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While the popularity of physics-informed neural networks (PINNs) is steadily rising, to this date PINNs have not been successful in simulating dynamical systems whose solution exhibits multi-scale, chaotic or turbulent behavior.
Deterministic nonperiodic flow
Edward N Lorenz · 1963
Earlier work this paper cites.
Persistent propagation of concentration waves in dissipative media far from thermal equilibrium
Yoshiki Kuramoto and Toshio Tsuzuki · 1976
Earlier work this paper cites.
Nonlinear analysis of hydrodynamic instability in laminar flames—i. derivation of basic equations
Gregory I Sivashinsky · 1977
Earlier work this paper cites.
A hybrid neural network-first principles approach to process modeling
Dimitris C Psichogios and Lyle H Ungar · 1992
Earlier work this paper cites.
Partial Differential Equations
L.C. Evans and American Mathematical Society · 1998
Earlier work this paper cites.
Artificial neural networks for solving ordinary and partial differential equations
Isaac E Lagaris, Aristidis Likas, and Dimitrios I Fotiadis · 1998
Earlier work this paper cites.
Exponential time differencing for stiff systems
Steven M Cox and Paul C Matthews · 2002
Earlier work this paper cites.
Partial differential equations: An introduction
Walter A Strauss · 2007
Earlier work this paper cites.
Matplotlib: A 2D graphics environment
John D Hunter · 2007
Earlier work this paper cites.
Evaluating derivatives: principles and techniques of algorithmic differentiation
Andreas Griewank and Andrea Walther · 2008
Earlier work this paper cites.
A first course in the numerical analysis of differential equations
Arieh Iserles · 2009
Earlier work this paper cites.
Understanding the difficulty of training deep feedforward neural networks
Xavier Glorot and Yoshua Bengio · 2010
Earlier work this paper cites.
Adam: A method for stochastic optimization
Diederik P Kingma and Jimmy Ba · 2014
Earlier work this paper cites.
Chebfun guide, 2014
Tobin A Driscoll, Nicholas Hale, and Lloyd N Trefethen · 2014
Earlier work this paper cites.
Model-agnostic meta-learning for fast adaptation of deep networks
Chelsea Finn, Pieter Abbeel, and Sergey Levine · 2017
Earlier work this paper cites.
Neural tangent kernel: Convergence and generalization in neural networks
Arthur Jacot, Franck Gabriel, and Clément Hongler · 2018
Earlier work this paper cites.
JAX: composable transformations of Python+NumPy programs, 2018
James Bradbury, Roy Frostig, Peter Hawkins, Matthew James Johnson, Chris Leary, Dougal Maclaurin, George Necula, Adam Paszke, Jake VanderPlas, Skye Wanderman-Milne, and Qiao Zhang · 2018
Earlier work this paper cites.
Deep hidden physics models: Deep learning of nonlinear partial differential equations
Maziar Raissi · 2018
Earlier work this paper cites.
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
Earlier work this paper cites.
Deep learning of turbulent scalar mixing
Maziar Raissi, Hessam Babaee, and Peyman Givi · 2019
Earlier work this paper cites.
Variational physics-informed neural networks for solving partial differential equations
Ehsan Kharazmi, Zhongqiang Zhang, and George Em Karniadakis · 2019
Earlier work this paper cites.
DeepXDE: A deep learning library for solving differential equations
Lu Lu, Xuhui Meng, Zhiping Mao, and George E Karniadakis · 2019
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Jesse Bettencourt, Matthew J Johnson, and David Duvenaud · 2019
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Quadratic residual networks: A new class of neural networks for solving forward and inverse problems in physics involving PDEs
Jie Bu and Anuj Karpatne · 2021
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Reproducing activation function for deep learning
Senwei Liang, Liyao Lyu, Chunmei Wang, and Haizhao Yang · 2021
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Ben Moseley, Andrew Markham, and Tarje Nissen-Meyer · 2021
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Aditi S Krishnapriyan, Amir Gholami, Shandian Zhe, Robert M Kirby, and Michael W Mahoney · 2021
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Nvidia simnet™: An ai-accelerated multi-physics simulation framework
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