Solutions to Elliptic and Parabolic Problems via Finite Difference Based Unsupervised Small Linear Convolutional Neural Networks

arXiv:2311.00259v2 Announce Type: replace
Abstract: In recent years, there has been a growing interest in leveraging deep learning and neural networks to address scientific problems, particularly in solving partial differential equations (PDEs). However, many neural network-based methods like PINNs rely on auto differentiation and sampling collocation points, leading to a lack of interpretability and lower accuracy than traditional numerical methods. As a result, we propose a fully unsupervised approach, requiring no training data, to estimate finite difference solutions for PDEs …

abstract arxiv auto convolutional neural networks cs.cv cs.lg cs.na deep learning difference differential differentiation however linear math.na network networks neural network neural networks scientific small solutions type unsupervised via