Stationary averaging for multi-scale continuous time Markov chains using parallel replica dynamics
This work provides a method for efficiently estimating stationary averages in metastable Markov chains, which is relevant for computational chemistry and physics simulations.
The paper proposes two parallel replica algorithms for simulating continuous time Markov chains with metastability, demonstrating that they correctly estimate stationary averages under ergodicity. Numerical simulations on multi-scale stochastic reaction networks show consistency and efficiency.
We propose two algorithms for simulating continuous time Markov chains in the presence of metastability. We show that the algorithms correctly estimate, under the ergodicity assumption, stationary averages of the process. Both algorithms, based on the idea of the parallel replica method, use parallel computing in order to explore metastable sets more efficiently. The algorithms require no assumptions on the Markov chains beyond ergodicity and the presence of identifiable metastability. In particular, there is no assumption on reversibility. For simpler illustration of the algorithms, we assume that a synchronous architecture is used throughout of the paper. We present error analyses, as well as numerical simulations on multi-scale stochastic reaction network models in order to demonstrate consistency of the method and its efficiency.