Steady state likelihood ratio sensitivity analysis for stiff kinetic Monte Carlo simulations

Kinetic Monte Carlo simulation is an integral tool in the study of complex physical phenomena present in applications ranging from heterogeneous catalysis to biological systems to crystal growth and atmospheric sciences. Sensitivity analysis is useful for identifying important parameters and rate-determining steps, but the finite-difference application of sensitivity analysis is computationally demanding. Techniques based on the likelihood ratio method reduce the computational cost of sensitivity analysis by obtaining all gradient information in a single run. However, we show that disparity in time scales of microscopic events, which is ubiquitous in real systems, introduces drastic statistical noise into derivative estimates for parameters affecting the fast events. In this work, the steady-state likelihood ratio sensitivity analysis is extended to singularly perturbed systems by invoking partial equilibration for fast reactions, that is, by working on the fast and slow manifolds of the chemistry. Derivatives on each time scale are computed independently and combined to the desired sensitivity coefficients to considerably reduce the noise in derivative estimates for stiff systems. The approach is demonstrated in an analytically solvable linear system.