Dynamic message-passing approach for kinetic spin models with reversible dynamics

摘要: A method to approximately close the dynamic cavity equations for synchronous reversible dynamics on a locally tree-like topology is presented. The builds $(a)$ graph expansion eliminate loops from normalizations of each step in dynamics, and $(b)$ an assumption that set auxilary probability distributions histories pairs spins mainly have dependencies are local time. closure then effectuated by projecting these $n$-step Markov processes. shown detail level ordinary processes ($n=1$), outlined higher-order approximations ($n>1$). Numerical validations technique provided reconstruction transient equilibrium kinetic Ising model random with arbitrary connectivity symmetry.