AeroTherm-GPT: A Verification-Centered LLM Framework for Thermal Protection System Engineering Workflows
Authors: Chuhan Qiao, Jinglai Zheng, Jie Huang, Buyue Zhao, Fan Li, Haiming Huang
Organizations: School of Civil Engineering, Beijing Jiaotong University, Beijing, 100044, China · Beijing Research Institute of Telemetry, Beijing, 100076, China
Integrating Large Language Models (LLMs) into hypersonic thermal protection system (TPS) design is bottlenecked by cascading constraint violations when generating executable simulation artifacts. General-purpose LLMs, treating generation as single-pass text completion, fail to satisfy the sequential, multi-gate constraints inherent in safety-critical engineering workflows. To address this, we propose AeroTherm-GPT, the first TPS-specialized LLM Agent, instantiated through a Constraint-Closed-Loop Generation (CCLG) framework. CCLG organizes TPS artifact generation as an iterative workflow comprising generation, validation, CDG-guided repair, execution, and audit. The Constraint Dependency Graph (CDG) encodes empirical co-resolution structure among constraint categories, directing repair toward upstream fault candidates based on lifecycle ordering priors and empirical co-resolution probabilities. This upstream-priority mechanism resolves multiple downstream violations per action, achieving a Root-Cause Fix Efficiency of 4.16 versus 1.76 for flat-checklist repair. Evaluated on HyTPS-Bench and validated against external benchmarks, AeroTherm-GPT achieves 88.7% End-to-End Success Rate (95% CI: 87.5-89.9), a gain of +12.5 pp over the matched non-CDG ablation baseline, without catastrophic forgetting on scientific reasoning and code generation tasks.
Figures & tables
Figure 1: Overview of the proposed approach. An engineering requirement enters the CCLG workflow (generation → validation → CDG-guided repair → execution → audit), producing an executable and traceable simulation artifact. AeroTherm-GPT is a TPS-oriented instantiation of this framework; HyTPS-Bench provides the workflow-aligned evaluation setting.
Figure 2: End-to-end architecture of AeroTherm-GPT. Solid-line modules (constraint-aware RAG, TPS-specific SFT, CDG-aware VER loop, constraint-aware DPO, reference executor) are fully implemented and evaluated in all experiments. Dashed-line extensions (probabilistic constraint bounds, multi-fidelity CDG, edge-deployed variants) represent directions for future work and are not evaluated here.
Figure 3: Constraint Dependency Graph (CDG) structure and regime-conditioned calibration. Top-left (Zone A): five-tier CDG with 23 nodes organized by lifecycle ordering (Unit → Physics → Numerical → Execution → Audit); directed edges represent empirical co-resolution probabilities calibrated from 4,206 repair episodes. Top-right: regime-conditioned adjacency matrix W(c) across four thermal contexts (nominal, moderate, high-flux, extreme), with edge weights stratified by flight regime; mean absolute calibration error =0.08 on 20% held-out split ( n=841 ). Bottom: per-regime CDG visualizations ( c1 – c4 ) illustrating how edge weight distributions shift across operating conditions.
Figure 4: Core computational mechanisms of AeroTherm-GPT. Zone B (top): PRM-guided constraint tree search (CDG priority, K=4 candidates scored by Vθ(s) ), terminating at Ready(s)=1 or budget exhaustion; right panel compares repair strategy trajectories. Zone C (middle): Transformer backbone with RAG cross-attention, frozen encoder, PRM head ( Vθ(s)∈[0,1] ), and LoRA adaptation ( r=32,α=64 ). Zone D (bottom): Three-tier DPO preference construction (binary, self-evolution, severity-graded) with implicit reward distribution.
Repair Strategy
Root-Cause Fix Efficiency
Avg Iter.
Rework Red.
Random
1.13
3.17
0.0%
Flat Checklist
1.76
2.43
23.3%
CDG Topological Order
3.67
1.58
50.2%
CDG + Severity Weighting
4.16
1.38
56.5%
Table 1: Upstream-Priority Fix Efficiency (RCFE, measured via HyTPS-Bench). CDG-aware repair targets upstream violations first, reducing iterations and downstream rework.
Component
Training
Evaluation
Shared
Leakage control
Constraint assets (schema)
Yes
Yes
Yes (API)
Shared schema/API only; no privileged repair traces or oracle outputs
Reference Executor
No
Yes
Yes
External scoring implementation, identical for all systems
Repair logs (CDG training)
Yes
No
No
Separate calibration pool; excluded from benchmark test construction
HyTPS-Bench test set
No
Yes
Yes
Held out at benchmark-instance and template-family level
Validator rules
No
Yes (post)
Yes
Applied uniformly post-generation to every system
Synthetic instance parameters
Subset
Remaining
N/A
Held-out parameter ranges with material-class-disjoint split
Table 2: Data leakage and evaluation integrity control. Each component’s role in training vs. evaluation is explicitly documented.
Item
HyTPS-Bench Value
Size
∼ 2,500 JSON instances
Task mixture (T1–T4)
25%/25%/30%/20%
Sources
Public lit. (NASA NTRS, AIAA); de-identified snippets; synthetic
Multilingual
EN/CN, q≈0.2
Input length
0.5–2 pages (500–1500 tokens)
Token stats
μtok≈900 , p95tok≈1500
Table 3: Dataset composition and baseline difficulty facts for HyTPS-Bench. The zero-shot SI-G results confirm the benchmark is not saturated by existing models.
Method
Retrieval
Validator feedback
Exec. backend
Iterative repair
CDG ordering
Domain SFT+DPO
Zero-Shot LLMs
×
×
×
×
×
×
Reasoning (w/ think)
×
×
×
×
×
×
RAG + Few-Shot
✓
×
×
×
×
×
GPT-4o+Refl.
×
✓
✓
✓
×
×
Tool-Agent
✓
✓
✓
✓
×
×
Flat-VER
✓
✓
✓
✓
×
×
Table 4: Baseline capability alignment. “Flat-VER + SFT + DPO” and “CDG-SFT Agent” are symmetric ablation baselines: the former adds SFT+DPO to flat repair (isolating CDG’s contribution); the latter adds CDG ordering to SFT-only training (isolating DPO’s contribution). AeroTherm-GPT combines both.
Figure 5: Ablation Study — Incremental EESR Contribution per Module with Violation Rate Trajectories. The waterfall chart decomposes the EESR gain from each framework component, while the overlaid lines track the corresponding reduction in unit, physics, and numerical violation rates.
Figure 6: Per-Gate Pass Rates — Five Methods × Five Verification Gates. The radar chart visualizes the compliance rate across unit, physics, numerical, execution, and audit gates, highlighting AeroTherm-GPT’s near-ceiling performance across all categories.
Figure 7: Stratified EESR by Task Complexity. Performance degrades gracefully with task complexity, from single-layer nominal tasks to multi-layer extreme-regime tasks and non-standard materials. Error bars denote 95% confidence intervals.
Model
Fund. Knowledge (Q1–Q30, %)
Formula Inv. (F1–F6, %)
Auto. Prog. (P1–P4, %)
TCR (%)
DeepSeek-R1 [ 54 ]
100.0
83.3
100.0
97.5
DeepSeek-V3 [ 54 ]
93.3
66.7
25.0
82.5
GPT-4o [ 54 ]
76.7
66.7
25.0
70.0
Qwen2.5 [ 54 ]
76.7
50.0
25.0
67.5
AeroTherm-GPT (ours)
96.7
100.0
100.0
97.5
Table 6: Results on HyperKFA-Bench [ 54 ] (hypersonic benchmark). Fund. Knowledge: accuracy on 30 hypersonic QA questions; Formula Inv.: correctness rate on 6 quantitative formula tasks (relative error <2% ); Auto. Prog.: code execution success rate on 4 programming tasks; TCR: overall Task Completion Rate. Baseline results are taken directly from the original publication; AeroTherm-GPT is evaluated zero-shot without TPS-specific scaffolding. AeroTherm-GPT achieves high TCR (97.5%), matching DeepSeek-R1’s 97.5% while substantially outperforming GPT-4o (70.0%) and Qwen2.5 (67.5%). The formula invocation advantage (+33.3 pp over DeepSeek-R1) reflects domain SFT’s internalization of hypersonic governing equations and unit-consistent numerical procedures.
Figure 8: Backbone Transfer — Zero-Shot vs Full Pipeline EESR. Marker size indicates active parameter count. The linear fit ( r=0.96 ) demonstrates that the CCLG pipeline’s performance gains are robust across diverse architectures (dense vs. MoE) and parameter scales.
Benchmark
n
Metric
Llama-3 70B
Aero- Therm
Δ
GPT-4o
SciBench
695
Acc
35.8
42.6
+6.8
44.3
GPQA-Diamond
198
Acc
33.1
38.9
+5.8
49.4
MMLU-STEM
3,014
5s-Acc
79.2
80.7
+1.5
87.4
Table 7: Cross-benchmark validation results (Track B). Panel (a): scientific reasoning; AeroTherm-GPT’s SFT provides meaningful gains on SciBench (+6.8) and GPQA (+5.8) with minimal MMLU-STEM forgetting (+1.5). Panel (b): code generation; the VER iterative repair mechanism improves pass@1 across all base models. AeroTherm-GPT exhibits the largest VER repair gain (+6.8 pp avg), suggesting that DPO alignment improves responsiveness to structured error feedback even outside the TPS domain. GPT-4o retains absolute leadership on general tasks.
Failure Pattern
Share of all tasks
Share within failed tasks
Impact
Mitigation
CDG weight miscalibration
5.2%
46.0%
Medium
Recalibrate on diverse cases
Physics bounds too restrictive
3.1%
27.4%
High
Extend bounds
Missing constraint assets
2.4%
21.2%
Medium
Expand asset library
VER convergence exceeds budget
0.6%
5.3%
Low
Optimize repair ordering
Total
11.3%
100% ∗
Table 8: Failure pattern frequency and mitigation strategies identified during HyTPS-Bench evaluation. “Share of all tasks” corresponds to the 11.3% overall failure rate; “Share within failed tasks” normalizes by the number of failed tasks only. The four patterns account for essentially all observed failures. ∗ Percentages are rounded to one decimal place; the sum is 99.9% due to rounding.
Gate
First Pass
Flat Repair (iter. 8)
CDG Repair (iter. 1)
Unit
×
×
✓
Physics
×
×
✓
Numerical
×
×
✓
Execution
×
×
✓
Audit
✓
✓
✓
EESR
×
×
✓
Table 9: Gate-level verification outcomes for the end-to-end case study. First pass: four gates fail due to unit transcription error. Flat repair: eight iterations of symptom-patching fail to resolve the upstream unit fault; all four downstream gates remain open. CDG-guided repair: upstream unit fix in iteration 1 resolves all dependent gates simultaneously (RCFE =3 ).
Iter.
Strategy
Action taken
Gates resolved
1
Flat
Reduce Δt by 10× (Fo violation → tighten time step)
None
2
Flat
Reduce Δt further 5× ; halve Δx (instability persists)
None
3
Flat
Clamp k1 heuristically to plausible range (physics gate open)
None
4
Flat
Relax physics bounds tolerance (bounds still violated)
None
5
Flat
Reduce heat flux by 20% (reduce thermal load to ease convergence)
None
6
Flat
Switch time-integration to implicit Euler (execution gate still open)
None
Table 10: Repair action trace for the end-to-end case study. Both strategies have identical tool access (same VER loop, RAG, and execution backend); the only difference is repair ordering. Flat-checklist repair exhausts the 8-iteration budget with symptom-directed but execution-focused actions, never reaching the upstream unit fault. CDG-guided repair identifies the unit constraint as the highest-priority root-cause node and resolves all four failing gates in a single action.(U, P, N, E = Unit, Physics, Numerical, Execution)
Figure 9: End-to-end CDG verification on the 1-D composite wall benchmark. (a) The pipeline extracts 14 constraints (dimensional, conservation, boundary, interface) and an 83-LOC Python solver from the NL requirement. Pass 1 triggers a cascade failure at the Unit gate ( k1 specified in W/cm K instead of W/m K); the fault propagates through Physics, Numerical, and Execution gates (purple arcs). The CDG repair agent traces the root cause via the constraint dependency graph, applies a single unit-scale correction, and Pass 2 clears all five gates (EESR = 5/5). Inset: fault DAG and per-gate confidence lift from Pass 1 to Pass 2. (b) Repair trajectory comparison. Flat repair (left) exhausts 8 iterations with symptom-directed actions targeting the Execution and Numerical gates—each locally rational given the observed divergence—without ever identifying the upstream Unit-gate fault as the root cause, terminating at budget exhaustion (EESR × ). CDG repair (right) resolves the entire cascade in a single iteration by targeting the root gate directly (EESR ✓). Bottom strip: aggregate efficiency metrics.
Figure 10: End-to-end TPS thermal analysis case study. (a) Two-layer stack geometry. (b) CDG constraint subgraph for this instance (RCFE = 3) with comparison against system-level benchmark statistics.
Figure 11: Spatial temperature distribution in the TPS. (a) Temperature field over 0–35 mm depth and 30 s duration; significant heating is confined to the outermost 10 mm. (b) Depth profiles at t=10 , 20 and 30 s; FD results match the semi-infinite analytical reference to within 0.02 % at the surface. (c) Pointwise relative error for x≤10 mm: maximum 0.1 % ( t=10 s) and 0.5 % ( t=20 s), well below the 2 % threshold.
Figure 12: Transient thermal response of a two-layer TPS to a triangular heat pulse (peak 800 kW/m² at t=10 s). (a) Temperature histories at the ceramic–substructure interface ( x=15 mm) and back wall ( x=35 mm); the 523 K structural limit is not exceeded. (b) Validation of the finite-difference solver against the semi-infinite analytical solution at x=0 ; relative error stays below 3 %, with late-time growth attributed to finite-thickness effects.
Method
EESR (5/5)
EESR-4 (4/5)
Macro-Gate
Best-Gate
GPT-5 (high)
0.480
0.612
0.646
0.782
Flat-VER
0.468
0.601
0.729
0.865
CDG-SFT Agent
0.784
0.851
0.871
0.941
AeroTherm-GPT
0.887
0.941
0.965
0.991
Table 11: Sensitivity of method rankings to EESR strictness. EESR-4: any 4 of 5 gates pass; Macro-Gate: macro-average of five gate pass rates; Best-Gate: highest individual gate (ceiling reference). Rankings are stable across all relaxations, confirming the advantage is not an artifact of the strict 5-gate product.
Method
EESR lang (pass@1)
EESR scaffold (gain)
EESR (full)
Flat-VER
0.219
0.249
0.468
Flat-VER + SFT + DPO
0.521
0.241
0.762
CDG-SFT Agent
0.312
0.472
0.784
AeroTherm-GPT
0.521
0.366
0.887
Table 12: EESR decomposition separating intrinsic language capability (EESR lang : pass@1 without VER) from scaffold contribution (EESR scaffold : incremental gain from VER). AeroTherm-GPT’s advantage is present in both components: its EESR lang ( +30.2 pp over Flat-VER) reflects genuine first-pass improvement from domain SFT+DPO alignment, while EESR scaffold captures the structural CDG repair benefit. The “Flat-VER + SFT + DPO” row shows that without CDG, domain training raises EESR lang substantially (+30.2 pp) but scaffold gain is modest; CDG-SFT Agent shows the inverse pattern (higher scaffold gain, lower first-pass). AeroTherm-GPT achieves the best balance across both dimensions.
Deploying LLMs as reasoning assistants in safety-critical aerospace engineering requires stricter evaluation criteria than general scientific benchmarks. In hypersonic thermal protection system (TPS) design, inaccurate stagnation-point heat flux or boundary-layer calculations may cause catastrophic design margin violations. Models with numerically reasonable but physically invalid answers are more dangerous than those declining to respond. Current scientific benchmarks only test abstract math and basic physics, evaluate final answers solely, ignore engineering reasoning processes, and cannot detect such critical failures. We propose TPS-CalcBench, the first diagnostic benchmark for closed-form analytical calculations in hypersonic aerodynamics and high-temperature gas dynamics that experienced TPS engineers conduct without simulations. Our contributions include domain-oriented task taxonomy with 4 difficulty levels and 8 categories from Anderson's textbook, dual-track evaluation measuring result accuracy and reasoning quality via an 8-dimension rubric and calibrated judge with human audit to identify right answer wrong reasoning issues, human-AI data pipeline producing 420 high-confidence core items and 810 noise-controlled pre-gating items from 4560 raw data, noise-sensitivity analysis measuring data quality impacts on model ranking, and three diagnostic intervention methods: DFA-TPS fine-tuning, RAG-EQ retrieval grounding and PA-CoT process-aware prompting. Tests on 13 models from 7 groups show wide performance differences (KPI 12.6-87.9), hidden formula selection defects, data-driven rank changes and effective intervention improvements, establishing a complete diagnose-evaluate-intervene framework for safety-critical engineering LLM deployment assessment.
Jinglai Zheng, Chuhan Qiao, Haiming Huang
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
LLMs increasingly generate workflow actions and repairs that may be well formed yet stale, infeasible, conflicting, or destructive of their own evidence. We introduce Agentic Transaction Processing (ATP), which treats generated actions as untrusted proposals until deterministic admission accepts them under an executable constraint set C. Its two-sided principle is: a proposal is not truth, and no proposal foresees every disruption. Anything may propose, but only the runtime admits and commits; unforeseen disruptions trigger bounded reactive repair whose output re-enters admission. Mnemosyne realizes ATP with an append-only transition log, effective-state projection, dependency-safe compensation, and active contract records. Under stated assumptions and relative to C, we prove four safety properties (authority separation, serial-equivalent generative admission, evidence-preserving repair, and obligation containment) and establish bounded reactive repair. Across nine safety benchmarks and a four-case Temporal SDK comparison, ATP rejects every targeted violation while admitting valid work. A matched data-size sweep measures 5.2-6.6% incremental throughput cost over the same local durable commit path and exposes local saturation. In a companion scheduling harness, local repair edits nearly an order of magnitude fewer operations than global recompute; a 12-scenario interruption stress test rejects every stale recovery candidate without losing observations or producing invalid commits. Two bounded pilots route 80 proposals from four heterogeneous LLMs through the same gate with zero invalid commits; 24 of 40 mid-execution proposals are admitted and 16 are rejected, including four explicit safety rejections.
Large Language Models (LLMs), deep learning architectures with typically over 10 billion parameters, have recently begun to be integrated into various cyber-physical systems (CPS) such as robotics, industrial automation, and autopilot systems. The abstract knowledge and reasoning capabilities of LLMs are employed for tasks like planning and navigation. However, a significant challenge arises from the tendency of LLMs to produce "hallucinations" - outputs that are coherent yet factually incorrect or contextually unsuitable. This characteristic can lead to undesirable or unsafe actions in the CPS. Therefore, our research focuses on assuring the LLM-enabled CPS by enhancing their critical properties. We propose SafePilot, a novel hierarchical neuro-symbolic framework that provides end-to-end assurance for LLM-enabled CPS according to attribute-based and temporal specifications. Given a task and its specification, SafePilot first invokes a hierarchical planner with a discriminator that assesses task complexity. If the task is deemed manageable, it is passed directly to an LLM-based task planner with built-in verification. Otherwise, the hierarchical planner applies a divide-and-conquer strategy, decomposing the task into sub-tasks, each of which is individually planned and later merged into a final solution. The LLM-based task planner translates natural language constraints into formal specifications and verifies the LLM's output against them. If violations are detected, it identifies the flaw, adjusts the prompt accordingly, and re-invokes the LLM. This iterative process continues until a valid plan is produced or a predefined limit is reached. Our framework supports LLM-enabled CPS with both attribute-based and temporal constraints. Its effectiveness and adaptability are demonstrated through two illustrative case studies.
Weizhe Xu, Mengyu Liu, Fanxin Kong
University of Notre Dame, Notre Dame, IN, USA · Washington State University, Richland, WA, USA