72 citations · 164 across the 18 of their papers we have counts for
6 papers · 1 filter
What do physics-informed DeepONets learn? Understanding and improving training for scientific computing applications
Emily Williams, Amanda Howard, Brek Meuris +1
Physics-informed deep operator networks (DeepONets) have emerged as a promising approach toward numerically approximating the solution of partial differential equations (PDEs). In…
SPIKANs: Separable Physics-Informed Kolmogorov-Arnold Networks
Bruno Jacob, Amanda A. Howard, Panos Stinis
Physics-Informed Neural Networks (PINNs) have emerged as a promising method for solving partial differential equations (PDEs) in scientific computing. While PINNs typically use mul…
Multifidelity Kolmogorov-Arnold Networks
Amanda A. Howard, Bruno Jacob, Panos Stinis
We develop a method for multifidelity Kolmogorov-Arnold networks (KANs), which use a low-fidelity model along with a small amount of high-fidelity data to train a model for the hig…
Self-adaptive weights based on balanced residual decay rate for physics-informed neural networks and deep operator networks
Wenqian Chen, Amanda A. Howard, Panos Stinis
Physics-informed deep learning has emerged as a promising alternative for solving partial differential equations. However, for complex problems, training these networks can still b…
Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems
Amanda A. Howard, Bruno Jacob, Sarah Helfert +2
Kolmogorov-Arnold networks (KANs) have attracted attention recently as an alternative to multilayer perceptrons (MLPs) for scientific machine learning. However, KANs can be expensi…
Multifidelity domain decomposition-based physics-informed neural networks and operators for time-dependent problems
Alexander Heinlein, Amanda A. Howard, Damien Beecroft +1
Multiscale problems are challenging for neural network-based discretizations of differential equations, such as physics-informed neural networks (PINNs). This can be (partly) attri…