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The physics-informed neural network (PINN) is effective in solving the partial differential equation (PDE) by capturing the physics constraints as a part of the training loss function through the Automatic Differentiation (AD).
Finite-difference methods
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Neural-network-based approximations for solving partial differential equations
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Finite elements method
S. B. Aruoba, J. Fernandez-Villaverde, and J. F. Rubio-Ramirez · 2003
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Automatic differentiation in machine learning: a survey
Atilim Gunes Baydin, Barak A. Pearlmutter, and Alexey Andreyevich Radul · 2015
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Tensorflow: Large-scale machine learning on heterogeneous distributed systems, 2016
Martín Abadi, Ashish Agarwal, Paul Barham, Eugene Brevdo, Zhifeng Chen, Craig Citro, Greg S. Corrado, Andy Davis, Jeffrey Dean, Matthieu Devin, Sanjay Ghemawat, Ian Goodfellow, Andrew Harp, Geoffrey Irving, Michael Isard, Yangqing Jia, Rafal Jozefowicz, Lukasz Kaiser, Manjunath Kudlur, Josh Levenberg, Dan Mane, Rajat Monga, Sherry Moore, Derek Murray, Chris Olah, Mike Schuster, Jonathon Shlens, Benoit Steiner, Ilya Sutskever, Kunal Talwar, Paul Tucker, Vincent Vanhoucke, Vijay Vasudevan, Fernanda Viegas, Oriol Vinyals, Pete Warden, Martin Wattenberg, Martin Wicke, Yuan Yu, and Xiaoqiang Zheng · 2016
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Dgm: A deep learning algorithm for solving partial differential equations
Justin Sirignano and Konstantinos Spiliopoulos · 2017
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Machine learning of linear differential equations using gaussian processes - sciencedirect
Maziar, Raissi, Paris, Perdikaris, George, Em, and Karniadakis · 2017
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Inferring solutions of differential equations using noisy multi-fidelity data
Maziar Raissi A, Paris Perdikaris B, and George Em Karniadakis A · 2017
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Numerical gaussian processes for time-dependent and non-linear partial differential equations
Maziar Raissi, Paris Perdikaris, and George Em Karniadakis · 2017
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Compact difference scheme for the burger’s equation
J. Zhang, L. I. Shucun, and J. Cao · 2017
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Dgm: A deep learning algorithm for solving partial differential equations, 2018
Justin Sirignano and Konstantinos Spiliopoulos · 2018
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Finite Volume Methods
O. Castro-Orgaz and W. H. Hager · 2019
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
Maziar Raissi, Paris Perdikaris, and George E Karniadakis · 2019
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Quantifying total uncertainty in physics-informed neural networks for solving forward and inverse stochastic problems
Dongkun Zhang, Lu Lu, Ling Guo, and George Em Karniadakis · 2019
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fpinns: Fractional physics-informed neural networks
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Xu Liu, Xiaoya Zhang, Wei Peng, Weien Zhou, and Wen Yao · 2021
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Self-adaptive loss balanced physics-informed neural networks for the incompressible navier-stokes equations, 2021
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Idrlnet: A physics-informed neural network library
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Solving inverse stochastic problems from discrete particle observations using the fokker–planck equation and physics-informed neural networks
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Liu Yang, Dongkun Zhang, and George Em Karniadakis · 2020
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