FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries

arXiv:2404.12063v1 Announce Type: new
Abstract: Variational Physics-Informed Neural Networks (VPINNs) utilize a variational loss function to solve partial differential equations, mirroring Finite Element Analysis techniques. Traditional hp-VPINNs, while effective for high-frequency problems, are computationally intensive and scale poorly with increasing element counts, limiting their use in complex geometries. This work introduces FastVPINNs, a tensor-based advancement that significantly reduces computational overhead and improves scalability. Using optimized tensor operations, FastVPINNs achieve a 100-fold reduction in the median training time per epoch compared …

abstract analysis arxiv cs.ce cs.lg cs.na cs.ne differential element function loss math.na networks neural networks physics physics-informed scale solve tensor type work