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Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases

4 October 2024

Robert M. Kirby

Papers citing "Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases"

32 / 32 papers shown

Title
AMR-Transformer: Enabling Efficient Long-range Interaction for Complex Neural Fluid SimulationComputer Vision and Pattern Recognition (CVPR), 2025 Zeyi Xu Jinfan Liu Kuangxu Chen Ye Chen Zhangli Hu Bingbing Ni 231 3 0 13 Mar 2025
RandONet: Shallow-Networks with Random Projections for learning linear and nonlinear operatorsJournal of Computational Physics (JCP), 2024 Gianluca Fabiani Ioannis G. Kevrekidis Constantinos Siettos A. Yannacopoulos 254 22 0 08 Jun 2024
PirateNets: Physics-informed Deep Learning with Residual Adaptive Networks Sizhuang He Bowen Li Yuhan Chen P. Perdikaris AI4CE PINN 503 78 0 01 Feb 2024
Domain Agnostic Fourier Neural OperatorsNeural Information Processing Systems (NeurIPS), 2023 Ning Liu S. Jafarzadeh Yue Yu AI4CE 345 41 0 30 Apr 2023
Lagrangian PINNs: A causality-conforming solution to failure modes of physics-informed neural networksComputer Methods in Applied Mechanics and Engineering (CMAME), 2022 R. Mojgani Maciej Balajewicz Pedram Hassanzadeh PINN 198 54 0 05 May 2022
Respecting causality is all you need for training physics-informed neural networks Sizhuang He Shyam Sankaran P. Perdikaris PINN CML AI4CE 380 232 0 14 Mar 2022
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problemsComputer Methods in Applied Mechanics and Engineering (CMAME), 2021 Jeremy Yu Lu Lu Xuhui Meng George Karniadakis PINN AI4CE 187 598 0 01 Nov 2021
Characterizing possible failure modes in physics-informed neural networks Aditi S. Krishnapriyan A. Gholami Shandian Zhe Robert M. Kirby Michael W. Mahoney PINN AI4CE 322 863 0 02 Sep 2021
Physics-informed neural networks (PINNs) for fluid mechanics: A reviewActa Mechanica Sinica (Acta Mech. Sin.), 2021 Shengze Cai Zhiping Mao Zhicheng Wang Minglang Yin George Karniadakis PINN AI4CE 324 1,551 0 20 May 2021
Exact imposition of boundary conditions with distance functions in physics-informed deep neural networksComputer Methods in Applied Mechanics and Engineering (CMAME), 2021 N. Sukumar Ankit Srivastava PINN AI4CE 309 328 0 17 Apr 2021
Physics-informed neural networks with hard constraints for inverse designSIAM Journal on Scientific Computing (SISC), 2021 Lu Lu R. Pestourie Wenjie Yao Zhicheng Wang F. Verdugo Steven G. Johnson PINN 290 645 0 09 Feb 2021
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sizhuang He Hanwen Wang P. Perdikaris 405 596 0 18 Dec 2020
Neural Pruning via Growing RegularizationInternational Conference on Learning Representations (ICLR), 2020 Huan Wang Can Qin Yulun Zhang Y. Fu 251 180 0 16 Dec 2020
Fourier Neural Operator for Parametric Partial Differential EquationsInternational Conference on Learning Representations (ICLR), 2020 Zong-Yi Li Nikola B. Kovachki Kamyar Azizzadenesheli Burigede Liu K. Bhattacharya Andrew M. Stuart Anima Anandkumar AI4CE 1.2K 3,220 0 18 Oct 2020
Physics Informed Neural Networks for Simulating Radiative TransferJournal of Quantitative Spectroscopy and Radiative Transfer (JQSRT), 2020 Siddhartha Mishra Roberto Molinaro PINN 226 130 0 25 Sep 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 412 574 0 07 Sep 2020
When and why PINNs fail to train: A neural tangent kernel perspectiveJournal of Computational Physics (JCP), 2020 Sizhuang He Xinling Yu P. Perdikaris 321 1,172 0 28 Jul 2020
Solving Allen-Cahn and Cahn-Hilliard Equations using the Adaptive Physics Informed Neural NetworksCommunications in Computational Physics (Commun. Comput. Phys.), 2020 Colby Wight Jia Zhao 192 283 0 09 Jul 2020
Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains Matthew Tancik Pratul P. Srinivasan B. Mildenhall Sara Fridovich-Keil N. Raghavan Utkarsh Singhal R. Ramamoorthi Jonathan T. Barron Ren Ng 533 2,976 0 18 Jun 2020
A Dual-Dimer Method for Training Physics-Constrained Neural Networks with Minimax ArchitectureNeural Networks (NN), 2020 Dehao Liu Yan Wang 236 93 0 01 May 2020
Frequency Bias in Neural Networks for Input of Non-Uniform DensityInternational Conference on Machine Learning (ICML), 2020 Ronen Basri Meirav Galun Amnon Geifman David Jacobs Yoni Kasten S. Kritchman 230 214 0 10 Mar 2020
Understanding and mitigating gradient pathologies in physics-informed neural networks Sizhuang He Yujun Teng P. Perdikaris AI4CE PINN 410 326 0 13 Jan 2020
Robust Training and Initialization of Deep Neural Networks: An Adaptive Basis ViewpointMathematical and Scientific Machine Learning (MSML), 2019 E. Cyr Mamikon A. Gulian Ravi G. Patel M. Perego N. Trask 169 82 0 10 Dec 2019
PyTorch: An Imperative Style, High-Performance Deep Learning LibraryNeural Information Processing Systems (NeurIPS), 2019 Adam Paszke Sam Gross Francisco Massa Adam Lerer James Bradbury ... Sasank Chilamkurthy Benoit Steiner Lu Fang Junjie Bai Soumith Chintala ODL 956 48,192 0 03 Dec 2019
Modeling the Dynamics of PDE Systems with Physics-Constrained Deep Auto-Regressive NetworksJournal of Computational Physics (JCP), 2019 N. Geneva N. Zabaras AI4CE 303 308 0 13 Jun 2019
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks Zhi-Qin John Xu Yaoyu Zhang Yaoyu Zhang Yan Xiao Zheng Ma 552 629 0 19 Jan 2019
Physics-Constrained Deep Learning for High-dimensional Surrogate Modeling and Uncertainty Quantification without Labeled Data Yinhao Zhu N. Zabaras P. Koutsourelakis P. Perdikaris PINN AI4CE 320 954 0 18 Jan 2019
On the Spectral Bias of Neural Networks Nasim Rahaman A. Baratin Devansh Arpit Felix Dräxler Min Lin Fred Hamprecht Yoshua Bengio Aaron Courville 497 1,829 0 22 Jun 2018
Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations M. Raissi P. Perdikaris George Karniadakis PINN AI4CE 222 1,062 0 28 Nov 2017
A unified deep artificial neural network approach to partial differential equations in complex geometries Jens Berg K. Nystrom AI4CE 169 639 0 17 Nov 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 343 2,280 0 24 Aug 2017
Tensorizing Neural Networks Alexander Novikov D. Podoprikhin A. Osokin Dmitry Vetrov 366 936 0 22 Sep 2015