Multilevel Picard approximations overcome the curse of dimensionality when approximating semilinear heat equations with gradient-dependent nonlinearities in $L^p$-sense
<|reference_start|>Multilevel Picard approximations overcome the curse of dimensionality when approximating semilinear heat equations with gradient-dependent nonlinearities in $L^p$-sense: We prove that multilevel Picard approximations are capable of approximating solutions of semilinear heat equations in $L^{p}$-sense, ${p}\in [2,\infty)$, in the case of gradient-dependent, Lipschitz-continuous nonlinearities, in the sense that the computational effort of the multilevel Picard approximations grow at most polynomially in both the dimension $d$ and the reciprocal $1/\epsilon$ of the prescribed accuracy $\epsilon$.<|reference_end|>
@article{nguyen2024multilevel,
    title={Multilevel Picard approximations overcome the curse of dimensionality
  when approximating semilinear heat equations with gradient-dependent
  nonlinearities in $L^p$-sense},
    author={Tuan Anh Nguyen},
    journal={arXiv preprint arXiv:2410.00203},
    year={2024},
    archivePrefix={arXiv},
    eprint={2410.00203},
    primaryClass={math.NA cs.NA math.AP}
}