Stochastic particle method with birth-death dynamics

2025/06/25 by Lei, Zhengyang, Shao, Sihong
#FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2506.20201

Abstract

In order to numerically solve high-dimensional nonlinear PDEs and alleviate the curse of dimensionality, a stochastic particle method (SPM) has been proposed to capture the relevant feature of the solution through the adaptive evolution of particles [J. Comput. Phys. 527 (2025) 113818]. In this paper, we introduce an active birth-death dynamics of particles to improve the efficiency of SPM. The resulting method, dubbed SPM-birth-death, sample new particles according to the nonlinear term and execute the annihilation strategy when the number of particles exceeds a given threshold. Preliminary numerical experiments on the Allen-Cahn equation demonstrate that SPM-birth-death can achieve smaller errors at the same computational cost compared with the original SPM.

Citations

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