Learning to reverse thermal diffusion

Thermal diffusion, which governs heat transfer across a wide range of systems-from electronics to industrial processes-is inherently irreversible under the second law of thermodynamics, thus obscuring time-dependent information. To overcome this ill-posedness, this study introduces a physics-informed framework that centers on a novel time-reversal operator learning approach. A finite-difference-based network is first employed to robustly derive heterogeneous material properties. Crucially, the core innovation lies in the operator for thermal retrodiction. Distinct from traditional point-wise solvers, this functional model learns the mapping between function spaces, enabling the direct projection of the final-state thermal field back to its initial state. By synergizing analytical eigenbasis decomposition with frequency-domain operator learning, the time-reversal operator effectively reconstructs the backward propagation of temperature fields. Validated on 3D-printed structures and chips, this operator-driven method achieves retrodiction errors [Formula: see text]0.1%, establishing a high-fidelity paradigm for spatiotemporal analysis. This breakthrough has broad implications for non-destructive testing in energy systems, with potential applications extending to a wide class of phenomena such as mass, charge, and light diffusion.