AI Agent Research Hub

Mar 24, 2026 · Artificial Intelligence

How PeRCNN Turns Convolution Kernels into Differential Operators for Physics‑Informed Learning

PeRCNN embeds physics directly into its architecture by replacing additive nonlinearities with element‑wise multiplication in Π‑blocks, enabling convolution kernels to act as finite‑difference operators, which yields superior forward and inverse PDE solving, accurate coefficient identification, robust equation discovery, and interpretable models, as demonstrated on multiple reaction‑diffusion benchmarks.