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Compositional Embedding Architecture for Physical Field Prediction in Componentized Aerospace Systems

Qineng Wang, Xinrui Zhou, Shuwen Yue, Kangli Bao, Hairun Xie, Yonghe Zhang

arXiv:2610.00237v1cs.CEcs.LG

TL;DR

Repeated high-fidelity simulations make spacecraft thermal-design screening difficult, and whole-configuration surrogates may not generalize to unseen component counts or factor combinations. TFCN composes component and boundary factors in a tree to predict temperature fields; it reports lower component-count OOD RMSE in both evaluated boundary settings and supports rapid pre-screening before detailed analysis.

  • Problem

    High-fidelity simulations are costly to repeat, while whole-configuration surrogates may not reliably predict temperature fields for unseen component counts and combinations of heat sources and boundaries.

    Source: §1 · p. 2

  • Method

    TFCN represents heat-source components and boundary segments as factors and recursively combines their encoded representations through a shared composer before decoding the temperature field.

    Source: §1 · p. 4, §5 · p. 20

  • Results

    4.21 K versus GINO’s 12.23 K mean K-OOD RMSE in Temp-BC, and 18.62 K versus 28.05 K in RadFlux-BC.

    Source: §5 · p. 21

  • Takeaways & Limitations

    The results support using TFCN to pre-screen candidate spacecraft thermal configurations before high-fidelity numerical analysis and verification.

    Source: §5 · p. 21

    Conclusions are restricted to two-dimensional steady-state problems, K-OOD evaluation, and factor and boundary types represented in the training data.

    Source: §5 · p. 21

Abstract

from arXiv · show

Spacecraft thermal design requires repeated evaluation of how variations in the number and spatial arrangement of heat-generating components and in thermal boundary conditions affect the temperature field. High-fidelity numerical simulations are computationally expensive and therefore difficult to use for large-scale design screening. Although surrogate models can accelerate temperature-field prediction, existing approaches generally encode each complete configuration as a whole and do not explicitly exploit the reusability of local physical constituents across configurations, which limits their accuracy for component counts and combinations not covered during training. To address this issue, we propose the Tree-Structured Factor Composition Network (TFCN), which decomposes complex spacecraft thermal configurations into reusable local physical factors and employs a tree-structured composition module to learn the global temperature-field response associated with different factor combinations. TFCN is evaluated on two-dimensional steady-state spacecraft thermal-analysis cases with prescribed-temperature and radiative-flux boundary conditions. The model is trained exclusively on configurations containing no more than 15 heat-generating components and evaluated on unseen configurations containing 16-25 components. For the prescribed-temperature and radiative-flux cases, TFCN achieves component-count out-of-distribution RMSE values of 4.21 K and 18.62 K, respectively, representing reductions of 65.6% and 33.6% relative to the strongest baseline. These results demonstrate that TFCN improves the reliability of temperature-field prediction under variations in component count and provides an efficient surrogate for rapid spacecraft thermal-design evaluation and large-scale configuration screening.

1. Introduction

Repeated high-fidelity simulations make rapid spacecraft thermal-design screening difficult, while whole-configuration surrogates may not generalize to unseen component counts and combinations. TFCN composes geometry-bearing component and boundary factors, and the paper reports improved high-component-count OOD prediction across two boundary-condition settings.

1. Introduction

  • Rapid full-field temperature prediction supports thermal-risk identification, alternative-layout comparison, and assessment of candidate thermal-control schemes.These uses are framed within spacecraft design and engineering decision-making.Source: §1 · p. 2
  • High-fidelity simulations require repeated model updates, numerical solutions, and post-processing after layout, power, or boundary-condition changes, hindering rapid screening.Surrogates offer low-cost approximations for early design comparison, while detailed verification remains with high-fidelity analysis.Source: §1 · pp. 2–3
  • Many existing surrogates encode each complete configuration globally, and strong in-distribution accuracy does not ensure reliable prediction for unseen component counts or new heat-source and boundary combinations.The paper frames OOD generalization as a central requirement for componentized spacecraft thermal surrogates.Source: §1 · p. 3
  • Related methods are organized by whether their main generalization bias acts on physical consistency, spatial or set representation, or mechanism/operator composition.The paper notes that existing methods primarily address variable-size representation or reuse of equation-level structures.Source: §1 · pp. 3–4, Table 1 · p. 4
  • TFCN represents each heat-source component and boundary segment as a factor, then recursively combines encoded factors into a global temperature-field response.Its shared tree composer operates on geometry-bearing tokens, distinguishing it from methods that aggregate variable-size inputs or compose equation-level blocks.Source: §1 · p. 4
  • Across prescribed-temperature and radiative-flux scenarios, TFCN substantially improves high-component-count OOD prediction over UNet, DeepONet, and GINO.Structural ablations and engineering thermal metrics further verify the shared recursive composition mechanism.Source: §1 · p. 5

2. Problem setup

The paper formulates steady-state temperature-field prediction for a two-dimensional spacecraft panel whose heat sources and boundary segments vary. It evaluates component-count extrapolation under prescribed-temperature and radiative-flux boundary conditions using data generated from sampled layouts and numerical solutions.

2. Problem setup

  • The HSL-TFP setup extends a planar heat-source benchmark to spacecraft panels with heterogeneous components, variable heat-rejection interfaces, and component counts K = 1–25.The setting retains equipment heat dissipation, in-plane conduction, and boundary heat transfer.Source: §2 · p. 5, Figure 1 · p. 6

2.1. Task definition and input representation

  • The model predicts a steady-state temperature field from domain coordinates, an internal heat-source set, and boundary conditions, with component and boundary-segment counts varying across samples.Evaluation focuses on extrapolation to increased component counts.Source: §2.1 · p. 6

2.2. Boundary physics

  • The two scenarios use the same component-layout sampling strategy but different boundary physics: prescribed boundary temperature or radiative flux.The radiative-flux condition introduces stronger source–boundary nonlinear coupling through a fourth-power radiation term.Source: §2.2 · pp. 6–7

2.3. Data construction and evaluation protocol

  • SeqLS generates non-overlapping square, circular, and capsule-shaped layouts; FEniCSx then computes the steady-state temperature field from assigned physical parameters.The generated samples pair six input channels with the temperature-field output; K-ID uses K = 1–15 and K-OOD uses K = 16–25, with BC2 as the default boundary setting.Source: §2.3 · pp. 7–8

3. Method

TFCN maps variable sets of geometry-bearing heat-source and boundary factors to a complete temperature field by recursively composing their latent representations. Its factorization, shared tree composer, and training and inference strategies support this composition across configurations.

3. Method

  • The method treats configuration changes as changes to the number, arrangement, and physical parameters of reusable source and boundary factors that jointly determine the temperature field.TFCN learns the mapping from this variable factor set to the complete field through shared recursive composition.Source: §3 · pp. 8–9

3.1. Overall framework: shared recursive composition of engineering factors

  • TFCN represents heat-source components and boundary segments as local factors, then recursively composes their latent tokens into a system representation for full-field decoding.The balanced tree is a parameter-shared computation schedule, not a representation of component adjacency or heat-flow topology.Source: §3.1 · p. 9

3.2. Factor representation and bucket encoding

  • Each factor combines a signed distance field for spatial support with normalized physical scalars, while TFCN-SP mixes source and boundary factors and TFCN-TP encodes them separately.The two variants share the tree composer and decoder; they differ in bucketing and encoder parameterization.Source: §3.2 · pp. 10–12

3.3. Tree composer and field decoder

  • A shared pairwise composer merges partial configurations through a low-order additive path and residual convolutional corrections for interactions and boundary physics.All tree layers share the composer, so its parameter count does not grow with component or bucket count; the decoder reconstructs the complete normalized temperature field.Source: §3.3 · pp. 12–13

3.4. Training and inference

  • Training samples composition depth while preserving a fixed tensor interface; evaluation aggregates multiple latent-composition paths before decoding the final field.Six paths use two bucket assignments at each of depths 1, 2, and 3; DBSCAN excludes noise representations before element-wise averaging, and the shared decoder processes the fused representation once.Source: §3.4 · pp. 13–14

4. Experiments and analysis

The experiments compare TFCN with global and operator-learning baselines on high-component-count extrapolation, then examine training coverage, composition depth, structural ablations, and intermediate representations. TFCN has the lowest reported K-OOD RMSE in both boundary settings, while the analyses show how coverage and composer structure relate to extrapolation performance.

4.1. Setup

  • Experiments assess K-OOD extrapolation, training coverage and composition depth, structural ablations, and intermediate-representation diagnostics against U-Net, DeepONet, and GINO.The baselines represent global and operator-learning approaches.Source: §4.1 · pp. 14–15

4.2. Main results

  • TFCN-TP achieves K-OOD RMSEs of 4.21 K in Temp-BC and 18.62 K in RadFlux-BC, the lowest mean values among the compared models.The results are means over five independent runs; TFCN-TP also achieves the lowest ID/OOD errors for four additional thermal indicators in both settings.Source: Table 2 · p. 15, §4.2 · p. 15

4.3. Training coverage, composition depth, and ablations

  • With Kmax = 5, greater composition depth still leaves high-K errors in the hundreds of Kelvin; at Kmax = 15, Dmax = 2 and 3 yield mean RMSEs of about 24.36 K and 22.33 K.Removing the learnable composer raises K-OOD RMSE to 110.57 K in RadFlux-BC and 54.03 K in Temp-BC; removing local-block merging raises it to 25.29 K and 18.49 K, respectively.Source: §4.3 · pp. 17–18

4.4. Intermediate-representation and field-level diagnostics

  • PHATE projections show closer ID and K-OOD representations for TFCN variants than for the no-composition ablation, which has the largest separation and MMD.In the RadFlux-BC sample, the final composed prediction preserves major hot spots and boundary gradients, with residuals concentrated near heat sources and high-gradient boundaries.Source: §4.4 · pp. 18–20

5. Conclusion

TFCN composes object-level heat-source and boundary factors to predict full temperature fields for spacecraft panels with varying component numbers and layouts. It achieves the lowest mean error on unseen component counts in both boundary settings, within the stated scope of two-dimensional steady-state problems.

5. Conclusion

  • TFCN represents heat-source components and boundary segments as object-level factors, progressively combining their encodings through a shared composer before full-field decoding.The approach targets rapid thermal-field evaluation across varying component numbers and layouts.Source: §5 · p. 20
  • 4.21 K versus GINO’s 12.23 K in Temp-BC, and 18.62 K versus 28.05 K in RadFlux-BC, are the mean K-OOD RMSE values reported for TFCN-TP and GINO, respectively.TFCN also preserved main hot-spot locations and boundary-induced gradients in qualitative field-level results.Source: §5 · pp. 20–21
  • The conclusions are restricted to two-dimensional steady-state problems, K-OOD evaluation, and factor and boundary types represented in the training data.The implementation also uses predefined factor capacity and balanced binary composition.Source: §5 · p. 21

Appendix A. Notation and model implementation details

The appendix summarizes TFCN notation and implementation details, including fixed-capacity factor-slot padding and the compared models’ network structures and parameter scales.

Appendix A.1. Principal notation

  • Table A.1 summarizes the principal notation used in TFCN.The supplied appendix passage identifies the notation table but does not state individual symbol meanings.Source: Appendix A.1 · p. 21, Table A.1 · p. 22

Appendix A.2. Factor-slot padding and masking

  • Source-factor buckets use a fixed capacity of 20 slots, with unused positions padded and excluded by a validity mask.Balanced assignment is valid when each bucket’s real-factor count is at most the capacity; padding is separate from the composer’s 4 × 4 spatial-window partition.Source: Appendix A.2 · pp. 22–23

Appendix A.3. Network structure and scale

Appendix B.1. Data distribution diagnostics

Figure B.11 presents low-dimensional distributions of temperature-field samples for the Temp-BC and RadFlux-BC scenarios.

Appendix B.1. Data distribution diagnostics

  • Figure B.11 shows low-dimensional distributions of temperature-field samples in the Temp-BC and RadFlux-BC scenarios.The figure is identified as temperature-field sample distribution diagnostics.Source: Appendix B.1 · p. 24, Figure B.11 · p. 25

Appendix B.2. Training and evaluation configuration

The appendix specifies the shared training schedule and validation-based checkpoint selection, with training and evaluation settings summarized in Table B.6.

Appendix B.2. Training and evaluation configuration

  • All models were trained with AdamW for 1500 epochs, batch size 32, weight decay 1 × 10−4, and gradient-norm clipping at 1.0.The learning rate warmed up to 8 × 10−4 over 60 epochs and then followed cosine decay to 1 × 10−5; early stopping was not used.Source: Appendix B.2 · p. 25
  • Checkpoints were selected using error on a fixed ID validation set, not OOD results.Table B.6 summarizes the training and evaluation configuration.Source: Appendix B.2 · p. 25, Table B.6 · p. 25

Appendix C. Supplementary evaluation metrics and efficiency

Appendix C reports physics-oriented thermal indicators and supplementary RMSE statistics, then describes TFCN’s computational efficiency and preliminary-screening role.

Appendix C.1. Physics-oriented thermal indicators

  • The indicator definitions specify a weighted 95th percentile, the domain’s diagonal length, and a one-grid-wide boundary band extracted separately from each boundary-SDF channel.The percentile uses stratified-sampling weights.Source: Appendix C.1 · p. 26, Table C.7 · p. 26
  • Table C.8 reports physics-oriented indicators and supplementary full-field RMSE statistics under ID/OOD evaluation, with RMSE (K = 25) limited to the K = 25 OOD subset.The first four rows are indicators defined in Table C.7; the last two report full-field RMSE statistics.Source: Appendix C.1 · pp. 26–27, Table C.8 · p. 27

Appendix C.2. Computational efficiency and workflow role

  • After one offline training run, TFCN reduces evaluation of 5,000 candidates from hours or days to seconds and serves preliminary screening before FEniCSx verification.The selected configurations are verified with FEniCSx.Source: Appendix C.2 · p. 27, Table C.9 · p. 27
  • The reported computational-efficiency comparisons cover two boundary-condition settings, with ideal parallelism, single-configuration latency estimates, and batched inference distinguished in the notes.The notes specify ideal 64-way parallelism, latency estimates from single-configuration timing, and batched inference at 2,800 samples/s.Source: Appendix C.2 · p. 27, Table C.9 · p. 27

Appendix D. Supplementary field-level prediction samples

The appendix presents two batches of RadFlux-BC temperature-field prediction samples as field-level comparisons of reference and predicted distributions.

Appendix D. Supplementary field-level prediction samples

  • The sample figures complement quantitative results with field-level comparisons of reference and predicted temperature distributions.The supplied text does not state a qualitative winner or outcome for these comparisons.Source: Appendix D · p. 28
  • Figure D.12 presents RadFlux-BC temperature-field prediction samples.It is one of two sample batches used for field-level comparisons of reference and predicted temperature distributions.Source: Figure D.12 · p. 28, Appendix D · p. 28
  • Figure D.13 presents supplementary RadFlux-BC temperature-field prediction samples.It is the second batch used for field-level comparisons of reference and predicted temperature distributions.Source: Appendix D · p. 28, Figure D.13 · p. 29
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