PINNsFormer: A Transformer-Based Framework For Physics-Informed Neural Networks

arXiv:2307.11833v3 Announce Type: replace-cross
Abstract: Physics-Informed Neural Networks (PINNs) have emerged as a promising deep learning framework for approximating numerical solutions to partial differential equations (PDEs). However, conventional PINNs, relying on multilayer perceptrons (MLP), neglect the crucial temporal dependencies inherent in practical physics systems and thus fail to propagate the initial condition constraints globally and accurately capture the true solutions under various scenarios. In this paper, we introduce a novel Transformer-based framework, termed PINNsFormer, designed to address this limitation. PINNsFormer …

abstract arxiv cs.ce cs.lg deep learning deep learning framework dependencies differential framework however mlp networks neural networks numerical physics physics-informed practical solutions systems temporal transformer type