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Physics-informed Neural Network (PINN) is a promising tool that has been applied in a variety of physical phenomena described by partial differential equations (PDE).
Mechanism of Fluid Displacement in Sands
S.E. Buckley and M.C. Leverett · 1942
Earlier work this paper cites.
A Simplified Method for Computing Oil Recovery by Gas or Water Drive
Henry J. Welge · 1952
Earlier work this paper cites.
An Eulerian differencing method for unsteady compressible flow problems
Richard A Gentry, Robert E Martin, and Bart J Daly · 1966
Earlier work this paper cites.
A numerical fluid dynamics calculation method for all flow speeds
Francis H Harlow and Anthony A Amsden · 1971
Earlier work this paper cites.
Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
Peter D. Lax · 1973
Earlier work this paper cites.
Multilayer feedforward networks are universal approximators
Kurt Hornik, Maxwell Stinchcombe, and Halbert White · 1989
Earlier work this paper cites.
Physics Informed Deep Learning for Transport in Porous Media. Buckley Leverett Problem
Cedric G. Fraces, Adrien Papaioannou, and Hamdi Tchelepi · 2001
Earlier work this paper cites.
Self-Adaptive Physics-Informed Neural Networks using a Soft Attention Mechanism
Levi McClenny and Ulisses Braga-Neto · 2009
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Thermodynamically consistent physics-informed neural networks for hyperbolic systems
Ravi G. Patel, Indu Manickam, Nathaniel A. Trask, Mitchell A. Wood, Myoungkyu Lee, Ignacio Tomas, and Eric C. Cyr · 2012
Earlier work this paper cites.
A space–time smooth artificial viscosity method for nonlinear conservation laws
J. Reisner, J. Serencsa, and S. Shkoller · 2012
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Residual-based artificial viscosity for simulation of turbulent compressible flow using adaptive finite element methods
Murtazo Nazarov and Johan Hoffman · 2013
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An Adaptive Multiresolution Discontinuous Galerkin Method for Time-Dependent Transport Equations in Multidimensions
Wei Guo and Yingda Cheng · 2017
Cited alongside, same era.
Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
M. Raissi, P. Perdikaris, and G. E. Karniadakis · 2018
Cited alongside, same era.
Prediction of Fluid Flow in Porous Media using Physics Informed Neural Networks
Muhammad Majid Almajid and Moataz Omar Abu-Alsaud · 2020
Cited alongside, same era.
Physics-Informed Neural Networks for Heat Transfer Problems
Shengze Cai, Zhicheng Wang, Sifan Wang, Paris Perdikaris, and George Em Karniadakis · 2021
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Understanding and Mitigating Gradient Flow Pathologies in Physics-Informed Neural Networks
Sifan Wang, Yujun Teng, and Paris Perdikaris · 2021
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When and why PINNs fail to train: A neural tangent kernel perspective
Sifan Wang, Xinling Yu, and Paris Perdikaris · 2021
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Physics Informed Deep Learning for Flow and Transport in Porous Media
Cedric Gasmi Fraces and Hamdi Tchelepi · 2021
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Ruben Rodriguez-Torrado, Pablo Ruiz, Luis Cueto-Felgueroso, Michael Cerny Green, Tyler Friesen, Sebastien Matringe, and Julian Togelius · 2021
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Physics-informed machine learning: case studies for weather and climate modelling
K. Kashinath, M. Mustafa, A. Albert, J-L. Wu, C. Jiang, S. Esmaeilzadeh, K. Azizzadenesheli, R. Wang, A. Chattopadhyay, A. Singh, A. Manepalli, D. Chirila, R. Yu, R. Walters, B. White, H. Xiao, H. A. Tchelepi, P. Marcus, A. Anandkumar, P. Hassanzadeh, and null Prabhat · 2020
Cited alongside, same era.
A Dual-Dimer method for training physics-constrained neural networks with minimax architecture
Dehao Liu and Yan Wang · 2020
Cited alongside, same era.
Limitations of Physics Informed Machine Learning for Nonlinear Two-Phase Transport in Porous Media
Olga Fuks and Hamdi A. Tchelepi · 2020
Cited alongside, same era.
A residual-based artificial viscosity finite difference method for scalar conservation laws
Vidar Stiernström, Lukas Lundgren, Murtazo Nazarov, and Ken Mattsson · 2020
Cited alongside, same era.
Later among the works it cites.
FC-based shock-dynamics solver with neural-network localized artificial-viscosity assignment
Oscar P. Bruno, Jan S. Hesthaven, and Daniel V. Leibovici · 2021
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TensorDiffEq: Scalable Multi-GPU Forward and Inverse Solvers for Physics Informed Neural Networks
Levi D. McClenny, Mulugeta A. Haile, and Ulisses M. Braga-Neto · 2021
Later among the works it cites.
PSO-PINN: Physics-Informed Neural Networks Trained with Particle Swarm Optimization
Caio Davi and Ulisses Braga-Neto · 2022
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