University of Cambridge > > DAMTP Statistical Physics and Soft Matter Seminar > Multilevel Monte Carlo simulation for scale-separated systems

Multilevel Monte Carlo simulation for scale-separated systems

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If you have a question about this talk, please contact Etienne Fodor.

Designing efficient Monte Carlo simulations for multiscale physical systems is often a difficult problem. The underlying Markov chain can typically only modify the system locally on a small-scale level. This means that the long length-scale degrees of freedom of the system tend to decorrelate very slowly. We propose a structured approach to circumvent slow simulations in this situation. Assume that the degrees of freedom corresponding to the long length scales give rise to a coarse grained system which can be simulated efficiently. Instead of simulation the full system, we first compute the coarse-grained approximation and subsequently correct the coarse-graining error by a simulation of the remaining fine degrees of freedom. This is inspired by the multilevel Monte Carlo approach that has been developed in recent mathematical studies for applications in Bayesian inference and mathematical finance. We develop a convergence theory of our method and apply it to the Asakura-Oosawa (AO) model and size-asymmetrical binary hard-sphere systems. This allows us to investigate equilibrium properties of systems with a large size-ratio where a naive simulation would have been computationally infeasible.

This talk is part of the DAMTP Statistical Physics and Soft Matter Seminar series.

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