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

Malliavin Weight Sampling: A Practical Guide

1,*  and 2,*
1 Unilever R&D Port Sunlight, Quarry Road East, Bebington, Wirral, CH63 3JW, UK 2 Scottish Universities Physics Alliance (SUPA), School of Physics and Astronomy, the University of Edinburgh, the Kings Buildings, Mayfield Road, Edinburgh, EH9 3JZ, UK
* Authors to whom correspondence should be addressed.
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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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 (CC BY 3.0).

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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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