# Compositional Embedding Architecture for Physical Field Prediction in Componentized Aerospace Systems

arXiv: https://arxiv.org/abs/2610.00237 · HTML: https://mlsanity.com/paper/2610.00237/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 23 Sep 2026.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Fourier Neural Operator for Parametric Partial Differential Equations](https://mlsanity.com/paper/2010.08895/) (2020)
- [DeepONet: Learning nonlinear operators for identifying differential equations based on the universal approximation theorem of operators](https://mlsanity.com/paper/1910.03193/) (2019)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [PDE-Net: Learning PDEs from Data](https://mlsanity.com/paper/1710.09668/) (2017)
- [Geometry-Informed Neural Operator for Large-Scale 3D PDEs](https://mlsanity.com/paper/2309.00583/) (2023)
- [PDE-Net 2.0: Learning PDEs from Data with A Numeric-Symbolic Hybrid Deep Network](https://mlsanity.com/paper/1812.04426/) (2018)
- [BENO: Boundary-embedded Neural Operators for Elliptic PDEs](https://mlsanity.com/paper/2401.09323/) (2024)
- [A Deep Neural Network Surrogate Modeling Benchmark for Temperature Field Prediction of Heat Source Layout](https://mlsanity.com/paper/2103.11177/) (2021)
- [CompNO: A Novel Foundation Model approach for solving Partial Differential Equations](https://mlsanity.com/paper/2601.07384/) (2026)
- [Enhancing generalization in endwall film cooling prediction: Incorporating the superposition principle into transformer-based neural operators](https://mlsanity.com/paper/2609.31633/) (2026)

## Abstract (arXiv)

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.