SLIDING WINDOW DYNAMIC WEIGHTED DATA-PHYSICS HYBRID LEARNING VIA U-NET CNN FOR STEADY-STATE HEAT CONDUCTION PREDICTION

Machine learning-based steady-state heat conduction prediction faces two critical limitations: data-driven methods depend on large datasets and often yield solutions inconsistent with the Laplace equation (heat conduction law), while physics-driven methods (e.g., PINNs) suffer from slow convergence. To address these challenges, this paper proposes a U-Net CNN-based data-physics hybrid learning method with sliding window dynamic weighting. The method employs a weighted loss function that integrates FVM-generated reference data and the Laplace equation. A sliding window mechanism adaptively adjusts the weight ratio between data-driven (temperature error) and physics-driven (Laplacian residual, LR) loss terms, thereby balancing convergence speed and physical consistency. Experimental results show that for data-driven training, the hybrid method significantly reduces iterations by 60.9% (single-case, E ≤ 0.005) and 13.59% (multi-case, 4374 samples), while accelerating LR convergence (a key indicator of heat conduction compliance). For physics-driven training, even with coarse references (e.g., downsampled FVM solutions), convergence speed improves by 49.0%. With an optimal window size (3-6), the average training speed increases by 16.34% with enhanced physical consistency of the temperature field. In conclusion, this method effectively resolves the over-reliance on datasets in data-driven approaches and the slow convergence in physics-driven methods. The sliding window mechanism optimizes efficiency and compliance with heat conduction laws, providing a practical solution for steady-state heat conduction prediction and a valuable reference for PDE-governed thermal problems.