Equation-free optimal switching policies for bistable reacting systems using coarse time-steppers

TL;DR

This paper introduces a computational method that uses coarse time-steppers to find optimal switching policies between stable states in stochastic chemical systems, bridging microscopic simulations and continuum optimization.

Contribution

The paper presents a novel approach combining kinetic Monte Carlo simulations with continuum optimization to determine optimal switching policies in bistable reacting systems.

Findings

Successfully applied to catalytic surface reactions

Achieved minimal intervention switching between stable states

Demonstrated effectiveness on two model systems

Abstract

We present a computer-assisted approach to locating approximate coarse optimal switching policies between stationary states of chemically reacting systems described by microscopic/stochastic evolution rules. The ``coarse time-stepper" constitutes a bridge between the underlying kinetic Monte Carlo simulation and traditional, continuum numerical optimization techniques formulated in discrete time. The approach is illustrated through two simple catalytic surface reaction models, implemented through kinetic Monte Carlo: NO reduction on Pt, and CO oxidation on Pt. The objective sought in both cases is to switch between two coexisting stable stationary states by minimal manipulation of a macroscopic system parameter.