Finite basis kolmogorov-arnold networks: domain decomposition for data-driven and physics-informed problems

AA Howard, B Jacob, SH Murphy, A Heinlein… - arXiv preprint arXiv …, 2024 - arxiv.org
Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to
multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be …

Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks

W Chen, AA Howard, P Stinis - arXiv preprint arXiv:2407.01613, 2024 - arxiv.org
Physics-informed deep learning has emerged as a promising alternative for solving partial
differential equations. However, for complex problems, training these networks can still be …

[PDF][PDF] Multifidelity domain decomposition-based physics-informed neural networks for time-dependent problems

A Heinlein, AA Howard, D Beecroft… - arXiv preprint arXiv …, 2024 - researchgate.net
Multiscale problems are challenging for neural network-based discretizations of differential
equations, such as physics-informed neural networks (PINNs). This can be (partly) attributed …

What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications

E Williams, A Howard, B Meuris, P Stinis - arXiv preprint arXiv:2411.18459, 2024 - arxiv.org
Physics-informed deep operator networks (DeepONets) have emerged as a promising
approach toward numerically approximating the solution of partial differential equations …