PyDEns: a Python Framework for Solving Differential Equations with Neural Networks
This provides a convenient tool for researchers and practitioners in computational science and engineering to experiment with neural network-based PDE solvers, though it is incremental as it builds on existing methods by offering a framework rather than a new solving technique.
The authors tackled the lack of a flexible framework for experimenting with neural networks to solve partial differential equations (PDEs) by introducing PyDEns, an open-source Python module that enables solving PDEs from a large family, searching for optimal neural network architectures, and controlling training processes.
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.