Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems

Autor:	Anandh, Thivin, Ghose, Divij, Jain, Himanshu, Sunkad, Pratham, Ganesan, Sashikumaar, John, Volker
Rok vydání:	2024
Předmět:	Mathematics - Numerical Analysis Computer Science - Computational Engineering Finance and Science Computer Science - Machine Learning
Druh dokumentu:	Working Paper
Popis:	This paper proposes and studies two extensions of applying hp-variational physics-informed neural networks, more precisely the FastVPINNs framework, to convection-dominated convection-diffusion-reaction problems. First, a term in the spirit of a SUPG stabilization is included in the loss functional and a network architecture is proposed that predicts spatially varying stabilization parameters. Having observed that the selection of the indicator function in hard-constrained Dirichlet boundary conditions has a big impact on the accuracy of the computed solutions, the second novelty is the proposal of a network architecture that learns good parameters for a class of indicator functions. Numerical studies show that both proposals lead to noticeably more accurate results than approaches that can be found in the literature. Comment: 25 pages, 11 figures, 8 tables
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2411.09329 Zobrazit plný text záznamu View this record from Arxiv