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The efficient characterization of the nonlinear dynamical response of kinetic molecular simulations is discussed. Following ideas originally proposed by Kevrekidis et al. [1, 2], one can empower molecular simulations as model-free equations and use them as a reference to perform bifurcation detection. Such a procedure requires the use of trajectories from the molecular simulation to generate low-order models (e.g. polynomial) that allow one to infer the location of a bifurcation. If such identification step can be performed robustly, a feedback control policy that drives the molecular simulation to the bifurcation point can be constructed. In previous work, the identification of the low-order model has been singled out as the key element in handling noise trajectories, such as those generated by low-resolution molecular simulations. Here, a procedure motivated by the use of Kalman Filter observers is proposed as a means to give robustness to the identification procedure. The potential of the technique to characterize the dynamical response of kinetic molecular simulations is illustrated using examples related to the CO oxidation over a catalytic surface.

Towards Bifurcation Detection in Kinetic Monte Carlo Simulations: Robust Identification with Artificial Neural Networks and Nonlinear Kalman Filters