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.
Algorithms for solving high dimensional PDEs: from nonlinear Monte Carlo to machine learning.Nonlinearity 35, 1 (2022), 278–310
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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.