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

Area of Science:

• Computational Physics
• Chemical Kinetics
• Materials Science

Background:

• Kinetic Monte Carlo (KMC) simulations are vital for studying complex physical phenomena.
• Sensitivity analysis identifies key parameters but finite-difference methods are computationally expensive.
• Likelihood ratio methods reduce cost but struggle with systems having disparate time scales.

Purpose of the Study:

• To extend likelihood ratio sensitivity analysis to stiff systems with vastly different time scales.
• To reduce statistical noise in derivative estimates for fast events in KMC simulations.
• To improve the computational efficiency and accuracy of sensitivity analysis in complex systems.

Main Methods:

• Developed a modified steady-state likelihood ratio method for singularly perturbed systems.
• Incorporated partial equilibration by analyzing fast and slow reaction manifolds.
• Computed derivatives independently on each time scale before combining them.

Main Results:

• Significantly reduced statistical noise in derivative estimates for stiff systems.
• Successfully extended likelihood ratio sensitivity analysis to systems with disparate time scales.
• Demonstrated the approach's effectiveness in an analytically solvable linear system.

Conclusions:

• The extended method provides a more robust and accurate sensitivity analysis for stiff KMC simulations.
• This work offers a computationally efficient way to analyze complex physical and chemical systems.
• The findings have broad implications for fields relying on KMC simulations, such as catalysis and materials science.