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

TL;DR

PyDEns is an open-source Python framework that simplifies solving various PDEs with neural networks, offering flexible experimentation, architecture search, and training control.

Contribution

Introduction of a versatile, open-source neural network-based PDE solver framework with customizable architecture and training options.

Findings

Supports solving multiple PDE types including heat and wave equations

Enables easy neural network architecture search with ResNet and DenseNet

Allows testing different point-sampling schemes during training

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.