@misc{ZhangWangHartmannetal., author = {Zhang, Wei and Wang, Han and Hartmann, Carsten and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Applications of the cross-entropy method to importance sampling and optimal control of diffusions}, issn = {1438-0064}, doi = {10.1137/14096493X}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-49720}, abstract = {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.}, language = {en} } @misc{WangHartmannSchuette, author = {Wang, Han and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Linear response theory and optimal control for a molecular system under nonequilibrium conditions}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-18944}, abstract = {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.}, language = {en} } @article{WangHartmannSchuetteetal.2013, author = {Wang, Han and Hartmann, Carsten and Sch{\"u}tte, Christof and Site, Luigi Delle}, title = {Grand-canonical-like molecular-dynamics simulations by using an adaptive-resolution technique}, series = {Phys. Rev. X}, volume = {3}, journal = {Phys. Rev. X}, doi = {10.1103/PhysRevX.3.011018}, pages = {011018}, year = {2013}, language = {en} } @article{ZhangWangHartmannetal., author = {Zhang, Wei and Wang, Han and Hartmann, Carsten and Weber, Marcus and Sch{\"u}tte, Christof}, title = {Applications of the cross-entropy method to importance sampling and optimal control of diffusions}, series = {Siam Journal on Scientific Computing}, volume = {36}, journal = {Siam Journal on Scientific Computing}, number = {6}, doi = {10.1137/14096493X}, pages = {A2654 -- A2672}, language = {en} } @article{WangHartmannSchuette, author = {Wang, Han and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Linear response theory and optimal control for a molecular system under nonequilibrium conditions}, series = {Molecular Physics}, volume = {111}, journal = {Molecular Physics}, doi = {10.1080/00268976.2013.844370}, pages = {3555 -- 3564}, language = {en} }