We will first outline the asymptotic-transition from quantum to classical, to kinetic and then the hydrodynamic equations, and then show how such asymptotics can guide the design and analysis of the so-called asymptotic-preserving schemes that offer efficient multiscale computations between different scales. Recent random batch methods for particle systems that are valid also for the mean-field regimes will be presented.

We will first outline the asymptotic-transition from quantum to classical, to kinetic and then the hydrodynamic equations, and then show how such asymptotics can guide the design and analysis of the so-called asymptotic-preserving schemes that offer efficient multiscale computations between different scales. Recent random batch methods for particle systems that are valid also for the mean-field regimes will be presented.