Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations

28 November 2017

Papers citing "Physics Informed Deep Learning (Part I): Data-driven Solutions of Nonlinear Partial Differential Equations"

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Title
An unsupervised learning approach to solving heat equations on chip based on Auto Encoder and Image Gradient Haiyang He Jay Pathak 61 24 0 19 Jul 2020
Modeling Stochastic Microscopic Traffic Behaviors: a Physics Regularized Gaussian Process Approach Yun Yuan Qinzheng Wang X. Yang 54 10 0 17 Jul 2020
Bayesian Sparse learning with preconditioned stochastic gradient MCMC and its applications Yating Wang Wei Deng Guang Lin 80 13 0 29 Jun 2020
Variational Autoencoding of PDE Inverse Problems Daniel J. Tait Theodoros Damoulas AI4CE 49 12 0 28 Jun 2020
Deep Orthogonal Decompositions for Convective Nowcasting Daniel J. Tait AI4Cl 23 1 0 28 Jun 2020
Learning Potentials of Quantum Systems using Deep Neural Networks Arijit Sehanobish H. Corzo Onur Kara David van Dijk 36 12 0 23 Jun 2020
Learning continuous-time PDEs from sparse data with graph neural networks V. Iakovlev Markus Heinonen Harri Lähdesmäki AI4CE 86 70 0 16 Jun 2020
Learning the geometry of wave-based imaging K. Kothari Maarten V. de Hoop Ivan Dokmanić AI4CE 70 8 0 10 Jun 2020
Fast Modeling and Understanding Fluid Dynamics Systems with Encoder-Decoder Networks Rohan Thavarajah X. Zhai Zhe-Rui Ma D. Castineira PINN AI4CE 38 8 0 09 Jun 2020
Bayesian Hidden Physics Models: Uncertainty Quantification for Discovery of Nonlinear Partial Differential Operators from Data Steven Atkinson 42 8 0 07 Jun 2020
ODEN: A Framework to Solve Ordinary Differential Equations using Artificial Neural Networks Liam L. H. Lau D. Werth 27 3 0 28 May 2020
A Combined Data-driven and Physics-driven Method for Steady Heat Conduction Prediction using Deep Convolutional Neural Networks Hao Ma Xiangyu Y. Hu Yuxuan Zhang Nils Thuerey O. Haidn AI4CE 41 12 0 16 May 2020
Active Training of Physics-Informed Neural Networks to Aggregate and Interpolate Parametric Solutions to the Navier-Stokes Equations Christopher J. Arthurs A. King PINN 152 52 0 02 May 2020
Numerical Solution of the Parametric Diffusion Equation by Deep Neural Networks Moritz Geist P. Petersen Mones Raslan R. Schneider Gitta Kutyniok 102 83 0 25 Apr 2020
Accelerating Physics-Informed Neural Network Training with Prior Dictionaries Wei Peng Weien Zhou Jun Zhang Wen Yao PINN AI4CE 117 31 0 17 Apr 2020
A Hybrid Objective Function for Robustness of Artificial Neural Networks -- Estimation of Parameters in a Mechanical System J. Sokołowski V. Schulz Udo Schröder H. Beise AAML 11 0 0 16 Apr 2020
Learning reduced systems via deep neural networks with memory Xiaohang Fu L. Chang D. Xiu 38 32 0 20 Mar 2020
Error bounds for PDE-regularized learning Carsten Gräser P. A. Srinivasan 10 0 0 14 Mar 2020
Integrating Scientific Knowledge with Machine Learning for Engineering and Environmental Systems J. Willard X. Jia Shaoming Xu M. Steinbach Vipin Kumar AI4CE 156 412 0 10 Mar 2020
Methods to Recover Unknown Processes in Partial Differential Equations Using Data Zhen Chen Kailiang Wu D. Xiu 55 3 0 05 Mar 2020
Turbulence Enrichment using Physics-informed Generative Adversarial Networks Akshay Subramaniam Man Long Wong Raunak Borker S. Nimmagadda S. Lele GAN AI4CE 111 38 0 04 Mar 2020
Implicit Geometric Regularization for Learning Shapes Amos Gropp Lior Yariv Niv Haim Matan Atzmon Y. Lipman AI4CE 139 863 0 24 Feb 2020
Comparing recurrent and convolutional neural networks for predicting wave propagation Stathi Fotiadis E. Pignatelli Mario Lino Valencia C. Cantwell Amos Storkey Anil A. Bharath 82 37 0 20 Feb 2020
Incorporating Symmetry into Deep Dynamics Models for Improved Generalization Rui Wang Robin Walters Rose Yu AI4CE 143 177 0 08 Feb 2020
On generalized residue network for deep learning of unknown dynamical systems Zhen Chen D. Xiu AI4CE 66 46 0 23 Jan 2020
Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem Cedric G. Fraces Adrien Papaioannou H. Tchelepi AI4CE PINN 59 19 0 15 Jan 2020
A comprehensive deep learning-based approach to reduced order modeling of nonlinear time-dependent parametrized PDEs S. Fresca Luca Dede' Andrea Manzoni AI4CE 92 267 0 12 Jan 2020
Temporal Normalizing Flows G. Both R. Kusters AI4TS 50 12 0 19 Dec 2019
Accelerating PDE-constrained Inverse Solutions with Deep Learning and Reduced Order Models Sheroze Sheriffdeen J. Ragusa J. Morel M. Adams T. Bui-Thanh AI4CE 55 15 0 17 Dec 2019
Trend to Equilibrium for the Kinetic Fokker-Planck Equation via the Neural Network Approach H. Hwang Jin Woo Jang Hyeontae Jo Jae Yong Lee 407 36 0 22 Nov 2019
Towards Physics-informed Deep Learning for Turbulent Flow Prediction Rui Wang K. Kashinath M. Mustafa A. Albert Rose Yu PINN AI4CE 93 372 0 20 Nov 2019
Highly-scalable, physics-informed GANs for learning solutions of stochastic PDEs Liu Yang Sean Treichler Thorsten Kurth Keno Fischer D. Barajas-Solano ... Valentin Churavy A. Tartakovsky Michael Houston P. Prabhat George Karniadakis AI4CE 87 39 0 29 Oct 2019
Data-Driven Deep Learning of Partial Differential Equations in Modal Space Kailiang Wu D. Xiu 127 153 0 15 Oct 2019
A deep surrogate approach to efficient Bayesian inversion in PDE and integral equation models Teo Deveney Amelia Gosse Peter Du 87 9 0 03 Oct 2019
Blending Diverse Physical Priors with Neural Networks Yunhao Ba Guangyuan Zhao A. Kadambi PINN AI4CE 43 32 0 01 Oct 2019
Learning Everywhere: A Taxonomy for the Integration of Machine Learning and Simulations Geoffrey C. Fox S. Jha AI4CE 65 13 0 29 Sep 2019
Data-driven discovery of free-form governing differential equations Steven Atkinson W. Subber Liping Wang Genghis Khan Philippe Hawi R. Ghanem 58 43 0 27 Sep 2019
D3M: A deep domain decomposition method for partial differential equations Ke Li Keju Tang Tianfan Wu Qifeng Liao AI4CE 89 117 0 24 Sep 2019
An Iterative Scientific Machine Learning Approach for Discovery of Theories Underlying Physical Phenomena N. Zobeiry K. D. Humfeld PINN AI4CE 33 6 0 24 Sep 2019
Potential Flow Generator with $L_2$ Optimal Transport Regularity for Generative Models Liu Yang George Karniadakis OT 63 43 0 29 Aug 2019
Predicting Critical Transitions in Multiscale Dynamical Systems Using Reservoir Computing Soon Hoe Lim L. T. Giorgini W. Moon J. Wettlaufer 62 4 0 10 Aug 2019
Deep Lagrangian Networks: Using Physics as Model Prior for Deep Learning M. Lutter Christian Ritter Jan Peters PINN AI4CE 65 381 0 10 Jul 2019
$Transfer learning enhanced physics informed neural network for phase-field modeling of fracture$ Transfer learning enhanced physics informed neural network for phase-field modeling of fracture S. Goswami C. Anitescu S. Chakraborty Timon Rabczuk PINN 94 617 0 04 Jul 2019
Meta-learning Pseudo-differential Operators with Deep Neural Networks Jordi Feliu-Fabà Yuwei Fan Lexing Ying 61 40 0 16 Jun 2019
Tackling Climate Change with Machine Learning David Rolnick P. Donti L. Kaack K. Kochanski Alexandre Lacoste ... Demis Hassabis John C. Platt F. Creutzig J. Chayes Yoshua Bengio AI4Cl AI4CE 108 813 0 10 Jun 2019
Encoding Invariances in Deep Generative Models Viraj Shah Ameya Joshi Sambuddha Ghosal B. Pokuri Soumik Sarkar Baskar Ganapathysubramanian Chinmay Hegde PINN GAN 66 30 0 04 Jun 2019
Learning to Discretize: Solving 1D Scalar Conservation Laws via Deep Reinforcement Learning Yufei Wang Ziju Shen Zichao Long Bin Dong AI4CE PINN 77 40 0 27 May 2019
Physics-informed Autoencoders for Lyapunov-stable Fluid Flow Prediction N. Benjamin Erichson Michael Muehlebach Michael W. Mahoney AI4CE PINN 73 141 0 26 May 2019
Structure-preserving Method for Reconstructing Unknown Hamiltonian Systems from Trajectory Data Kailiang Wu Tong Qin D. Xiu 78 31 0 24 May 2019
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks Dongkun Zhang Ling Guo George Karniadakis AI4CE 90 214 0 03 May 2019