@article{HartmannSchuetteWeberetal.2017, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Weber, Marcus and Zhang, Wei}, title = {Importance sampling in path space for diffusion processes with slow-fast variables}, journal = {Probability Theory and Related Fields}, doi = {10.1007/s00440-017-0755-3}, pages = {1 -- 52}, year = {2017}, abstract = {Importance sampling is a widely used technique to reduce the variance of a Monte Carlo estimator by an appropriate change of measure. In this work, we study importance sampling in the framework of diffusion process and consider the change of measure which is realized by adding a control force to the original dynamics. For certain exponential type expectation, the corresponding control force of the optimal change of measure leads to a zero-variance estimator and is related to the solution of a Hamilton-Jacobi-Bellmann equation. We focus on certain diffusions with both slow and fast variables, and the main result is that we obtain an upper bound of the relative error for the importance sampling estimators with control obtained from the limiting dynamics. We demonstrate our approximation strategy with an illustrative numerical example.}, language = {en} } @misc{ZhangHartmannSchuette2016, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective Dynamics Along Given Reaction Coordinates, and Reaction Rate Theory}, issn = {1438-0064}, doi = {10.1039/C6FD00147E}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-59706}, year = {2016}, abstract = {In molecular dynamics and related fields one considers dynamical descriptions of complex systems in full (atomic) detail. In order to reduce the overwhelming complexity of realistic systems (high dimension, large timescale spread, limited computational resources) the projection of the full dynamics onto some reaction coordinates is examined in order to extract statistical information like free energies or reaction rates. In this context, the effective dynamics that is induced by the full dynamics on the reaction coordinate space has attracted considerable attention in the literature. In this article, we contribute to this discussion: We first show that if we start with an ergodic diffusion processes whose invariant measure is unique then these properties are inherited by the effective dynamics. Then, we give equations for the effective dynamics, discuss whether the dominant timescales and reaction rates inferred from the effective dynamics are accurate approximations of such quantities for the full dynamics, and compare our findings to results from approaches like Zwanzig-Mori, averaging, or homogenization. Finally, by discussing the algorithmic realization of the effective dynamics, we demonstrate that recent algorithmic techniques like the "equation-free" approach and the "heterogeneous multiscale method" can be seen as special cases of our approach.}, language = {en} } @article{ZhangSchuette2017, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Reliable approximation of long relaxation timescales in molecular dynamics}, volume = {19}, journal = {Entropy}, number = {7}, doi = {10.3390/e19070367}, year = {2017}, language = {en} } @article{ZhangHartmannSchuette2016, author = {Zhang, Wei and Hartmann, Carsten and Sch{\"u}tte, Christof}, title = {Effective dynamics along given reaction coordinates, and reaction rate theory}, journal = {Faraday Discussions}, number = {195}, doi = {10.1039/C6FD00147E}, pages = {365 -- 394}, year = {2016}, language = {en} } @article{HartmannRichterSchuetteetal.2017, author = {Hartmann, Carsten and Richter, Lorenz and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Variational characterization of free energy: theory and algorithms}, volume = {19}, journal = {Entropy}, number = {11}, doi = {10.3390/e19110626}, pages = {626}, year = {2017}, language = {en} } @article{ZhangWangHartmannetal.2014, 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}, volume = {36}, journal = {Siam Journal on Scientific Computing}, number = {6}, doi = {10.1137/14096493X}, pages = {A2654 -- A2672}, year = {2014}, language = {en} } @article{HartmannSchuetteZhang2016, author = {Hartmann, Carsten and Sch{\"u}tte, Christof and Zhang, Wei}, title = {Model reduction algorithms for optimal control and importance sampling of diffusions}, volume = {29}, journal = {Nonlinearity}, number = {8}, doi = {10.1088/0951-7715/29/8/2298}, pages = {2298 -- 2326}, year = {2016}, abstract = {We propose numerical algorithms for solving optimal control and importance sampling problems based on simplified models. The algorithms combine model reduction techniques for multiscale diffusions and stochastic optimization tools, with the aim of reducing the original, possibly high-dimensional problem to a lower dimensional representation of the dynamics, in which only a few relevant degrees of freedom are controlled or biased. Specifically, we study situations in which either a reaction coordinate onto which the dynamics can be projected is known, or situations in which the dynamics shows strongly localized behavior in the small noise regime. No explicit assumptions about small parameters or scale separation have to be made. We illustrate the approach with simple, but paradigmatic numerical examples.}, language = {en} } @misc{ZhangWangHartmannetal.2014, 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}, year = {2014}, 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} } @article{PetkovaJanuszewskiBlakelyetal.2025, author = {Petkova, Mariela D. and Januszewski, MichaƂ and Blakely, Tim and Herrera, Kristian J. and Schuhknecht, Gregor F.P. and Tiller, Robert and Choi, Jinhan and Schalek, Richard L. and Boulanger-Weill, Jonathan and Peleg, Adi and Wu, Yuelong and Wang, Shuohong and Troidl, Jakob and Vohra, Sumit Kumar and Wei, Donglai and Lin, Zudi and Bahl, Armin and Tapia, Juan Carlos and Iyer, Nirmala and Miller, Zachary T. and Hebert, Kathryn B. and Pavarino, Elisa C. and Taylor, Milo and Deng, Zixuan and Stingl, Moritz and Hockling, Dana and Hebling, Alina and Wang, Ruohong C. and Zhang, Lauren L. and Dvorak, Sam and Faik, Zainab and King, Jr., Kareem I. and Goel, Pallavi and Wagner-Carena, Julian and Aley, David and Chalyshkan, Selimzhan and Contreas, Dominick and Li, Xiong and Muthukumar, Akila V. and Vernaglia, Marina S. and Carrasco, Teodoro Tapia and Melnychuck, Sofia and Yan, TingTing and Dalal, Ananya and DiMartino, James and Brown, Sam and Safo-Mensa, Nana and Greenberg, Ethan and Cook, Michael and Finley, Samantha and Flynn, Miriam A. and Hopkins, Gary Patrick and Kovalyak, Julie and Leonard, Meghan and Lohff, Alanna and Ordish, Christopher and Scott, Ashley L. and Takemura, Satoko and Smith, Claire and Walsh, John J. and Berger, Daniel R. and Pfister, Hanspeter and Berg, Stuart and Knecht, Christopher and Meissner, Geoffrey W. and Korff, Wyatt and Ahrens, Misha B and Jain, Viren and Lichtman, Jeff W. and Engert, Florian}, title = {A connectomic resource for neural cataloguing and circuit dissection of the larval zebrafish brain}, journal = {bioRxiv}, doi = {10.1101/2025.06.10.658982}, year = {2025}, abstract = {We present a correlated light and electron microscopy (CLEM) dataset from a 7-day-old larval zebrafish, integrating confocal imaging of genetically labeled excitatory (vglut2a) and inhibitory (gad1b) neurons with nanometer-resolution serial section EM. The dataset spans the brain and anterior spinal cord, capturing >180,000 segmented soma, >40,000 molecularly annotated neurons, and 30 million synapses, most of which were classified as excitatory, inhibitory, or modulatory. To characterize the directional flow of activity across the brain, we leverage the synaptic and cell body annotations to compute region-wise input and output drive indices at single cell resolution. We illustrate the dataset's utility by dissecting and validating circuits in three distinct systems: water flow direction encoding in the lateral line, recurrent excitation and contralateral inhibition in a hindbrain motion integrator, and functionally relevant targeted long-range projections from a tegmental excitatory nucleus, demonstrating that this resource enables rigorous hypothesis testing as well as exploratory-driven circuit analysis. The dataset is integrated into an open-access platform optimized to facilitate community reconstruction and discovery efforts throughout the larval zebrafish brain.}, language = {en} } @misc{ZhangSchuette2017, author = {Zhang, Wei and Sch{\"u}tte, Christof}, title = {Reliable approximation of long relaxation timescales in molecular dynamics}, issn = {1438-0064}, doi = {10.3390/e19070367}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-63718}, year = {2017}, abstract = {Many interesting rare events in molecular systems like ligand association, protein folding or con- formational changes happen on timescales that often are not accessible by direct numerical simulation. Therefore rare event approximation approaches like interface sampling, Markov state model building or advanced reaction coordinate based free energy estimation have attracted huge attention recently. In this article we analyze the reliability of such approaches: How precise is an estimate of long relaxation timescales of molecular systems resulting from various forms of rare event approximation methods? Our results give a theoretical answer to this question by relating it with the transfer operator approach to molecular dynamics. By doing so they also allow for understanding deep connections between the different approaches.}, language = {en} }