137 附属社会創造数学センター主催 北大MMCセミナー :Particle and Game Theoretic Methods for Front Speeds in Fluid Flows(Jack Xin 氏)

Event Date: May 09, 2023


Time:     2023年 5月 9日(火) 16時30分 ~ 2023年5月9日(火) 18時00分

Place:  北海道大学電子科学研研究所 中央キャンパス総合研究棟2号館5階講義室

Speaker: Jack Xin 氏(University of California, Irvine)

Title: Particle and Game Theoretic Methods for Front Speeds in Fluid


We study and compute large time front speeds of Fisher-Kolmogorov-Petrovsky-Piskunov equation in fluid flows with chaotic and stochastic streamlines based on a normalized Feynman-Kac representation and the associated genetic interacting particle (IP) method.    

Examples of such flows are Arnold-Beltrami-Childress (ABC) flows and their random perturbations. The method is mesh-free and self-adaptive, providing training data for efficient deep learning of the invariant measure of IP evolution in the small molecular diffusivity regime. We analyze a curvature dependent level set Hamilton-Jacobi equation arising in turbulent combustion, and show the existence of effective front speeds in cellular (BC) flow.

To overcome non-coercivity and non-convexity of the Hamiltonian, we rely on a notion of reachability through Kohn-Serfaty deterministic game characterization, the ordered streamline structure of the BC flow, and comparison principle.