72 citations · 363 across the 68 of their papers we have counts for
8 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…
Multiscale modeling framework of a constrained fluid with complex boundaries using twin neural networks
Peiyuan Gao, George Em Karniadakis, Panos Stinis
The properties of constrained fluids have increasingly gained relevance for applications ranging from materials to biology. In this work, we propose a multiscale model using twin n…
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…
Scientific machine learning for closure models in multiscale problems: a review
Benjamin Sanderse, Panos Stinis, Romit Maulik +1
Closure problems are omnipresent when simulating multiscale systems, where some quantities and processes cannot be fully prescribed despite their effects on the simulation's accura…
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…