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"

36 / 336 papers shown

Title
Gradient-enhanced physics-informed neural networks for forward and inverse PDE problems Jeremy Yu Lu Lu Xuhui Meng George Karniadakis PINN AI4CE 19 449 0 01 Nov 2021
CAN-PINN: A Fast Physics-Informed Neural Network Based on Coupled-Automatic-Numerical Differentiation Method P. Chiu Jian Cheng Wong C. Ooi M. Dao Yew-Soon Ong PINN 23 205 0 29 Oct 2021
On Computing the Hyperparameter of Extreme Learning Machines: Algorithm and Application to Computational PDEs, and Comparison with Classical and High-Order Finite Elements S. Dong Jielin Yang 72 52 0 27 Oct 2021
Fast PDE-constrained optimization via self-supervised operator learning Sifan Wang Mohamed Aziz Bhouri P. Perdikaris 40 28 0 25 Oct 2021
Multi-Objective Loss Balancing for Physics-Informed Deep Learning Rafael Bischof M. Kraus PINN AI4CE 33 92 0 19 Oct 2021
Physics informed neural networks for continuum micromechanics Alexander Henkes Henning Wessels R. Mahnken PINN AI4CE 8 139 0 14 Oct 2021
Physics-informed neural network simulation of multiphase poroelasticity using stress-split sequential training E. Haghighat Daniel Amini R. Juanes PINN AI4CE 13 95 0 06 Oct 2021
Improved architectures and training algorithms for deep operator networks Sifan Wang Hanwen Wang P. Perdikaris AI4CE 47 105 0 04 Oct 2021
CENN: Conservative energy method based on neural networks with subdomains for solving variational problems involving heterogeneous and complex geometries Yi-Zhou Wang Jia Sun Wei Li Zaiyuan Lu Yinghua Liu 47 37 0 25 Sep 2021
Learning in Sinusoidal Spaces with Physics-Informed Neural Networks Jian Cheng Wong C. Ooi Abhishek Gupta Yew-Soon Ong AI4CE PINN SSL 18 76 0 20 Sep 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 25 607 0 02 Sep 2021
Wasserstein Generative Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yihang Gao Michael K. Ng 27 28 0 30 Aug 2021
Reconstructing a dynamical system and forecasting time series by self-consistent deep learning Zhe Wang C. Guet AI4TS 6 4 0 04 Aug 2021
Finite Basis Physics-Informed Neural Networks (FBPINNs): a scalable domain decomposition approach for solving differential equations Benjamin Moseley Andrew Markham T. Nissen‐Meyer PINN 45 209 0 16 Jul 2021
Inverse-Dirichlet Weighting Enables Reliable Training of Physics Informed Neural Networks S. Maddu D. Sturm Christian L. Müller I. Sbalzarini AI4CE 18 80 0 02 Jul 2021
Lagrangian dual framework for conservative neural network solutions of kinetic equations H. Hwang Hwijae Son 9 7 0 23 Jun 2021
Polyconvex anisotropic hyperelasticity with neural networks Dominik K. Klein Mauricio Fernández Robert J. Martin P. Neff Oliver Weeger 28 151 0 20 Jun 2021
Interval and fuzzy physics-informed neural networks for uncertain fields J. Fuhg Ioannis Kalogeris A. Fau N. Bouklas AI4CE 41 18 0 18 Jun 2021
Long-time integration of parametric evolution equations with physics-informed DeepONets Sifan Wang P. Perdikaris AI4CE 17 117 0 09 Jun 2021
Optimal Transport Based Refinement of Physics-Informed Neural Networks Vaishnav Tadiparthi R. Bhattacharya OT 10 2 0 26 May 2021
Physics-informed neural networks (PINNs) for fluid mechanics: A review Shengze Cai Zhiping Mao Zhicheng Wang Minglang Yin George Karniadakis PINN AI4CE 12 1,127 0 20 May 2021
Deep learning in physics: a study of dielectric quasi-cubic particles in a uniform electric field Zhe Wang C. Guet 9 5 0 11 May 2021
Mosaic Flows: A Transferable Deep Learning Framework for Solving PDEs on Unseen Domains Hengjie Wang R. Planas Aparna Chandramowlishwaran Ramin Bostanabad AI4CE 42 61 0 22 Apr 2021
Physics-informed neural networks for the shallow-water equations on the sphere Alexander Bihlo R. Popovych 9 77 0 01 Apr 2021
Solving and Learning Nonlinear PDEs with Gaussian Processes Yifan Chen Bamdad Hosseini H. Owhadi Andrew M. Stuart 20 153 0 24 Mar 2021
Learning the solution operator of parametric partial differential equations with physics-informed DeepOnets Sifan Wang Hanwen Wang P. Perdikaris AI4CE 38 661 0 19 Mar 2021
Quadratic Residual Networks: A New Class of Neural Networks for Solving Forward and Inverse Problems in Physics Involving PDEs Jie Bu Anuj Karpatne 17 47 0 20 Jan 2021
Reproducing Activation Function for Deep Learning Senwei Liang Liyao Lyu Chunmei Wang Haizhao Yang 28 21 0 13 Jan 2021
Hybrid FEM-NN models: Combining artificial neural networks with the finite element method Sebastian K. Mitusch S. Funke M. Kuchta AI4CE 26 93 0 04 Jan 2021
On the eigenvector bias of Fourier feature networks: From regression to solving multi-scale PDEs with physics-informed neural networks Sifan Wang Hanwen Wang P. Perdikaris 131 438 0 18 Dec 2020
$NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework$ NVIDIA SimNet^{TM}: an AI-accelerated multi-physics simulation framework O. Hennigh S. Narasimhan M. A. Nabian Akshay Subramaniam Kaustubh Tangsali M. Rietmann J. Ferrandis Wonmin Byeon Z. Fang S. Choudhry PINN AI4CE 93 126 0 14 Dec 2020
Physics-informed neural networks for myocardial perfusion MRI quantification R. L. M. V. Herten A. Chiribiri M. Breeuwer M. Veta C. Scannell 12 43 0 25 Nov 2020
Gradient Starvation: A Learning Proclivity in Neural Networks Mohammad Pezeshki Sekouba Kaba Yoshua Bengio Aaron Courville Doina Precup Guillaume Lajoie MLT 45 257 0 18 Nov 2020
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism L. McClenny U. Braga-Neto PINN 26 442 0 07 Sep 2020
Physics-informed learning of governing equations from scarce data Zhao Chen Yang Liu Hao-Lun Sun PINN AI4CE 6 373 0 05 May 2020
B-PINNs: Bayesian Physics-Informed Neural Networks for Forward and Inverse PDE Problems with Noisy Data Liu Yang Xuhui Meng George Karniadakis PINN 180 758 0 13 Mar 2020