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Sasanka Are, Markos A. Katsoulakis, Petr Plechac, Luc Rey-Bellet

Multi-body interactions in coarse-graining schemes for extended systems

In this paper we address the role of multi-body interactions for the coarse-grained approximation of stochastic lattice systems. Such interaction potentials are often not included in coarse-graining schemes as they can be computationally expensive. The multi-body interactions are obtained from the error expansion of the reference measure which is, in many cases, chosen as a Gibbs measure corresponding to a local mean-field approximation. We identify the parameter $\epsilon$ that characterizes the level of approximation and its relation to the underlying interaction potential. The error analysis suggests strategies to overcome the computational costs due to evaluations of multi-body interactions by additional approximation steps with controlled errors. We present numerical examples demonstrating that the inclusion of multi-body interactions shows substantial improvement in dynamical simulations, e.g., of rare events and metastability in phase transitions regimes.

Bibliographical note: to appear in SIAM J. Sci. Computing