Approximating High-Dimensional Minimal Surfaces with Physics-Informed
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Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks

5 September 2023

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Papers citing "Approximating High-Dimensional Minimal Surfaces with Physics-Informed Neural Networks"

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Title
A unified scalable framework for causal sweeping strategies for Physics-Informed Neural Networks (PINNs) and their temporal decompositions Michael Penwarden Ameya Dilip Jagtap Shandian Zhe George Karniadakis Robert M. Kirby PINN AI4CE 66 61 0 28 Feb 2023
Augmented Physics-Informed Neural Networks (APINNs): A gating network-based soft domain decomposition methodology Zheyuan Hu Ameya Dilip Jagtap George Karniadakis Kenji Kawaguchi 58 82 0 16 Nov 2022
Error estimates for physics informed neural networks approximating the Navier-Stokes equations Tim De Ryck Ameya Dilip Jagtap S. Mishra PINN 93 118 0 17 Mar 2022
Physics-informed neural networks for inverse problems in supersonic flows Ameya Dilip Jagtap Zhiping Mao Nikolaus Adams George Karniadakis PINN 43 221 0 23 Feb 2022
When Do Extended Physics-Informed Neural Networks (XPINNs) Improve Generalization? Zheyuan Hu Ameya Dilip Jagtap George Karniadakis Kenji Kawaguchi AI4CE PINN 52 88 0 20 Sep 2021
Parallel Physics-Informed Neural Networks via Domain Decomposition K. Shukla Ameya Dilip Jagtap George Karniadakis PINN 162 284 0 20 Apr 2021
SPINN: Sparse, Physics-based, and partially Interpretable Neural Networks for PDEs A. A. Ramabathiran P. Ramachandran PINN AI4CE 101 79 0 25 Feb 2021
Estimates on the generalization error of Physics Informed Neural Networks (PINNs) for approximating a class of inverse problems for PDEs Siddhartha Mishra Roberto Molinaro PINN 82 266 0 29 Jun 2020
nPINNs: nonlocal Physics-Informed Neural Networks for a parametrized nonlocal universal Laplacian operator. Algorithms and Applications G. Pang M. DÉlia M. Parks George Karniadakis PINN 48 155 0 08 Apr 2020
Neural Networks Trained to Solve Differential Equations Learn General Representations M. Magill F. Qureshi H. W. Haan 45 64 0 29 Jun 2018
A Deep Neural Network Surrogate for High-Dimensional Random Partial Differential Equations M. A. Nabian Hadi Meidani AI4CE 55 102 0 08 Jun 2018
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 85 931 0 28 Nov 2017
A unified deep artificial neural network approach to partial differential equations in complex geometries Jens Berg K. Nystrom AI4CE 63 586 0 17 Nov 2017
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 123 1,389 0 30 Sep 2017
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 2.0K 150,312 0 22 Dec 2014

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