(2) Homogenization, multiscale analysis and model reduction of open dynamical systems


Many models of noisy systems are too complex to be analyzed and solved analytically or even numerically if a large range of time scales is involved. For a wide class of high-dimensional dynamical systems it may be possible to approximate them by deriving lower-dimensional reduced models. The reduced models are often easier to analyze and faster to integrate numerically, while still capturing the essential features of the full system. When time scale separations exist one can apply and develop multiscale methods such as averaging and homogenization to study model reduction. This is in fact one of the main goals in statistical physics, when one is given a microscopic (first-principle) model for the full system.

We focus on stochastic homogenization for dynamics and functionals of multiscale generalized Langevin systems, an important class of non-Markovian open dynamical systems with memory in nonequilibrium statistical mechanics. A canonical example of such systems describes a Brownian particle interacting with a heat bath. We work at the level of sample paths to obtain strong convergence results using techniques from stochastic analysis. We combine our theoretical results and insights from statistical mechanics to understand noise-induced phenomena in effective dynamics and thermodynamics of relevant physical diffusive systems. Check out the relevant research outputs here.