72 citations · 164 across the 18 of their papers we have counts for
18 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…
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…
Conformalized-KANs: Uncertainty Quantification with Coverage Guarantees for Kolmogorov-Arnold Networks (KANs) in Scientific Machine Learning
Amirhossein Mollaali, Christian Bolivar Moya, Amanda A. Howard +3
This paper explores uncertainty quantification (UQ) methods in the context of Kolmogorov-Arnold Networks (KANs). We apply an ensemble approach to KANs to obtain a heuristic measure…
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…
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…
Physics-Guided Continual Learning for Predicting Emerging Aqueous Organic Redox Flow Battery Material Performance
Yucheng Fu, Amanda Howard, Chao Zeng +3
Aqueous organic redox flow batteries (AORFBs) have gained popularity in renewable energy storage due to their low cost, environmental friendliness and scalability. The rapid discov…
Stacked networks improve physics-informed training: applications to neural networks and deep operator networks
Amanda A Howard, Sarah H Murphy, Shady E Ahmed +1
Physics-informed neural networks and operator networks have shown promise for effectively solving equations modeling physical systems. However, these networks can be difficult or i…
Efficient kernel surrogates for neural network-based regression
Saad Qadeer, Andrew Engel, Amanda Howard +4
Despite their immense promise in performing a variety of learning tasks, a theoretical understanding of the limitations of Deep Neural Networks (DNNs) has so far eluded practitione…
A multifidelity approach to continual learning for physical systems
Amanda Howard, Yucheng Fu, Panos Stinis
We introduce a novel continual learning method based on multifidelity deep neural networks. This method learns the correlation between the output of previously trained models and t…
Multifidelity Deep Operator Networks For Data-Driven and Physics-Informed Problems
Amanda A. Howard, Mauro Perego, George E. Karniadakis +1
Operator learning for complex nonlinear systems is increasingly common in modeling multi-physics and multi-scale systems. However, training such high-dimensional operators requires…
Machine Learning in Heterogeneous Porous Materials
Marta D'Elia, Hang Deng, Cedric Fraces +21
The "Workshop on Machine learning in heterogeneous porous materials" brought together international scientific communities of applied mathematics, porous media, and material scienc…