FastVPINNs: Tensor-Driven Acceleration of VPINNs for Complex Geometries

Autor:	Anandh, Thivin, Ghose, Divij, Jain, Himanshu, Ganesan, Sashikumaar
Rok vydání:	2024
Předmět:	Computer Science - Machine Learning Computer Science - Computational Engineering Finance and Science Computer Science - Neural and Evolutionary Computing Mathematics - Numerical Analysis
Druh dokumentu:	Working Paper
Popis:	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 to traditional hp-VPINNs. With proper choice of hyperparameters, FastVPINNs surpass conventional PINNs in both speed and accuracy, especially in problems with high-frequency solutions. Demonstrated effectiveness in solving inverse problems on complex domains underscores FastVPINNs' potential for widespread application in scientific and engineering challenges, opening new avenues for practical implementations in scientific machine learning. Comment: 31 pages, 19 figures, 4 algorithms
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.12063 Zobrazit plný text záznamu View this record from Arxiv