# Learning to Reconstruct Temperature Field from Sparse Observations with Implicit Physics Priors

arXiv: https://arxiv.org/abs/2512.01196 · HTML: https://mlsanity.com/paper/2512.01196/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 20 of its 42 references that are in the map.
- First posted on arXiv 1 Dec 2025.

## Builds on (most cited first, 20 of 20)

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- [The Random Feature Model for Input-Output Maps between Banach Spaces](https://mlsanity.com/paper/2005.10224/) (2020)
- [Global field reconstruction from sparse sensors with Voronoi tessellation-assisted deep learning](https://mlsanity.com/paper/2101.00554/) (2021)
- [Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data](https://mlsanity.com/paper/2109.12482/) (2021)
- [RecFNO: a resolution-invariant flow and heat field reconstruction method from sparse observations via Fourier neural operator](https://mlsanity.com/paper/2302.09808/) (2023)
- [A Deep Neural Network Surrogate Modeling Benchmark for Temperature Field Prediction of Heat Source Layout](https://mlsanity.com/paper/2103.11177/) (2021)
- [Efficient deep data assimilation with sparse observations and time-varying sensors](https://mlsanity.com/paper/2310.16187/) (2023)
- [A Machine Learning Surrogate Modeling Benchmark for Temperature Field Reconstruction of Heat-Source Systems](https://mlsanity.com/paper/2108.08298/) (2021)
- [Temperature Field Inversion of Heat-Source Systems via Physics-Informed Neural Networks](https://mlsanity.com/paper/2201.06880/) (2022)
- [Multi-fidelity surrogate modeling for temperature field prediction using deep convolution neural network](https://mlsanity.com/paper/2301.06674/) (2023)
- [Dynamical system prediction from sparse observations using deep neural networks with Voronoi tessellation and physics constraint](https://mlsanity.com/paper/2409.00458/) (2024)
- [Convex Optimization of Launch Vehicle Ascent Trajectory with Heat-Flux and Splash-Down Constraints](https://mlsanity.com/paper/2008.13239/) (2020)
- [Joint Deep Reversible Regression Model and Physics-Informed Unsupervised Learning for Temperature Field Reconstruction](https://mlsanity.com/paper/2106.11929/) (2021)
- [FR-Mamba: Time-Series Physical Field Reconstruction Based on State Space Model](https://mlsanity.com/paper/2505.16083/) (2025)

## Abstract (arXiv)

Accurate reconstruction of temperature field of heat-source systems (TFR-HSS) is crucial for thermal monitoring and reliability assessment in engineering applications such as electronic devices and aerospace structures. However, the high cost of measurement acquisition and the substantial distributional shifts in temperature field across varying conditions present significant challenges for developing reconstruction models with robust generalization capabilities. Existing DNNs-based methods typically formulate TFR-HSS as a one-to-one regression problem based solely on target sparse measurements, without effectively leveraging reference simulation data that implicitly encode thermal knowledge. To address this limitation, we propose IPTR, an implicit physics-guided temperature field reconstruction framework that introduces sparse monitoring-temperature field pair from reference simulations as priors to enrich physical understanding. To integrate both reference and target information, we design a dual physics embedding module consisting of two complementary branches: an implicit physics-guided branch employing cross-attention to distill latent physics from the reference data, and an auxiliary encoding branch based on Fourier layers to capture the spatial characteristics of the target observation. The fused representation is then decoded to reconstruct the full temperature field. Extensive experiments under single-condition, multi-condition, and few-shot settings demonstrate that IPTR consistently outperforms existing methods, achieving state-of-the-art reconstruction accuracy and strong generalization capability.