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Physics informed neural networks (PINNs) have recently been widely used for robust and accurate approximation of PDEs.
Partial differential equations of the parabolic type
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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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D. Yarotsky · 2017
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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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Error analysis for physics informed neural networks (pinns) approximating kolmogorov pdes
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Iterative surrogate model optimization (ismo): An active learning algorithm for pde constrained optimization with deep neural networks
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Estimates on the generalization error of physics informed neural networks (pinns) for approximating pdes ii: A class of inverse problems
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Enhancing accuracy of deep learning algorithms by training with low-discrepancy sequences
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On the convergence and generalization of physics informed neural networks
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