1. Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems
- Author
-
Anandh, Thivin, Ghose, Divij, Jain, Himanshu, Sunkad, Pratham, Ganesan, Sashikumaar, and John, Volker
- Subjects
Mathematics - Numerical Analysis ,Computer Science - Computational Engineering, Finance, and Science ,Computer Science - Machine Learning - 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., Comment: 25 pages, 11 figures, 8 tables
- Published
- 2024