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.
The deep Ritz method: A deep learning-based numerical algorithm for solving variational problems.Commun
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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.