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Applications of the cross-entropy method to importance sampling and optimal control of diffusions
(2014)
We study the cross-entropy method for diffusions. One of the results is a versatile cross-entropy algorithm that can be used to design efficient importance sampling strategies for rare events or to solve optimal control problems. The approach is based on the minimization of a suitable cross-entropy functional, with a parametric family of exponentially tilted probability distributions. We illustrate the new algorithm with several numerical examples and discuss algorithmic issues and possible extensions of the method.
Linear response theory and optimal control for a molecular system under nonequilibrium conditions
(2013)
In this paper, we propose a straightforward generalization of linear
response theory to systems in nonequilibrium that are subject to
nonequilibrium driving. We briefly revisit the standard linear response
result for equilibrium systems, where we consider Langevin dynamics
as a special case, and then give an alternative derivation using a
change-of-measure argument that does not rely on any stationarity or
reversibility assumption. This procedure moreover easily enables us
to calculate the second order correction to the linear response formula
(which may or may not be useful in practice). Furthermore, we outline
how the novel nonequilibirum linear response formula can be used to
compute optimal controls of molecular systems for cases in which one
wants to steer the system to maximize a certain target expectation
value. We illustrate our approach with simple numerical examples.
Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique
(2013)