Penn Engineers Develop 'Mollifier Layers' — AI Breakthrough for Solving Inverse Partial Differential Equations

Researchers at the University of Pennsylvania developed 'Mollifier Layers,' a novel technique that integrates classical mathematical smoothing functions into neural networks to solve inverse partial differential equations (PDEs) with greater stability and efficiency. The method replaces recursive automatic differentiation with convolutional operations using analytically defined mollifiers, reducing peak memory use for fourth-order PDEs from 2.70 GB to significantly lower levels. Applications span genomics, materials science, climate modeling, and chromatin biology. The findings were accepted for publication in Transactions on Machine Learning Research and will be presented at NeurIPS 2026.