PyDEns: a Python Framework for Solving Differential Equations with Neural Networks

Abstract

Recently, a lot of papers proposed to use neural networks to approximately solve partial differential equations (PDEs). Yet, there has been a lack of flexible framework for convenient experimentation. In an attempt to fill the gap, we introduce a PyDEns-module open-sourced on GitHub. Coupled with capabilities of BatchFlow, open-source framework for convenient and reproducible deep learning, PyDEns-module allows to 1) solve partial differential equations from a large family, including heat equation and wave equation 2) easily search for the best neural-network architecture among the zoo, that includes ResNet and DenseNet 3) fully control the process of model-training by testing different point-sampling schemes. With that in mind, our main contribution goes as follows: implementation of a ready-to-use and open-source numerical solver of PDEs of a novel format, based on neural networks.