Physics-informed neural networks: A deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations
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Cites background or methods from "Physics-informed neural networks: A..."
...Most existing methods, ranging from classical finite elements, finite differences, and finite volumes to modern machine learning approaches such as physics-informed neural networks (PINNs) (Raissi et al., 2019) aim at the latter and can therefore be computationally expensive....
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...(PINNs) (Raissi et al., 2019) aim at the latter and can therefore be computationally expensive....
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...Machine learning methods may hold the key to revolutionizing scientific disciplines by providing fast solvers that approximate or enhance traditional ones (Raissi et al., 2019; Jiang et al., 2020; Greenfeld et al., 2019; Kochkov et al., 2021)....
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...The second approach directly parameterizes the solution function as a neural network (E & Yu, 2018; Raissi et al., 2019; Bar & Sochen, 2019; Smith et al., 2020; Pan & Duraisamy, 2020)....
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References
111,197 citations
"Physics-informed neural networks: A..." refers background or methods in this paper
...For larger data-sets a more computationally efficient mini-batch setting can be readily employed using stochastic gradient descent and its modern variants [36,37]....
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...For larger data-sets, such as the data-driven model discovery examples discussed in section 4, a more computationally efficient mini-batch setting can be readily employed using stochastic gradient descent and its modern variants [36,37]....
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"Physics-informed neural networks: A..." refers methods in this paper
...In this work we take a different approach by employing deep neural networks and leverage their well known capability as universal function approximators [11]....
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