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Physics informed neural networks (PINNs) require regularity of solutions of the underlying PDE to guarantee accurate approximation.
Neural-network-based approximations for solving partial differential equations
M. Dissanayake and N. Phan-Thien · 1994
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Neural-network methods for boundary value problems with irregular boundaries
I. E. Lagaris, A. Likas, and P. G. D · 2000
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Artificial neural networks for solving ordinary and partial differential equations
I. E. Lagaris, A. Likas, and D. I. Fotiadis · 2000
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Total variation minimization with finite elements: convergence and iterative solution
S. Bartels · 2012
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Generative adversarial networks
I. Goodfellow, J. Pouget-Abadie, M. Mirza, B. Xu, D. Warde-Farley, S. Ozair, A. Courville, and Y. Bengio · 2014
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Front tracking for hyperbolic conservation laws
H. Holden and N. H. Risebro · 2015
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Deep learning
Y. LeCun, Y. Bengio, and G. Hinton · 2015
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M. Arjovsky, S. Chintala, and L. Bottou · 2017
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Deep learning-based numerical methods for high-dimensional parabolic partial differential equations and backward stochastic differential equations
W. E, J. Han, and A. Jentzen · 2017
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Optimal approximation of piecewise smooth functions using deep relu neural networks
P. Petersen and F. Voigtlaender · 2018
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Hidden physics models: Machine learning of nonlinear partial differential equations
M. Raissi and G. E. Karniadakis · 2018
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M. Raissi, A. Yazdani, and G. E. Karniadakis · 2018
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Variational physics informed neural networks for solving partial differential equations
E. Kharazmi, Z. Zhang, and G. E. Karniadakis · 2019
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L. Lu, P. Jin, and G. E. Karniadakis · 2019
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fPINNs: Fractional physics-informed neural networks
G. Pang, L. Lu, and G. E. Karniadakis · 2019
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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 · 2019
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Deep learning in high dimension: Neural network expression rates for generalized polynomial chaos expansions in uq
C. Schwab and J. Zech · 2019
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Extended physics-informed neural networks (XPINNs): A generalized space-time domain decomposition based deep learning framework for nonlinear partial differential equations
A. D. Jagtap and G. E. Karniadakis · 2020
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Conservative physics-informed neural networks on discrete domains for conservation laws: Applications to forward and inverse problems
A. D. Jagtap, E. Kharazmi, and G. E. Karniadakis · 2020
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Fourier neural operator for parametric partial differential equations, 2020
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Iterative surrogate model optimization (ISMO): An active learning algorithm for pde constrained optimization with deep neural networks
K. O. Lye, S. Mishra, D. Ray, and P. Chandrashekar · 2021
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Estimates on the generalization error of physics-informed neural networks for approximating a class of inverse problems for pdes
S. Mishra and R. Molinaro · 2021
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Physics informed neural networks for simulating radiative transfer
S. Mishra and R. Molinaro · 2021
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Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences
S. Mishra and T. K. Rusch · 2021
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A physics-informed neural network for quantifying the microstructural properties of polycrystalline nickel using ultrasound data: A promising approach for solving inverse problems
K. Shukla, A. D. Jagtap, J. L. Blackshire, D. Sparkman, and G. E. Karniadakis · 2021
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Scientific machine learning through physics-informed neural networks: Where we are and what’s next
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