Suppressing the Numerical Sign Problem in Branching Random Walk Algorithm
Time: 2021-10-25
Published By: He Liu
Speaker(s): Yunfeng Xiong (PKU)
Time: 15:15-17:00 October 27, 2021
Venue: Room 29, Quan Zhai, BICMR
The random walk algorithm to PDE was initialized by Courant, Friedrich and Lewy in their celebrated work “On the partial difference equation of mathematical physics”, along with the birth of the CFL stability condition for finite difference method. Following their pioneering idea, we would like to discuss our recent progress in designing the branching random walk algorithm for solving the high dimensional PDE, e.g., the many-body quantum Wigner dynamics in phase space. We point out that the fundamental obstacle to the negative particle-based random walk algorithm is the numerical sign problem, say, both the particle number and stochastic variance will grow exponentially in time. To ameliorate such problem, we utilize the cancelation of random paths by combining the stationary phase approximation and the stochastic interpretation to PDE, and introduce a particle annihilation algorithm to kill the redundant particles. If time is allowed, we would like to discuss some topics, such as how to use the idea of the mean-field limit to reduce the challenge induced by the high dimensionality.
