Goal-oriented sensitivity analysis for lattice kinetic Monte Carlo simulations.

Area of Science:

• Computational Physics and Chemistry
• Statistical Mechanics
• Materials Science

Background:

• Sensitivity analysis of stochastic systems often relies on finite difference methods with independent samples, leading to high variance.
• Existing coupling methods for stochastic systems, like Common Random Number, can be computationally intensive for high-dimensional problems.
• Kinetic Monte Carlo (KMC) simulations are crucial for modeling complex systems but require efficient sensitivity analysis.

Purpose of the Study:

• To develop a novel, variance-reducing coupling method for sensitivity analysis of high-dimensional stochastic systems.
• To introduce goal-oriented sensitivity analysis tailored to specific observables in lattice KMC simulations.
• To significantly enhance the computational efficiency of KMC-based sensitivity analysis.

Main Methods:

• Proposed a new class of coupling methods by developing strongly correlated stochastic processes for perturbed and unperturbed systems.
• Introduced goal-oriented sensitivity analysis where coupled process rates are optimized based on target observables (e.g., coverage, Hamiltonian).
• Implemented the algorithm using a Bortz-Kalos-Lebowitz approach, classifying events based on observable level sets.

Main Results:

• Demonstrated significant variance reduction in sensitivity estimators compared to independent sampling methods.
• Achieved up to two orders of magnitude speedup in lattice KMC simulations for adsorption, desorption, and diffusion compared to Common Random Number.
• Validated the effectiveness of the variance minimization functional as a diagnostic tool for coupling design.

Conclusions:

• The proposed goal-oriented sensitivity analysis offers a highly efficient and accurate approach for high-dimensional stochastic systems.
• This method provides a substantial computational advantage for KMC simulations, enabling faster parameter exploration and model evaluation.
• The developed algorithm is readily implementable and applicable to various spatial KMC processes.