Thermal diffusion—a fundamental physical process pervasive in applications ranging from electronics to industrial systems—is inherently irreversible under the second law of thermodynamics. As temperature gradients spontaneously smooth out over time, crucial information regarding the initial thermal state is permanently lost due to entropy increase. This fundamental information loss leads to a severe ill-posedness in inverse thermal problems, where infinitesimal errors in the final observation can cause enormous uncertainties in the reconstructed initial state.
Recently, a collaborative research team led by Prof. Ying Li and Prof. Hongsheng Chen from Zhejiang University, alongside Prof. Jiping Huang from Fudan University, has made a significant breakthrough in tackling this longstanding challenge. Published in National Science Review and co-first-authored by master’s graduate Hanqi Chen, as well as PhD students Qiang-Kai-Lai Huang and Yanxiang Wang from Prof. Ying Li’s research group at Zhejiang University, the paper titled “Learning to reverse thermal diffusion” introduces a deep learning framework for inverse diffusion capable of deducing initial thermal states based on final-state observations.
The proposed methodology overcomes the limitations of conventional computational methods, particularly when analyzing heterogeneous materials, by employing two synergistic deep learning components. First, the team introduced the Thermal Field Evolution Network (TE-Net), a finite-difference-based convolutional architecture that accurately estimates spatial material properties—specifically thermal diffusivity—from time-dependent cooling data.
Crucially, this accurately derived diffusivity serves as essential physical prior knowledge for the framework’s core innovation: the Time-Reversal Operator (TRO). Drawing inspiration from generative diffusion models and Fourier Neural Operators, the TRO learns mappings between function spaces rather than relying on traditional point-wise solutions. By synergizing analytical eigenbasis decomposition with frequency-domain operator learning, the TRO effectively filters high-frequency noise and directly projects the final-state thermal field back to its initial distribution.
The research team rigorously validated their approach through comprehensive simulations and real-world infrared imaging experiments using 3D-printed structures and practical semiconductor chips. The operator-driven method demonstrated exceptional performance, achieving a thermal diffusivity estimation error of less than 10% and an astonishing retrodiction numerical error below 0.1%.
This breakthrough establishes a high-fidelity paradigm for spatiotemporal thermal analysis. It holds broad implications for advanced non-destructive testing, defect detection in densely integrated circuits, and next-generation thermal management, with potential applications extending to a wider class of physical phenomena such as mass and charge diffusion.
National Science Review