When and why PINNs fail to train: A neural tangent kernel perspective

28 July 2020

Papers citing "When and why PINNs fail to train: A neural tangent kernel perspective"

50 / 336 papers shown

Title
HyResPINNs: Hybrid Residual Networks for Adaptive Neural and RBF Integration in Solving PDEs Madison Cooley Robert M. Kirby Shandian Zhe Varun Shankar PINN AI4CE 23 0 0 04 Oct 2024
Fourier PINNs: From Strong Boundary Conditions to Adaptive Fourier Bases Madison Cooley Varun Shankar Robert M. Kirby Shandian Zhe 22 2 0 04 Oct 2024
Deep Learning Alternatives of the Kolmogorov Superposition Theorem Leonardo Ferreira Guilhoto P. Perdikaris 38 7 0 02 Oct 2024
On the expressiveness and spectral bias of KANs Yixuan Wang Jonathan W. Siegel Ziming Liu Thomas Y. Hou 32 9 0 02 Oct 2024
Explain Like I'm Five: Using LLMs to Improve PDE Surrogate Models with Text Cooper Lorsung Amir Barati Farimani AI4CE 58 1 0 02 Oct 2024
Beyond Derivative Pathology of PINNs: Variable Splitting Strategy with Convergence Analysis Yesom Park Changhoon Song Myungjoo Kang 26 2 0 30 Sep 2024
SetPINNs: Set-based Physics-informed Neural Networks M. Nagda Phil Ostheimer Thomas Specht Frank Rhein F. Jirasek Stephan Mandt Sophie Fellenz Sophie Fellenz PINN 3DPC 46 0 0 30 Sep 2024
Frequency-adaptive Multi-scale Deep Neural Networks Jizu Huang Rukang You Tao Zhou AI4CE 23 1 0 28 Sep 2024
Dual Cone Gradient Descent for Training Physics-Informed Neural Networks Youngsik Hwang Dong-Young Lim AI4CE 28 2 0 27 Sep 2024
Physics-aligned Schrödinger bridge Zeyu Li Hongkun Dou Shen Fang Wang Han Yue Deng Lijun Yang AI4CE DiffM 28 0 0 26 Sep 2024
Physics-Informed Graph-Mesh Networks for PDEs: A hybrid approach for complex problems M. Chenaud Frédéric Magoulès José Alves AI4CE PINN 26 1 0 25 Sep 2024
Physics-informed kernel learning Nathan Doumèche Francis Bach Gérard Biau Claire Boyer PINN 29 2 0 20 Sep 2024
Physics-Informed Variational State-Space Gaussian Processes Oliver Hamelijnck Arno Solin Theodoros Damoulas 21 0 0 20 Sep 2024
Physics-Informed Neural Networks with Trust-Region Sequential Quadratic Programming Xiaoran Cheng Sen Na PINN 31 1 0 16 Sep 2024
Transformed Physics-Informed Neural Networks for The Convection-Diffusion Equation Jiajing Guan Howard Elman 24 0 0 12 Sep 2024
Component Fourier Neural Operator for Singularly Perturbed Differential Equations Ye Li Ting Du Yiwen Pang Zhongyi Huang 19 1 0 07 Sep 2024
Two-stage initial-value iterative physics-informed neural networks for simulating solitary waves of nonlinear wave equations Jin Song Ming Zhong George Karniadakis Zhenya Yan PINN 23 12 0 02 Sep 2024
Physics-Informed Neural Networks and Extensions Maziar Raissi P. Perdikaris Nazanin Ahmadi George Karniadakis PINN AI4CE 33 4 0 29 Aug 2024
Fourier Spectral Physics Informed Neural Network: An Efficient and Low-Memory PINN Tianchi Yu Yiming Qi Ivan V. Oseledets Shiyi Chen 24 0 0 29 Aug 2024
General-Kindred Physics-Informed Neural Network to the Solutions of Singularly Perturbed Differential Equations Sen Wang Peizhi Zhao Qinglong Ma Tao Song PINN 23 3 0 27 Aug 2024
Functional Tensor Decompositions for Physics-Informed Neural Networks Sai Karthikeya Vemuri Tim Buchner Julia Niebling Joachim Denzler PINN 38 4 0 23 Aug 2024
Point Source Identification Using Singularity Enriched Neural Networks Tianhao Hu Bangti Jin Zhi Zhou 3DPC 27 0 0 17 Aug 2024
Why Rectified Power Unit Networks Fail and How to Improve It: An Effective Theory Perspective Taeyoung Kim Myungjoo Kang 22 0 0 04 Aug 2024
Improving PINNs By Algebraic Inclusion of Boundary and Initial Conditions Mohan Ren Zhihao Fang Keren Li Anirbit Mukherjee PINN AI4CE 39 0 0 30 Jul 2024
Improved physics-informed neural network in mitigating gradient related failures Pancheng Niu Yongming Chen Jun Guo Yuqian Zhou Minfu Feng Yanchao Shi PINN AI4CE 16 0 0 28 Jul 2024
Adaptive Training of Grid-Dependent Physics-Informed Kolmogorov-Arnold Networks Spyros Rigas M. Papachristou Theofilos Papadopoulos Fotios Anagnostopoulos Georgios Alexandridis AI4CE 34 21 0 24 Jul 2024
Deep Learning without Global Optimization by Random Fourier Neural Networks Owen Davis Gianluca Geraci Mohammad Motamed BDL 52 0 0 16 Jul 2024
Separable Operator Networks Xinling Yu S. Hooten Z. Liu Yequan Zhao M. Fiorentino T. Van Vaerenbergh Zheng-Wei Zhang 43 4 0 15 Jul 2024
Data-Guided Physics-Informed Neural Networks for Solving Inverse Problems in Partial Differential Equations Wei Zhou Y. F. Xu AI4CE PINN 26 1 0 15 Jul 2024
Stable Weight Updating: A Key to Reliable PDE Solutions Using Deep Learning A. Noorizadegan R. Cavoretto D. Young C. S. Chen 19 7 0 10 Jul 2024
SGM-PINN: Sampling Graphical Models for Faster Training of Physics-Informed Neural Networks John Anticev Ali Aghdaei Wuxinlin Cheng Zhuo Feng AI4CE 26 0 0 10 Jul 2024
Weak baselines and reporting biases lead to overoptimism in machine learning for fluid-related partial differential equations N. McGreivy Ammar Hakim AI4CE 29 42 0 09 Jul 2024
Randomized Physics-Informed Neural Networks for Bayesian Data Assimilation Yifei Zong D. Barajas-Solano A. Tartakovsky 46 1 0 05 Jul 2024
Finite basis Kolmogorov-Arnold networks: domain decomposition for data-driven and physics-informed problems Amanda A. Howard Bruno Jacob Sarah H. Murphy Alexander Heinlein P. Stinis AI4CE 36 26 0 28 Jun 2024
A Nonoverlapping Domain Decomposition Method for Extreme Learning Machines: Elliptic Problems Chang-Ock Lee Youngkyu Lee Byungeun Ryoo 44 3 0 22 Jun 2024
An Advanced Physics-Informed Neural Operator for Comprehensive Design Optimization of Highly-Nonlinear Systems: An Aerospace Composites Processing Case Study Milad Ramezankhani A. Deodhar Rishi Parekh Dagnachew Birru AI4CE 38 3 0 20 Jun 2024
Two-level overlapping additive Schwarz preconditioner for training scientific machine learning applications Youngkyu Lee Alena Kopanicáková George Karniadakis AI4CE 41 0 0 16 Jun 2024
Equivariant Neural Tangent Kernels Philipp Misof Pan Kessel Jan E. Gerken 50 0 0 10 Jun 2024
Error Analysis and Numerical Algorithm for PDE Approximation with Hidden-Layer Concatenated Physics Informed Neural Networks Yianxia Qian Yongchao Zhang Suchuan Dong PINN 29 0 0 10 Jun 2024
VS-PINN: A fast and efficient training of physics-informed neural networks using variable-scaling methods for solving PDEs with stiff behavior Seungchan Ko Sang Hyeon Park 35 1 0 10 Jun 2024
Adapting Physics-Informed Neural Networks to Improve ODE Optimization in Mosquito Population Dynamics D. V. Cuong Branislava Lalić Mina Petrić Binh Nguyen M. Roantree PINN AI4CE 47 2 0 07 Jun 2024
Chebyshev Spectral Neural Networks for Solving Partial Differential Equations Pengsong Yin Shuo Ling Wenjun Ying 18 0 0 06 Jun 2024
GFN: A graph feedforward network for resolution-invariant reduced operator learning in multifidelity applications Oisín M. Morrison F. Pichi J. Hesthaven AI4CE 31 6 0 05 Jun 2024
Physics informed cell representations for variational formulation of multiscale problems Yuxiang Gao Soheil Kolouri R. Duddu AI4CE 27 0 0 27 May 2024
Kronecker-Factored Approximate Curvature for Physics-Informed Neural Networks Felix Dangel Johannes Müller Marius Zeinhofer ODL 21 6 0 24 May 2024
RoPINN: Region Optimized Physics-Informed Neural Networks Haixu Wu Huakun Luo Yuezhou Ma Jianmin Wang Mingsheng Long AI4CE 32 6 0 23 May 2024
A finite element-based physics-informed operator learning framework for spatiotemporal partial differential equations on arbitrary domains Yusuke Yamazaki Ali Harandi Mayu Muramatsu A. Viardin Markus Apel T. Brepols Stefanie Reese Shahed Rezaei AI4CE 28 12 0 21 May 2024
Discovering Physics-Informed Neural Networks Model for Solving Partial Differential Equations through Evolutionary Computation Bo Zhang Chao Yang PINN 29 3 0 18 May 2024
PTPI-DL-ROMs: pre-trained physics-informed deep learning-based reduced order models for nonlinear parametrized PDEs Simone Brivio S. Fresca Andrea Manzoni AI4CE 38 6 0 14 May 2024
Unveiling the optimization process of Physics Informed Neural Networks: How accurate and competitive can PINNs be? Jorge F. Urbán P. Stefanou José A. Pons PINN 43 6 0 07 May 2024