(264f) Coarse Regularization and Optimization of Microscopic Monte-Carlo Based Time-Steppers

Nowadays, there is an increase number of industrial and biological processes whose coarse-grained (mean-field) model equations do not conceptually exist or simply can not capture the complex interactions in the process. Instead, a detailed microspic (often stochastic) description can be alternatively used (i.e. kinetic Monte Carlo [1]). In this scenario, while the optimization is performed on a set of macroscopic variables, the simulation operates on the microscopic level. In order to bridge the macroscopic optimization-microscopic simulation, the coarse time-stepper concept is exploited [2,3]. Due to the natural random noise in the stochastic coarse time-stepper, any optimization problem (optimal control or parameter estimation) will be mathematically ill-posed.

In this presentation, we use a regularization strategy aimed to control the noise propagation (coming from the microscopic simulation) that prevents convergence and in this way it overcomes the ill-posedness of the optimization problem at the macroscopic level. When the optimal regularization is used, convergence is achieved where no further precision in the control variables is possible. The performance of the strategy is evaluated using a stochastic reacting system as a case study and using either local (deterministic) and global (stochastic) optimization methods

[1] Gillespie, D. T. (1977) J. Phys. Chem., 81(25), 2340-2361

[2] Theodoropoulos, C. et al. (2000) PNAS USA, 97(18), 9840-9843

[3] Kevrekidis, I. G. et al. (2003) Comm. Math. Sci., 1(14), 715-762