Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems

Understand

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.