Speaker: Mauricio del Razo ( Freie Universität Berlin)
Title: Dynamical coarse-graining and multiscale simulation of complex systems
Abstract: In this presentation, we will focus on two modeling and computational challenges of complex systems. The first part introduces a data-driven dynamical coarse-graining method for condensed matter systems inspired by the Mori-Zwanzig formalism. This formalism shows that macroscopic systems with a large number of degrees of freedom are often well described by a small number of relevant variables plus additional noise and memory terms. Our coarse-graining method consists of numerical integrators for the distinguished components of the system, where the noise and interaction terms of the equations are substituted by a random variable sampled from a data-driven model. Applied to various sample systems, we show that the resulting coarse-grained models are not only capable of reproducing the correct equilibrium distributions but also the dynamic behavior due to memory effects. The second part introduces a mathematical formalism to derive emergent models of complex systems with a varying number of particles at different scales. The formalism is constructed using creation and annihilation operators as well as bracket notation from quantum mechanics. The goal is to introduce a systematic procedure to derive multiscale models and numerical discretizations for complex systems with a varying number of particles.
