DNNs with ReLU/leaky ReLU/softplus activations approximate solutions of semilinear heat PDEs in L^p without curse of dimensionality, assuming initial data are approximable without COD.
Deep neural network approximation for high- dimensional parabolic Hamilton–Jacobi–Bellman equations.arXiv:2103.05744 (2021), 23 pages
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Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for Kolmogorov partial differential equations with Lipschitz nonlinearities in the $L^p$-sense
DNNs with ReLU/leaky ReLU/softplus activations approximate solutions of semilinear heat PDEs in L^p without curse of dimensionality, assuming initial data are approximable without COD.