value; unit; range Uncertainty; provenance Dependencies Checks Schema; unit; range Equation consistency Artifact Recorded fields Location; format; creator Checksum; revision Configuration Checks Existence; integrity Compatibility; staleness Assumption Recorded fields Rationale; scope Confidence; expiration Checks Applicability Required approval Decision Recorded fields Alternatives; criteria Selection; rationale Approver Checks Evidence completeness Approval policy Evidence Recorded fields Method; inputs; outputs Convergence; uncertainty Acceptance result Checks Numerical and physical acceptance constrains used by assessed in supports qualifies authorizes revision Solid arrows: information relationships Dashed arrow: revision authorization Figure D.15: Shared Design IR record relationships. Boxes separate fields from usage checks; solid arrows indicate information links, and the dashed arrow denotes authorization of a parameter revision subject to the state-transition contract. dependency and the reason for changing it, allowing the revision mechanism to trace affected outputs without discarding unrelated records. Fig. D.16 shows how an individual task updates those records. The forward path connects Agent capabil- ity selection to a skill, its adapter, and the engineering backend. The returned artifact then enters validation and any required approval before commitment to the Design IR. The dashed blue return paths make that accepted state available to subsequent planning and skill invocation. Separating artifact production from state commitment ensures that the next task reads a checked result; a failed validation instead retains the prior state and provides feedback for continuation. Appendix D.2. Embodiment-Design Settings Performance and contour.. The evaluated RocketCEA calculation used estimate_Ambient_Isp with equi- librium expansion (frozen=0 and frozenAtThroat=0), g 0 = 9.80665 m s −2 , and sea-level exit-pressure match- ing when no expansion ratio was prescribed. An inclusive grid and bounded golden-section refinement re- 38 Coding Agent Context Intent; plan; current state Responsibility Select; assess; diagnose Capability Task definition Engineering task; evidence goal Eligibility Prerequisites; acceptance criteria Skill Interface Declared inputs and outputs Contract Validators; write scope; recovery Tool adapter Interface Shared state ↔ backend inputs Operations Convert units; invoke; normalize Engineering backend Execution Calculation; geometry; simulation Returns Native outputs; solver metadata Artifact Execution record Inputs; outputs; logs; reports Lineage Producing configuration; revision Validate + required approval Schema; units; dependencies; gates Pass: admit the proposed transition Fail: retain the prior state Design IR Authoritative accepted state Values; dependencies; provenance; maturity Revision history; downstream invalidation selectsvia invokes runsemits proposed update commit Accepted state for planning and skill invocation Figure D.16: Contract-bound execution: capability selection, skill invocation, adapter/backend execution, and checked state commitment. Dashed arrows show accepted-state reads for subsequent planning and execution. tained endpoints over r Ox/Fuel = 0.4–4.0. Optional prior-design performance bounds required compatible nozzle mode, propellants, chamber pressure, and thrust range or engine class. Without such evidence, the calculated optimum remained the design value. Pressure was converted from the MPa interface convention to the backend convention. The RPA geometry output comprised R c , L cyl , L c , β, R 2 , R 1 , R t , R n , θ n , θ e , R e , L e , exit-area ratio, mass flow, and profile coordinates. Here, β is the contraction angle and θ n , θ e are the initial and exit nozzle angles. Conical and TOC profiles were extracted from RPA. Parabolic-bell reconstruction combined RPA sizing, throat rounding, and a tangent-matched quadratic Bézier curve. The evaluated configurations used A c /A t = 6, a 15 ◦ cone, and a 30 ◦ /10 ◦ bell. Dimensions were quantized to 0.1 m and rechecked for positivity, R c > R t , R e > R t , 0 < L cyl < L c , monotonic axial coordinates, and consistent injector-face, chamber, throat, and exit anchors. 39 Cooling search.. The nominal GA used population 20, five generations, four elites, tournament size three, crossover probability 0.85, mutation probability 0.25, mutation scale 0.12, and two random immigrants. The bounded space contained 16–34 channels, inlet/outlet depths of 2–5/1–3.5 m, widths of 1–1.8 m, hot-wall thickness of 1.2–2.0 m, and channel angle of 0–30 ◦ , with coolant-flow factor one. Dimensions were quantized to 0.1 m, and channel widths or depths below 1.0 m were rejected. The prefilter also checked rib width, aspect ratio, and width-to-pitch compatibility. RPA NozzleCooling used addChannelWallSegment with 75 stations, the Ievlev correlation, radiation emissivity 0.8, and no film cooling. A radiation-only fallback was rejected. Grid, Latin-hypercube, and feasibility-oriented candidate generators were also available; GA attribution required the corresponding recorded search mode and evolutionary settings. Run records separated invalid/pre-solver candidates, com- pleted evaluations, hard-feasible candidates, Pareto-admissible candidates, and nondominated fronts. Con- servative robustness criteria were evaluated separately from hard admission. The selected artifact retained the nozzle-exit coolant-inlet plan and stationwise structural-screen outputs. Injector domain.. The ten geometry or derived GPR features were R Ox,out = 1.5–1.7 m, R Fuel,out = 2.8– 3.1 m, L Fuel,out = 4.4 m, L Fuel,out /(2R Fuel,out ) = 0.7097–0.7857, L Ox,inner,out = 10.5–13.5 m, swirl angle 80–89.9 ◦ , swirl-pitch angle 0–20 ◦ , outlet-divergent angle 30–42 ◦ , R Ox,swirl = 0.7–1.1 m, and R Fuel,swirl = 0.5–0.9 m. Fixed original-propellant flow features covered 0.025–0.040 kg/s for LOX and 0.025–0.050 kg/s for RP-1. Applicability was checked after count-specific flow allocation. Training-data water substitution used reference densities of 1145, 791.3, and 1000 kg/m 3 for LOX, RP-1, and water, respectively. The fixed geometry context was w inj = 0.75 m, R Ox,in = 4.0 m, and R Fuel,in = 5.0 m. Search outputs were quantized to 0.1 m and 0.1 ◦ before fresh prediction and joint screening. Geometry and artifact handoff.. PicoGK used millimetres, applied configuration changes transactionally, and restored the external configuration after execution. Completed runs retained nonempty assembled-solid and combined-fluid STLs, the applied geometric mapping, and generation logs. Binary validity, topology, local dimensions, connectivity, and meshing suitability required separate validator records. In the nozzle- configuration test, the TOC, 15 ◦ conical, and 30 ◦ /10 ◦ parabolic-bell profiles retained 18, 14, and 18 sparse points, with minimum axial spacings of 0.9, 1.1, and 1.1 m, respectively. 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