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Entropic Convergence of Random Batch Methods for Interacting Particle Diffusion [article]

Dheeraj Nagaraj
2022 arXiv   pre-print
We propose a co-variance corrected random batch method for interacting particle systems.  ...  By establishing a certain entropic central limit theorem, we provide entropic convergence guarantees for the law of the entire trajectories of all particles of the proposed method to the law of the trajectories  ...  The author would like to thank Katy Craig and Matthew Jacobs for introducing them to this problem and for multiple lengthy and extremely helpful discussions.  ... 
arXiv:2206.03792v1 fatcat:vr54jubtwbh43crmdzy5dztsda

Optimized ensemble Monte Carlo simulations of dense Lennard-Jones fluids

Simon Trebst, Emanuel Gull, Matthias Troyer
2005 Journal of Chemical Physics  
Interstitial states in the vicinity of these barriers are identified with unprecedented accuracy by sharp signatures in the quickly converging histogram and measurements of the local diffusivity.  ...  Equilibration of the simulated fluid is improved by sampling an optimized histogram in radial coordinates that shifts statistical weight towards the entropic barriers between the shells of the liquid.  ...  As another application of the optimized ensemble method we have studied a simple particlesolvent model where we vary the strength ⑀ given in Eq. ͑1͒ of an attractive interaction between a pair of particles  ... 
doi:10.1063/1.2121709 pmid:16351275 fatcat:sakevdzidjeq5iqqt2iimpbnpa

Ensemble Optimization Techniques for the Simulation of Slowly Equilibrating Systems [article]

S. Trebst, D.A. Huse, E. Gull, H.G. Katzgraber, U.H.E. Hansmann, M. Troyer
2006 arXiv   pre-print
Competing phases or interactions in complex many-particle systems can result in free energy barriers that strongly suppress thermal equilibration.  ...  We briefly discuss a number of examples including low-temperature states of magnetic systems with competing interactions and dense liquids.  ...  The interaction between particles in the fluid is described by a pairwise Lennard-Jones potential of the form where ǫ is the interaction strength, σ a length parameter, and R the distance between two particles  ... 
arXiv:cond-mat/0606005v1 fatcat:b7r5nlv4ejghrncopnezi2udqq

DeepParticle: learning invariant measure by a deep neural network minimizing Wasserstein distance on data generated from an interacting particle method [article]

Zhongjian Wang, Jack Xin, Zhiwen Zhang
2022 arXiv   pre-print
We introduce the so called DeepParticle method to learn and generate invariant measures of stochastic dynamical systems with physical parameters based on data computed from an interacting particle method  ...  We present numerical results to demonstrate the performance of our method for accelerating IPM computation of invariant measures of stochastic dynamical systems arising in computing reaction-diffusion  ...  Acknowledgements The research of JX is partially supported by NSF grants DMS-1924548  ... 
arXiv:2111.01356v3 fatcat:atl7vpps4faapnbc3535vaz4ri

Learning Moment Closure in Reaction-Diffusion Systems with Spatial Dynamic Boltzmann Distributions [article]

Oliver K. Ernst, Tom Bartol, Terrence Sejnowski, Eric Mjolsness
2019 arXiv   pre-print
The reduced model can treat systems in continuous space (described by continuous random variables), for which we formulate a variational learning problem using the adjoint method for the right hand sides  ...  Given the form of the reduced model Boltzmann distribution, we introduce an autonomous differential equation system for the interactions appearing in the energy function.  ...  Markov Chain Monte Carlo (MCMC) methods [27] . Typically, a graphical model for the distribution is introduced and learned by determining interaction parameters between random variables.  ... 
arXiv:1808.08630v2 fatcat:rgubej7c4vc6hele3yxbl45one

Particle Dual Averaging: Optimization of Mean Field Neural Networks with Global Convergence Rate Analysis [article]

Atsushi Nitanda, Denny Wu, Taiji Suzuki
2022 arXiv   pre-print
We propose the particle dual averaging (PDA) method, which generalizes the dual averaging method in convex optimization to the optimization over probability distributions with quantitative runtime guarantee  ...  An important application of the proposed method is the optimization of neural network in the mean field regime, which is theoretically attractive due to the presence of nonlinear feature learning, but  ...  Erdogdu and anonymous NeurIPS reviewers for their helpful feedback. AN was partially supported by JSPS Kakenhi (19K20337) and JST-PRESTO (JPMJPR1928).  ... 
arXiv:2012.15477v4 fatcat:zuffdnlgxrfdpm4dgpe5xwgqcy

Spatial heterogeneity of the cytosol revealed by machine learning-based 3D particle tracking

Grace A. McLaughlin, Erin M. Langdon, John M. Crutchley, Liam J. Holt, M. Gregory Forest, Jay M. Newby, Amy S. Gladfelter, Sophie Martin
2020 Molecular Biology of the Cell  
We find evidence that the physical structure of the cytosol is a fundamental source of variability in biological systems.  ...  Here we present tools to measure the physical state of the cytosol by analyzing the 3D motion of nanoparticles expressed in cells.  ...  The distribution of these larger particles was random, though possibly elevated somewhat near tips.  ... 
doi:10.1091/mbc.e20-03-0210 fatcat:rd565i6ku5etzcjpmzi5gee2qe

Sliced-Wasserstein Gradient Flows [article]

Clément Bonet, Nicolas Courty, François Septier, Lucas Drumetz
2022 arXiv   pre-print
However, this method comes with a high computational cost and stability issues.  ...  However, it requires solving a nested optimization problem at each iteration, and is known for its computational challenges, especially in high dimension.  ...  In the same setting that Section 4.2, we report on Figure 9 the evolution of the diffusion for the interaction functional (24), that we recall here: W(µ) = 1 2 W (x − y)dµ(x)dµ(y) (58) with W (x) = x  ... 
arXiv:2110.10972v2 fatcat:tfy6peefebfzbdyzwe22amf6oi

Collective Proposal Distributions for Nonlinear MCMC samplers: Mean-Field Theory and Fast Implementation [article]

Grégoire Clarté, Antoine Diez, Jean Feydy
2022 arXiv   pre-print
Under the double limit in number of iterations and number of particles we prove that this algorithm converges.  ...  of particles.  ...  Acknowledgments The authors wish to thank Pierre Degond, Robin Ryder and Christian Robert for their support and useful advice.  ... 
arXiv:1909.08988v6 fatcat:f2cp2yyhavditianb4q6esrwcu

3D neural network-based particle tracking reveals spatial heterogeneity of the cytosol [article]

Grace A McLaughlin, Erin M Langdon, John M Crutchley, Liam J Holt, Mark Gregory Forest, Jay M Newby, Amy S Gladfelter
2019 bioRxiv   pre-print
Using these probes to spatially resolve diffusivity of a cytoplasmic volume within a cell requires accurate and automated 3D tracking methods.  ...  We apply a neural network to track particles in 3D, generate surface meshes to project data on representations of the cell, and create dynamic visualizations of local diffusivities.  ...  This work was supported by Google Cloud, the National Science Foundation (NSF), the National Institutes of Health (NIH), and the Natural Sciences and Engineering Research Council of Canada (NSERC).  ... 
doi:10.1101/823286 fatcat:yus7mtkluvcgxkjhqmjf4rfeta

Stochastically Dominant Distributional Reinforcement Learning [article]

John D. Martin, Michal Lyskawinski, Xiaohu Li, Brendan Englot
2020 arXiv   pre-print
We propose a particle-based algorithm for which we prove optimality and convergence.  ...  This compares the inherent dispersion of random returns induced by actions, producing a more comprehensive and robust evaluation of the environment's uncertainty.  ...  Acknowledgements The authors wish to thank the anonymous reviewers for their feedback. A special thanks goes to Marc G. Bellemare and to Shruti Mishra for their thoughtful reviews of earlier drafts.  ... 
arXiv:1905.07318v4 fatcat:4m4ps6suk5cy5nnhngr7a4ioga

Thermal Fluctuations in Amphipol A8-35 Particles: A Neutron Scattering and Molecular Dynamics Study

Moeava Tehei, Jason D. Perlmutter, Fabrice Giusti, Jonathan N. Sachs, Giuseppe Zaccai, Jean-Luc Popot
2014 Journal of Membrane Biology  
Experimental results and simulations converge, from their respective time-scales, to show that A8-35 particles feature a more fluid hydrophobic core, predominantly containing the octyl chains, and a more  ...  In aqueous solutions, A8-35 self-organizes into globular particles with a molecular mass of *40 kDa.  ...  Data extracted from all-atom MD trajectories for particles made up of A8-35 (random distribution of the various groups) after coarsegrained and reverse coarse-grained simulations (Perlmutter et al. 2011  ... 
doi:10.1007/s00232-014-9725-1 pmid:25204390 fatcat:snsdj6ofovbwxog5u6pfxyn454

Master Index Volumes 1-100

2002 Stochastic Processes and their Applications  
-M., A note on the law of large numbers for directed random walks in random environments 54 (1994) 275 Jourdain, B., Convergence of moderately interacting particle systems to a diffusionconvection equation  ...  model for two interacting species 4 (1976) 271 Prajneshu, Diffusion approximations for models of population growth with logarithmic interactions 10 (1980) 87 Prakasa Rao, B.L.S., see Basawa, I.V. 10 (  ...  ., A CLT for the periodograms of a r * -mixing random field 60 (1995) 313 Miller, D.R., A continuity theorem and some counterexamples for the theory of maintained systems 5 (1977) 307 Miller, D.R., Limit  ... 
doi:10.1016/s0304-4149(02)00154-0 fatcat:5zmghyapt5d5fp272vy3x63bbq

Adaptive Monte Carlo augmented with normalizing flows [article]

Marylou Gabrié, Grant M. Rotskoff, Eric Vanden-Eijnden
2022 arXiv   pre-print
Markov Chain Monte Carlo (MCMC) algorithms, the ubiquitous tool for this task, typically rely on random local updates to propagate configurations of a given system in a way that ensures that generated  ...  We provide a theoretical analysis of the convergence properties of this algorithm, and investigate numerically its efficiency, in particular in terms of its propensity to equilibrate fast between metastable  ...  (random fields, transition paths, and interacting particle systems at phase coexistence) and show that it dramatically accelerates the sampling.  ... 
arXiv:2105.12603v3 fatcat:2yapy3snzfak3ldwg7awjtzaaq

Diffusion in Zeolites [chapter]

Jörg Kärger, Sergey Vasenkov, Scott Auerbach
2003 Handbook of Zeolite Science and Technology  
ACKNOWLEDGMENTS We gratefully acknowledge our research coworkers for their invaluable contributions and for many stimulating discussions. S.M.A. especially thanks Dr.  ...  This model accounts for entropic effects of finite loadings but not energetic effects.  ...  II.B), which form linear, square, or cubic sets of identical sorption sites. Such systems ignore particle-particle interactions, except for exclusion of multiple site occupancy.  ... 
doi:10.1201/9780203911167.ch10 fatcat:un5buf4tk5flfai7nuohylsnwm
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