Reproduce “Physics-informed Convolutional Neural Networks for Temperature Field Prediction of Heat Source Layout without Labeled Data” on OpenResearch

About this paper

Xiaoyu Zhao, Zhiqiang Gong, Yunyang Zhang, Wen Yao, Xiaoqian Chen

A Physics-informed UNet (PI-UNet) rapidly predicts steady-state temperature fields for diverse heat source layouts, learning complex physical phenomena directly from governing equations without labeled simulation data. This model achieves mean absolute errors below 0.03K and demonstrates precision comparable to supervised learning models trained with thousands of data points.

Key insights

• Computing the 'ideal' temperature value for the physics-informed loss without automatic differentiation (no-auto-grad mode) from its neighboring points is critical for training stability and preventing trivial network outputs.
• Directly enforcing hard boundary conditions and utilizing 'reflect' padding in CNN layers significantly enhances network convergence speed, stability, and prediction accuracy, particularly at the domain boundaries.
• Optimized architectural choices like Group Normalization (over Batch Normalization for sparse inputs) and bilinear interpolation for upsampling are vital for robust performance in physics-informed image-to-image regression tasks.

Summary by alphaXiv.