SEP 3, 2026 · PREPRINT
Residual neural networks overcome the curse of dimensionality for semilinear heat equations
arXiv
This is a theoretical mathematics paper proving computational properties of neural networks for PDEs, not an empirical study or clinical evidence, and does not address any health or medical question.
Reported
Parameter bound (general case)ηd^η ε^{-η}
Parameter bound (ridge-sum case)C_ξ d^{4+ξ} ε^{-(3+ξ)}
Approximation error (L^2)at most ε