Improving hp-Variational Physics-Informed Neural Networks for Steady-State Convection-Dominated Problems
This work addresses accuracy issues in physics-informed neural networks for convection-dominated problems, which is an incremental improvement for computational physics and engineering applications.
The paper tackles convection-dominated convection-diffusion-reaction problems by extending hp-variational physics-informed neural networks with SUPG-like stabilization and learned indicator functions, resulting in noticeably more accurate numerical solutions compared to existing approaches.
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.