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

TL;DR

This work tackles the ill-posed problem of reconstructing full temperature fields from sparse sensor data in heat-source systems. It introduces IPTR, which conditions reconstruction on a reference sparse-field pair to embed implicit physics priors, and uses a Dual Physics Embedding Module (implicit cross-attention plus Fourier-based auxiliary encoding) combined with a SPADE decoder to produce high-fidelity fields. Across single-condition, multi-condition, and few-shot settings, IPTR achieves state-of-the-art accuracy and strong generalization, outperforming Voronoi-based and operator-learning baselines and demonstrating robust performance with varying sensor counts. The results highlight the value of leveraging reference simulations as implicit physics priors to guide ill-posed field reconstructions in engineering applications.

Abstract

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.

Figures (13)

• Figure 1: An illustration of the region $\Omega$ of the HSS subject to Dirichlet boundary condition.
• Figure 2: Overview of our reconstruction paradigm. (a) Existing methods directly regress the temperature field $T_t$ from sparse measurements $M_t$, ignoring auxiliary information. (b) Our approach leverages a reference pair $(M_s, T_s)$ from similar thermal conditions to provide implicit physics guidance. By modeling the relation between $(M_t, M_s)$ and $(T_t, T_s)$, the network learns to reconstruct $T_t$ via the mapping $g_\theta(M_t, M_s, T_s) \rightarrow \hat{T_t}$.
• Figure 3: Architecture of the proposed IPTR framework. (a) shows the overall pipeline for temperature field reconstruction. Given a reference pair consisting of sparse monitoring data $M_s$, and corresponding temperature field $T_s$, along with target sparse monitoring data $M_t$, we first obtain interpolated field $V_s$, $V_t$ via Voronoi-based encoding (b). These are passed to the Dual Physics Embedding Module (c), where the Implicit Physics-Guided Branch performs cross-attention among $V_s$, $T_s$ and $V_t$ to extract $I_p$, and the Auxiliary Encoding Branch encodes $V_t$ into $E_p$. The fused representation $I_p$ C$E_p$ is decoded to reconstruct the full temperature field $\hat{T_t}$, supervised by the ground-truth $T_t$.
• Figure 4: Voronoi-based pseudo-field generation.
• Figure 5: Architecture of the Auxiliary Encoding Branch. The target sparse interpolated field $V_t$ undergoes a dimensional lifting, followed by spectral transformation through Fourier layers, and is subsequently projected to obtain auxiliary embeddings $E_p$ for enhancing the reconstruction process.