Monte Carlo methods, such as Gillespie’s direct SSA, are widely used to simulate chemical reaction networks. These simulations can then be used to estimate properties such as the mean value of an observable at some time horizon, or the sensitivity of mean values with respect to system parameter. However, when there are multiscale dynamics in the reaction network, direct simulation methods become ineffective because they can only advance the system on the smallest scale. This results in a prohibitive computational burden to reach a time horizon for the large scale dynamics.
We shall show how stochastic averaging may be employed to speed computations and obtain estimates of mean values and sensitivities with respect to the steady state distribution. Further, we shall establish bounds which show the bias induced by the averaging method decays to zero as the disparity between the scales increases.
Araz Hashemi currently a postdoctoral researcher in the Department of Mathematics at the University of Delaware. He is working with Petr Plechac on a Department of Energy research project investigating mathematical foundations for uncertainty quantification in materials design.
This talk presents joint work with P. Plechac, M. Nunez, and D. G. Vlachos.
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