9 papers
SINDy-KANs: Sparse identification of non-linear dynamics through Kolmogorov-Arnold networks
Amanda A. Howard, Nicholas Zolman, Bruno Jacob +2
Kolmogorov-Arnold networks (KANs) have arisen as a potential way to enhance the interpretability of machine learning. However, solutions learned by KANs are not necessarily interpr…
Bridging quantum and classical computing for partial differential equations through multifidelity machine learning
Bruno Jacob, Amanda A. Howard, Panos Stinis
Quantum algorithms for partial differential equations (PDEs) face severe practical constraints on near-term hardware: limited qubit counts restrict spatial resolution to coarse gri…
Domain-Decomposed Graph Neural Network Surrogate Modeling for Ice Sheets
Adrienne M. Propp, Mauro Perego, Eric C. Cyr +5
Accurate yet efficient surrogate models are essential for large-scale simulations of partial differential equations (PDEs), particularly for uncertainty quantification (UQ) tasks t…
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…
E-PINNs: Epistemic Physics-Informed Neural Networks
Bruno Jacob, Ashish S. Nair, Amanda A. Howard +2
Physics-informed neural networks (PINNs) have demonstrated promise as a framework for solving forward and inverse problems involving partial differential equations. Despite recent…
Self-adaptive weighting and sampling for physics-informed neural networks
Wenqian Chen, Amanda Howard, Panos Stinis
Physics-informed deep learning has emerged as a promising framework for solving partial differential equations (PDEs). Nevertheless, training these models on complex problems remai…