第137回北大MMCセミナー

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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.