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
The role of artificial intelligence in achieving the Sustainable Development Goals Ricardo Vinuesa Hossein Azizpour Iolanda Leite Madeline Balaam Virginia Dignum S. Domisch Anna Felländer S. Langhans Max Tegmark F. F. Nerini 66 1,517 0 30 Apr 2019
A Discussion on Solving Partial Differential Equations using Neural Networks Tim Dockhorn 58 62 0 15 Apr 2019
Unsupervised Deep Learning Algorithm for PDE-based Forward and Inverse Problems Leah Bar N. Sochen 58 71 0 10 Apr 2019
On the approximation of the solution of partial differential equations by artificial neural networks trained by a multilevel Levenberg-Marquardt method H. Calandra Serge Gratton E. Riccietti X. Vasseur 28 7 0 09 Apr 2019
Informed Machine Learning -- A Taxonomy and Survey of Integrating Knowledge into Learning Systems Laura von Rueden S. Mayer Katharina Beckh B. Georgiev Sven Giesselbach ... Rajkumar Ramamurthy Michal Walczak Jochen Garcke Christian Bauckhage Jannis Schuecker 128 647 0 29 Mar 2019
Physics Enhanced Artificial Intelligence Patrick O'Driscoll Jaehoon Lee Bo Fu 48 3 0 11 Mar 2019
Learning Everywhere: Pervasive Machine Learning for Effective High-Performance Computation Geoffrey C. Fox J. Glazier J. Kadupitiya V. Jadhao Minje Kim ... Madhav Marathe Abhijin Adiga Jiangzhuo Chen O. Beckstein S. Jha 48 53 0 27 Feb 2019
Shallow Neural Networks for Fluid Flow Reconstruction with Limited Sensors N. Benjamin Erichson L. Mathelin Z. Yao Steven L. Brunton Michael W. Mahoney J. Nathan Kutz AI4CE 61 34 0 20 Feb 2019
Differentiable Physics-informed Graph Networks Sungyong Seo Yan Liu PINN AI4CE 94 67 0 08 Feb 2019
Physics-informed deep generative models Yibo Yang P. Perdikaris AI4CE PINN 87 59 0 09 Dec 2018
Adversarial Uncertainty Quantification in Physics-Informed Neural Networks Yibo Yang P. Perdikaris AI4CE PINN 148 361 0 09 Nov 2018
Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations Siyu Dai Shawn Schaffert Andreas G. Hofmann 134 367 0 05 Nov 2018
The Newton Scheme for Deep Learning Junqing Qiu Guoren Zhong Yihua Lu Kun Xin Huihuan Qian Xi Zhu PINN 32 3 0 16 Oct 2018
On the Art and Science of Machine Learning Explanations Patrick Hall FAtt XAI 92 30 0 05 Oct 2018
Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems Dongkun Zhang Lu Lu Ling Guo George Karniadakis UQCV 124 414 0 21 Sep 2018
Data-driven discovery of PDEs in complex datasets Jens Berg K. Nystrom AI4CE PINN 82 141 0 31 Aug 2018
Deep Learning of Vortex Induced Vibrations M. Raissi Zhicheng Wang M. Triantafyllou George Karniadakis AI4CE 81 378 0 26 Aug 2018
Hidden Fluid Mechanics: A Navier-Stokes Informed Deep Learning Framework for Assimilating Flow Visualization Data M. Raissi A. Yazdani George Karniadakis AI4CE PINN 99 161 0 13 Aug 2018
Machine Learning of Space-Fractional Differential Equations Mamikon A. Gulian M. Raissi P. Perdikaris George Karniadakis 109 47 0 02 Aug 2018
Neural-net-induced Gaussian process regression for function approximation and PDE solution G. Pang Liu Yang George Karniadakis 78 73 0 22 Jun 2018
Deep Multiscale Model Learning Yating Wang Siu Wun Cheung Eric T. Chung Y. Efendiev Min Wang AI4CE 76 82 0 13 Jun 2018
Deep learning based inverse method for layout design Yujie Zhang W. Ye 3DV 49 39 0 07 Jun 2018
General solutions for nonlinear differential equations: a rule-based self-learning approach using deep reinforcement learning Shiyin Wei Xiaowei Jin Hui Li AI4CE 75 40 0 13 May 2018
Optimal Neural Network Feature Selection for Spatial-Temporal Forecasting E. Covas Emmanouil Benetos AI4TS 31 8 0 30 Apr 2018
Forward-Backward Stochastic Neural Networks: Deep Learning of High-dimensional Partial Differential Equations M. Raissi 116 188 0 19 Apr 2018
Convolutional Neural Networks combined with Runge-Kutta Methods Mai Zhu Bo Chang Chong Fu AI4CE 108 52 0 24 Feb 2018
Deep Hidden Physics Models: Deep Learning of Nonlinear Partial Differential Equations M. Raissi PINN AI4CE 130 758 0 20 Jan 2018
Multistep Neural Networks for Data-driven Discovery of Nonlinear Dynamical Systems M. Raissi P. Perdikaris George Karniadakis PINN 158 266 0 04 Jan 2018
A unified deep artificial neural network approach to partial differential equations in complex geometries Jens Berg K. Nystrom AI4CE 74 587 0 17 Nov 2017
DGM: A deep learning algorithm for solving partial differential equations Justin A. Sirignano K. Spiliopoulos AI4CE 107 2,069 0 24 Aug 2017