Penn engineers introduce Mollifier Layers for solving inverse PDEs using neural networks

Researchers at University of Pennsylvania School of Engineering introduced Mollifier Layers, a technique that integrates classical mathematical smoothing functions into neural networks to solve inverse partial differential equations (PDEs). The approach addresses a longstanding challenge where high-order derivative computations on noisy real-world data tend to fail. Applications span genomics, materials science, climate modeling, and chromatin biology. The findings are set to appear in Transactions on Machine Learning Research and will be presented at NeurIPS 2026.