Approximations of continuous functionals by neural networks with application to dynamic systems

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fPINNs: Fractional Physics-Informed Neural Networks (2018, methodology): “In this paper, we focus on the NN approaches due to the high expressive power of NNs in function approximation [24, 25, 26, 27].”
Physics-Informed Multi-LSTM Networks for Metamodeling of Nonlinear Structures (2020, background): “Recently, artiﬁcial neural networks (ANNs) have been proven to be a powerful metamod-eling tool and approximator [31, 32], which often outperforms conventional metamodeling techniques in terms of both prediction accuracy and capability of capturing underlying non-linear input-output relationship…”
Learning in Modal Space: Solving Time-Dependent Stochastic PDEs Using Physics-Informed Neural Networks (2019, methodology): “This approximation of the nonlinear operators by the DNN is justiﬁed theoretically based on the pioneering work of [2, 3], which goes well beyond the universal function approximation theorem of [4].”