REVIEW 1 cited by
Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
abstract
We prove that deep neural networks are capable of approximating solutions of semilinear Kolmogorov PDE in the case of gradient-independent, Lipschitz-continuous nonlinearities, while the required number of parameters in the networks grow at most polynomially in both dimension $d \in \mathbb{N}$ and prescribed reciprocal accuracy $\varepsilon$. Previously, this has only been proven in the case of semilinear heat equations.
Forward citations
Cited by 1 Pith paper
-
Deep neural networks can provably solve Bellman equations for Markov decision processes without the curse of dimensionality
Q-functions of infinite-horizon discounted MDPs with finite action sets are approximable by leaky ReLU networks with polynomially growing parameter counts, provided rewards and transitions are themselves DNN-approximable.
Discussion (0). Continue with ORCID to comment.