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

2024/11/14 by Anandh, Thivin, Ghose, Divij, Jain, Himanshu +3
#Computational Engineering #FOS: Computer and information sciences #FOS: Mathematics #Finance #Machine Learning (cs.LG) #Numerical Analysis (math.NA) #and Science (cs.CE)

paper · doi:10.48550/arxiv.2411.09329

Abstract

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.

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