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Entropy 2014, 16(1), 221-232; doi:10.3390/e16010221
Article

Malliavin Weight Sampling: A Practical Guide

1,*  and 2,*
Received: 25 September 2013 / Revised: 9 October 2013 / Accepted: 18 October 2013 / Published: 27 December 2013
(This article belongs to the Special Issue Molecular Dynamics Simulation)
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Abstract

Malliavin weight sampling (MWS) is a stochastic calculus technique for computing the derivatives of averaged system properties with respect to parameters in stochastic simulations, without perturbing the system’s dynamics. It applies to systems in or out of equilibrium, in steady state or time-dependent situations, and has applications in the calculation of response coefficients, parameter sensitivities and Jacobian matrices for gradient-based parameter optimisation algorithms. The implementation of MWS has been described in the specific contexts of kinetic Monte Carlo and Brownian dynamics simulation algorithms. Here, we present a general theoretical framework for deriving the appropriate MWS update rule for any stochastic simulation algorithm. We also provide pedagogical information on its practical implementation.
Keywords: stochastic calculus; Brownian dynamics stochastic calculus; Brownian dynamics
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Warren, P.B.; Allen, R.J. Malliavin Weight Sampling: A Practical Guide. Entropy 2014, 16, 221-232.

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