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Physics informed neural networks (PINNs) have recently been very successfully applied for efficiently approximating inverse problems for PDEs.
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Lecture notes on regularity theory for the Navier-Stokes equations
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Deep learning
Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Y. Chen, L. Lu, G. E. Karniadakis, and L. D. Negro · 2019
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Machine learning for fast and reliable solution of time-dependent differential equations
L. D. F. Regazzoni and A. Quarteroni · 2019
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Efficient approximation of solutions of parametric linear transport equations by reludnns
F. Laakmann and P. Petersen · 2019
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Deepxde: A deep learning library for solving differential equations
L. Lu, X. Meng, Z. Mao, and G. E. Karniadakis · 2019
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A machine learning framework for data driven acceleration of computations of differential equations
S. Mishra · 2019
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I. Goodfellow, Y. Bengio, and A. Courville · 2016
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Stability estimates for the navier-stokes equations and applications to inverse problems
F. C. M. Badra and J. Darde · 2016
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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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Geometric control condition for the wave equation with a time-dependent observation domain
J. L. Rousseau, G. Lebeau, P. Terpolilli, and E. Trélat · 2017
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Error bounds for approximations with deep relu networks
D. Yarotsky · 2017
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Stabilized nonconfirming finite element methods for data assimilation in incompressible flows
E. Burman and P. Hansbo · 2018
Cited alongside, same era.
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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A finite element data assimilation method for the wave equation
E. Burman, A. Feizmohammadi, and L. Oksanen · 2020
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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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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
A. D. Jagtap, K. Kawaguchi, 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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Y. Liu, X. Meng, and G. E. Karniadakis · 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, P. Chandrasekhar, and D. Ray · 2020
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A multi-level procedure for enhancing accuracy of machine learning algorithms
K. O. Lye, S. Mishra, and R. Molinaro · 2020
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Deep learning observables in computational fluid dynamics
K. O. Lye, S. Mishra, and D. Ray · 2020
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Physics-informed neural networks for high-speed flows
Z. Mao, A. D. Jagtap, and G. E. Karniadakis · 2020
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Estimates on the generalization error of physics informed neural networks (pinns) for approximating pdes
S. Mishra and R. Molinaro · 2020
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Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences
S. Mishra and T. K. Rusch · 2020
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On the convergence and generalization of physics informed neural networks
Y. Shin, J. Darbon, and G. E. Karniadakis · 2020
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Physics-informed neural network for ultrasound nondestructive quantification of surface breaking cracks
K. Shukla, P. C. Di Leoni, J. Blackshire, D. Sparkman, and G. E. Karniadakis · 2020
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