FastVPINNs: A fast, versatile and robust Variational PINNs framework for forward and inverse problems in science
Keywords: Physics informed neural networks, Domain decomposition, Forward modelling, Inverse modelling, Scalable PINNs, Variational Physics informed neural networks, Petrov-Galerkin formulation, hp-refinement
TL;DR: A novel framework for hp-Variational Physics Informed Nerual Networks that provides up to 100x speed-ups and can handle any complex geometry.
Abstract: Variational physics-informed neural networks (VPINNs), with h- and p-refinement, show promise over conventional PINNs. But existing frameworks are computationally inefficient and unable to deal with complex meshes. As such, VPINNs have had limited application when it comes to practical problems in science and engineering. In the present work, we propose a novel VPINNs framework, that achieves up to a 100x speed-up over SOTA codes. We demonstrate the flexibility of this framework by solving different forward and inverse problems on complex geometries, and by applying VPINNs to vector-valued partial differential equations.
Submission Number: 100
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