Mathematical Strategies for Coarse-graining and Sensitivity Analysis of High-dimensional Stochastic Systems

In this talk we discuss mathematical and computational strategies for obtaining coarse-grained stochastic approximations of extended (many-body) microscopic systems. Examples of such models include stochastic lattice models of reaction kinetics in catalysis modeling, or more complex off-lattice models of macromolecules (e.g., polymers). We explain how information-theory-based methods (e.g., using relative entropy, Fisher information) can be used for analysis of the derived approximation schemes. We present an extension of these tools to analysis on the path space and its application to the treatment of non-equilibrium systems.  

From the computational point of view the multilevel nature of the methods allows for speeding up sampling algorithms such as kinetic Monte Carlo applied to systems with complex lattice geometries and particle interactions. The information-based methods also give a different perspective on construction of effective interaction potentials which are often used by computational scientists. If time permits, we will briefly discuss related mathematical, numerical and algorithmic issues arising in the parallelization of spatially distributed kinetic Monte Carlo simulations.