A Block-Coordinate Approach of Multi-level Optimization with an
Application to Physics-Informed Neural Networks

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A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks

23 May 2023

Valentin Mercier

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Papers citing "A Block-Coordinate Approach of Multi-level Optimization with an Application to Physics-Informed Neural Networks"

18 / 18 papers shown

Title
Momentum Diminishes the Effect of Spectral Bias in Physics-Informed Neural Networks G. Farhani Alexander Kazachek Boyu Wang 100 6 0 29 Jun 2022
Subspace Decomposition based DNN algorithm for elliptic type multi-scale PDEs Xi-An Li Z. Xu Lei Zhang 52 28 0 10 Dec 2021
Training of deep residual networks with stochastic MG/OPT Cyrill Planta Alena Kopanicáková Rolf Krause 62 3 0 09 Aug 2021
Globally Convergent Multilevel Training of Deep Residual Networks Alena Kopanicáková Rolf Krause 93 15 0 15 Jul 2021
Physics-informed neural networks (PINNs) for fluid mechanics: A review Shengze Cai Zhiping Mao Zhicheng Wang Minglang Yin George Karniadakis PINN AI4CE 82 1,201 0 20 May 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 187 459 0 18 Dec 2020
When and why PINNs fail to train: A neural tangent kernel perspective Sizhuang He Xinling Yu P. Perdikaris 141 916 0 28 Jul 2020
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
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 130 2,440 0 18 Jun 2020
A Multigrid Method for Efficiently Training Video Models Chaoxia Wu Ross B. Girshick Kaiming He Christoph Feichtenhofer Philipp Krahenbuhl 76 94 0 02 Dec 2019
The Convergence Rate of Neural Networks for Learned Functions of Different Frequencies Ronen Basri David Jacobs Yoni Kasten S. Kritchman 80 218 0 02 Jun 2019
Frequency Principle: Fourier Analysis Sheds Light on Deep Neural Networks Zhi-Qin John Xu Yaoyu Zhang Yaoyu Zhang Yan Xiao Zheng Ma 124 519 0 19 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 154 1,455 0 22 Jun 2018
The Deep Ritz method: A deep learning-based numerical algorithm for solving variational problems E. Weinan Ting Yu 123 1,390 0 30 Sep 2017
Stable Architectures for Deep Neural Networks E. Haber Lars Ruthotto 152 733 0 09 May 2017
Hierarchical Multiscale Recurrent Neural Networks Junyoung Chung Sungjin Ahn Yoshua Bengio BDL 104 538 0 06 Sep 2016
Adam: A Method for Stochastic Optimization Diederik P. Kingma Jimmy Ba ODL 2.1K 150,364 0 22 Dec 2014
Iteration Complexity of Randomized Block-Coordinate Descent Methods for Minimizing a Composite Function Peter Richtárik Martin Takáč 100 772 0 14 Jul 2011

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