Residual neural networks overcome the curse of dimensionality for semilinear heat equations
math.NA, cs.LG, cs.NA, math.AP, math.PR
Submitted: 2026-09-03
Updated: 2026-09-03
Comments: 29 pages, 1 figure
License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
Terminology
Sources
- 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
- Deep neural networks with ReLU, leaky ReLU, and softplus activation provably overcome the curse of dimensionality for space-time solutions of semilinear partial differential equations
- Deep neural networks overcome the curse of dimensionality in the numerical approximation of semilinear partial differential equations
- Multilevel Picard approximations for high-dimensional semilinear second-order PDEs with Lipschitz nonlinearities
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