Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems
This work addresses performance issues in PINNs for multiscale time-dependent problems, which is incremental for researchers in scientific machine learning.
The paper tackled the challenge of multiscale time-dependent problems in physics-informed neural networks (PINNs) by combining multifidelity stacking PINNs with domain decomposition-based finite basis PINNs, showing that this approach clearly improves performance over standard PINN and stacking PINN methods in tests on a pendulum, a two-frequency problem, and the Allen-Cahn equation.
Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed to the so-called spectral bias of neural networks. To improve the performance of PINNs for time-dependent problems, a combination of multifidelity stacking PINNs and domain decomposition-based finite basis PINNs is employed. In particular, to learn the high-fidelity part of the multifidelity model, a domain decomposition in time is employed. The performance is investigated for a pendulum and a two-frequency problem as well as the Allen-Cahn equation. It can be observed that the domain decomposition approach clearly improves the PINN and stacking PINN approaches. Finally, it is demonstrated that the FBPINN approach can be extended to multifidelity physics-informed deep operator networks.