Particle and Game Theoretic Methods for Multi-scale and High Dimensional Problems

Explore particle and game theoretic approaches for analyzing and computing solutions to multi-dimensional partial differential equations through three case studies. Delve into Lagrangian methods for calculating large time front speeds in Fisher-Kolmogorov-Petrovsky-Piskunov equations within chaotic and stochastic fluid flows. Examine entropy production rates for reverse-time diffusion processes in high dimensions, focusing on eigenvalue problems of non-selfadjoint advection-diffusion operators. Investigate curvature-dependent level set Hamilton-Jacobi equations in turbulent combustion, utilizing game theory to overcome non-coercivity and non-convexity challenges in cellular flows. Learn how these methods address complex problems in fluid dynamics, diffusion processes, and combustion analysis.