Numerical schemes for coarse-graining of stochastic lattice dynamics

Song, Yan
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University of Delaware
This dissertation is focused on numerical schemes of coarse-graining (CG) for stochastic many-body microscopic models with short- and long-range interactions on 1-dimensional lattice systems. In this thesis, we focus on the numerical schemes of the coarse-graining (CG) Monte Carlo (CGMC) algorithms for 1) equilibrium states of 1-dimensional Ising-type models and 2) evolution of the dynamics on the path-wise level. Microscopic computational models for stochastic many particle systems such as Monte Carlo (MC) algorithms are typically formulated in terms of simple rules describing interactions between individual particles or spin variables. Due to the large size of particles and interactions between them, it represents a costly computational task for the direct numerical simulations. In contrast, the CGMC algorithms decrease the CPU times and substantial accelerate the resolution of the dynamics. In this thesis, I investigate the role of multi-body interactions in the construction of CG dynamics and demonstrate the efficiency and reliability of the two-body and three-body coarse-grained schemes. Furthermore, I explore the micro-macro parareal algorithm to study the evolution of dynamics of the stochastic lattice models described by continuous time Markov chains. Finally, I apply the information-theoretic tools for the parametrized coarse-graining method and estimate the evolution of the dynamics on the path-wise level. The results ae tested on model examples of lattice spin flip dynamics of one-dimensional Ising-type models.