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Physics-informed neural networks (PINNs) have become a popular choice for solving high-dimensional partial differential equations (PDEs) due to their excellent approximation power and generalization ability.
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On the theory of implicit deep learning: Global convergence with implicit layers
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Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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A priori estimates of the generalization error for two-layer neural networks
E Weinan, Chao Ma, and Lei Wu · 2019
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Physics-informed neural networks for inverse problems in nano-optics and metamaterials
Yuyao Chen, Lu Lu, George Em Karniadakis, and Luca Dal Negro · 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
Ameya D Jagtap and George Em Karniadakis · 2020
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Adaptive activation functions accelerate convergence in deep and physics-informed neural networks
Ameya D Jagtap, Kenji Kawaguchi, and George Em Karniadakis
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Physics-Informed Neural Networks for Heat Transfer Problems
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Error estimates for physics informed neural networks approximating the navier-stokes equations
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