Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 231, Issue 21, Pages 7170-7186Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2012.06.037
Keywords
Stochastic; Gradient estimation; Likelihood ratio; Finite difference; Kinetic Monte Carlo; Sensitivity analysis
Funding
- NSF [CMMI-0835673]
- Directorate For Engineering
- Div Of Civil, Mechanical, & Manufact Inn [0835548] Funding Source: National Science Foundation
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While many optimization and control methods for stochastic processes require gradient information from the process of interest, obtaining gradient information from experiments is prohibitively expensive and time-consuming. As a result, such information is often obtained from stochastic process simulations. Computing gradients efficiently and accurately from stochastic simulations is challenging, especially for simulations involving computationally expensive models with significant inherent noise. In this work, we analyze and characterize the applicability of two gradient estimation methods for kinetic Monte Carlo simulations: finite differencing and likelihood ratio. We developed a systematic method for choosing an optimal perturbation size for finite differencing and discuss, for both methods, important implementation issues such as scaling with respect to the number of elements in the gradient vector. Through a series of numerical experiments, the methods were compared across different time and size regimes to characterize the precision and accuracy associated with each method. We determined that the likelihood ratio method is appropriate for estimating gradients at short (transient) times or for systems with small population sizes, whereas finite differencing is better-suited for gradient estimation at long times (steady state) or for systems with large population sizes. (C) 2012 Elsevier Inc. All rights reserved.
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