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09/18/2023
Deep smoothness WENO scheme for two-dimensional hyperbolic conservation laws: A deep learning approach for learning smoothness indicators
In this paper, we introduce an improved version of the fifth-order weigh...
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02/28/2023
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions
Physics-informed neural networks (PINNs) as a means of solving partial d...
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02/23/2023
Learning stiff chemical kinetics using extended deep neural operators
We utilize neural operators to learn the solution propagator for the cha...
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11/16/2022
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology
In this paper, we propose the augmented physics-informed neural network ...
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09/06/2022
How important are activation functions in regression and classification? A survey, performance comparison, and future directions
Inspired by biological neurons, the activation functions play an essenti...
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03/17/2022
Error estimates for physics informed neural networks approximating the Navier-Stokes equations
We prove rigorous bounds on the errors resulting from the approximation ...
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02/23/2022
Physics-informed neural networks for inverse problems in supersonic flows
Accurate solutions to inverse supersonic compressible flow problems are ...
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02/07/2022
Deep learning of inverse water waves problems using multi-fidelity data: Application to Serre-Green-Naghdi equations
We consider strongly-nonlinear and weakly-dispersive surface water waves...
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09/20/2021
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization?
Physics-informed neural networks (PINNs) have become a popular choice fo...
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05/20/2021
Deep Kronecker neural networks: A general framework for neural networks with adaptive activation functions
We propose a new type of neural networks, Kronecker neural networks (KNN...
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04/20/2021
Parallel Physics-Informed Neural Networks via Domain Decomposition
We develop a distributed framework for the physics-informed neural netwo...
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09/25/2019