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Non-empirical weighted Langevin mechanics for the potential escape problem: Parallel algorithm and application to the Argon clusters

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PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS 2019年 528卷 121481-000页

作者： Nagornoy, Yuri S. Akashi, Ryosuke Univ Tokyo Dept Phys Bunkyo Ku Tokyo 1130033 Japan

Recently a non-empirical stochastic walker algorithm has been developed to search for the minimum-energy escape paths (MEP) from the minima of the potential surface (Akashi and Nagorno, 2018). This algorithm is novel in that it tracks the MEP monotonically and does not use the whole Hessian matrix but only gradient and Laplacian of the potential. In this work, we implement an parallelized version of this algorithm in a simple way. We also explore efficient ways to reduce the number of walkers required for the accurate tracking of the MEP and generate initial positions automatically. We apply the whole scheme to the Lennard-Jones argon cluster with 7-38 atoms to demonstrate the successful tracking of the reaction paths. This achievement paves the path to non-empirical simulation of rare reactions without coarse-graining or artificial potential. (C) 2019 Elsevier B.V. All rights reserved.

关键词： Reaction paths Hyperdynamics Non-empirical scheme Minimum-energy escape paths Potential surface stochastic algorithm Parallel implementation Argon cluster

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AtomREM: Non-empirical seeker of the minimum energy escape paths on many-dimensional potential landscapes without coarse graining

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COMPUTER PHYSICS COMMUNICATIONS 2020年 254卷 107260-107260页

作者： Nagornov, Yuri S. Akashi, Ryosuke Univ Tokyo Dept Phys Bunkyo Ku Tokyo 1130033 Japan

Recently a non-empirical stochastic walker algorithm has been developed to search for the minimum-energy escape paths from the minima of the potential surface (Akashi and Nagornov, 2018;Nagornov and Akashi, 2019). This method is based on the Master equation for the distribution function of the atomic configuration which has a nature to seek the reaction path up along the valley of the potential surface. This paper introduces AtomREM (Atomistic Rare Event Manager), which is an MPI parallelized solver program package for executing this method, which yields reaction pathways in terms of the microscopic evolution of atomic positions. It is open-source and released under the GNU General Public License (GPL). A feature AtomREM interfaces with the LAMMPS Molecular Dynamics Simulator as a library of versatile potential functions for application to various systems. Examples of the applications to molecular and solid systems are presented. Program summary Program Title: AtomREM (Atomistic Rare-Event Manager) Program Files doi: http://***/10.17632/ys5mpgjfc8.1 Licensing provisions: GNU General Public License 3 Programming language: Fortran 90 and C Supplementary material: Result movies of simulation for argon solid and (CH2)(4) molecule Nature of problem: AtomREM has been developed to help to find a reaction path on the atomic level using weighted Langevin mechanics on the inverse potential landscape. The method describes the low temperature transformation of complex systems without artificial forces or/and collective variables. Solution method: Recently [1] we designed a non-empirical scheme to search for the minimum-energy escape paths from the minima of the potential surface to unknown saddle points nearby with one dimensional application. The method is based on the Master equation and its solver algorithm is constructed to move the walkers up the surface through the potential valleys [2]. The stochastic algorithm uses a birth/death stochastic processes for numerous

关键词： Potential landscape Reaction paths Minimum-energy escape paths Langevin mechanics Non-empirical scheme stochastic algorithm Parallel MPI implementation

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Lattice Boltzmann simulation of oxygen diffusion and electrochemical reaction inside catalyst layer of PEM fuel cells

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INTERNATIONAL JOURNAL OF HEAT AND MASS TRANSFER 2019年 143卷 118538-000页

作者： Deng, Hao Hou, Yuze Chen, Wenmiao Pan, Fengwen Jiao, Kui Tianjin Univ State Key Lab Engines 135 Yaguan Rd Tianjin 300350 Peoples R China Weichai Power Co Ltd 197A Fushou St E Weifang 261016 Peoples R China

An in-depth understanding of pore-scale transport process and electrode reaction kinetics is critical to ease the sluggish oxygen reduction reaction of proton exchange membrane fuel cells. In this study, the effects of catalyst layer microstructure on the oxygen diffusion and electrochemical reaction consumption are analyzed, based on the developed 3D single-phase lattice Boltzmann model and optimized stochastic reconstruction algorithm. The results suggest that increasing the ionomer content and platinum loading are beneficial to increasing the active sites, while the oxygen transport along the thickness direction becomes more difficult due to the narrowed pores, so the platinum particles in the back region have less participation in the reaction, which causes the significant catalyst waste and limits the further cost reduction and improvement of power density. Improving the carbon particle diameter ensures the enlarged pores and more effective Pt particles covered by ionomer, thus enhances the oxygen supply and electrochemical reaction rate. (C) 2019 Elsevier Ltd. All rights reserved.

关键词： Catalyst layer Oxygen transport Electrochemical reaction Lattice Boltzmann stochastic algorithm

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Balancing exploration and exploitation: An image-based approach to item retrieval with enhanced diversity

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COMPUTERS & ELECTRICAL ENGINEERING 2020年 84卷 106605-106605页

作者： Pereira, Artur Maia Vieira, Thales Costa, Evandro de Barros Univ Fed Alagoas Inst Comp Maceio Alagoas Brazil Univ Fed Alagoas Inst Math Maceio Alagoas Brazil

We propose a machine learning approach based on relevance feedback to visually retrieve e-commerce items, represented by images, from huge catalogs. A threefold strategy is presented to deal with the exploration-exploitation dilemma: retrieve user-relevant items;retrieve items that do not comply with user learned preferences, to avoid convergence to local minima;and retrieve items from uncertainty regions, to improve the learning curve, all in a stochastic manner. To mitigate the cold start problem, we present a novel sampling method to improve the diversity of retrieved items that employs a combination of a multidimensional projection method with an adaptive spatial data structure. We performed quantitative and qualitative user experiments using an annotated catalog of clothing items. Results revealed that our approach can rapidly improve the retrieval of appropriate items in a few user iterations while providing higher diversity than other relevant and recent approaches. (c) 2020 Elsevier Ltd. All rights reserved.

关键词： Concept-based retrieval Relevance feedback Dimensionality reduction stochastic algorithm Exploration-exploitation Item retrieval

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Thinning and weighting of large planar arrays by simulated annealing

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IEEE TRANSACTIONS ON ULTRASONICS FERROELECTRICS AND FREQUENCY CONTROL 1999年第2期46卷 347-355页

作者： Trucco, A Univ Genoa Dept Biophys & Elect Engn I-16145 Genoa Italy

Two-dimensional arrays offer the potential for producing three-dimensional acoustic imaging. The major problem is the complexity arising from the large number of elements in such arrays. In this paper, a synthesis method is proposed that is aimed at designing an aperiodic sparse two-dimensional array to be used with a conventional beamformer. The stochastic algorithm of simulated annealing has been utilized to minimize the number of elements necessary to produce a spatial response that meets given requirements. The proposed method is highly innovative, as it can design very large arrays, optimize both positions and weight coefficients, synthesize asymmetric arrays, and generate array configurations that are valid for every steering direction. Several results are presented, showing notable improvements in the array characteristics and performances over those reported in the literature.

关键词： acoustic arrays acoustic imaging simulated annealing beam pattern optimization planar array stochastic algorithm synthesis three-dimensional acoustic imaging two-dimensional array simulated annealing Weighing beam mode two-dimensional array Planar antennas THINNING Thinning synthesis acoustic arrays weighting Acoustic images

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Modeling and simulation of cell migration on the basis of force equilibrium

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INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING 2021年第2期38卷 e3550-e3550页

作者： Chang, Chia-Yu Dai, Zhi-Xuan Shih, Po-Jen Natl Taiwan Univ Dept Mech Engn Taipei Taiwan Natl Taiwan Univ Dept Biomed Engn 1 Sec 4Roosevelt Rd Taipei 10617 Taiwan

To study cell behavior, we developed a cell model to simulate cell movements and the interacting forces among cells and between cells and obstacles. The developed model simulates several cells simultaneously and examines correlations among characteristic parameters between cells and substrates during migration. We modified Odde's model to develop fundamental model, applied Gillespie's stochastic algorithm to design time during in the migration simulation, and employed Keren's membrane theory to analyze the equilibrium at the leading edges. Thus, the proposed model can analyze stresses due to substrate, the intracellular body, and the external interaction between cells and obstacles. Simulation results indicate that cell-cell interaction depends on the equilibrium between the forces at the leading edge of the membrane, namely the cell-substrate interaction force, cell-cell interaction forces, and the cell membrane force. These results also indicate that the migration direction is dependent on the resultant forces. The membrane force and substrate force directions are "low correlation," and the polymerization rate exhibits "little correlative" with the migration direction. We propose a modified cell migration model for simulating allocation and interaction among multiple cells. This model helps indicate the weightings of characteristic parameters that affect the cell migration direction and velocity.

关键词： migration multiple cells stochastic algorithm trajectories

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On the Convergence of Simulation-based Iterative Methods for Solving Singular Linear Systems

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stochastic Systems 2013年第1期3卷 1-321页

作者： Mengdi Wang Dimitri P. Bertsekas

We consider the simulation-based solution of linear systems of equations, Ax = b , of various types frequently arising in large-scale applications, where A is singular. We show that the convergence properties of iterative solution methods are frequently lost when they are implemented with simulation (e.g., using sample average approximation), as is often done in important classes of large-scale problems. We focus on special cases of algorithms for singular systems, including some arising in least squares problems and approximate dynamic programming, where convergence of the residual sequence { Ax k − b } may be obtained, while the sequence of iterates { x k } may diverge. For some of these special cases, under additional assumptions, we show that the iterate sequence is guaranteed to converge. For situations where the iterates diverge but the residuals converge to zero, we propose schemes for extracting from the divergent sequence another sequence that converges to a solution of Ax = b .

关键词： stochastic algorithm singular system Monte-Carlo estimation simulation proximal method regularization approximate dynamic programming

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Gradient-free algorithm for saddle point problems under

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CHAOS SOLITONS & FRACTALS 2024年 185卷

作者： Statkevich, Ekaterina Bondar, Sofiya Dvinskikh, Darina Gasnikov, Alexander Lobanov, Aleksandr Moscow Inst Phys & Technol Dept Appl Math & Comp Sci Inst Sky Lane 9 Dolgoprudnyi 141701 Russia HSE Univ Myasnitskaya St 20 Moscow 101000 Russia Skolkovo Inst Sci & Technol Bolshoy Blvd 30P 1 Moscow 121205 Russia ISP RAS Res Ctr Trusted Artificial Intelligence Alexander Solzhenitsyn St 25 Moscow 109004 Russia

This paper focuses on solving a stochastic saddle point problem (SPP) under an overparameterized regime for the case, when the gradient computation is impractical. As an intermediate step, we generalize Same-sample stochastic Extra-gradient algorithm (Gorbunov et al., 2022) to a biased oracle and estimate novel convergence rates. As the result of the paper we introduce an algorithm, which uses gradient approximation instead of a gradient oracle. We also conduct an analysis to find the maximum admissible level of adversarial noise and the optimal number of iterations at which our algorithm can guarantee achieving the desired accuracy.

关键词： Saddle point problem Gradient-free oracle stochastic algorithm Bounded noise Overparametrization

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The Battery Life Estimation of a Battery under Different Stress Conditions

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BATTERIES-BASEL 2021年第4期7卷 88页

作者： Andrenacci, Natascia Vellucci, Francesco Sglavo, Vincenzo CR ENEA Casaccia Via Anguillarese 301 I-00123 Rome Italy

The prediction of capacity degradation, and more generally of the behaviors related to battery aging, is useful in the design and use phases of a battery to help improve the efficiency and reliability of energy systems. In this paper, a stochastic model for the prediction of battery cell degradation is presented. The proposed model takes its cue from an approach based on Markov chains, although it is not comparable to a Markov process, as the transition probabilities vary with the number of cycles that the cell has performed. The proposed model can reproduce the abrupt decrease in the capacity that occurs near the end of life condition (80% of the nominal value of the capacity) for the cells analyzed. Furthermore, we illustrate the ability of this model to predict the capacity trend for a lithium-ion cell with nickel manganese cobalt (NMC) at the cathode and graphite at the anode, subjected to a life cycle in which there are different aging factors, using the results obtained for cells subjected to single aging factors.

关键词： cycle aging lithium battery stochastic algorithm

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A parallelized Monte Carlo algorithm for the nonlinear Poisson-Boltzmann equation in two dimensions

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APPLIED COMPUTATIONAL ELECTROMAGNETICS SOCIETY JOURNAL 2007年第3期22卷 333-339页

作者： Chatterjee, Kausik Poggie, Jonathan Dept Elect & Comp Engn Cooper Union New York NY 10003 USA Ctr Comp Sci Air Force Res Lab Wright Patterson AFB OH 45433 USA

This paper presents the parallelization of a previously-developed two-dimensional floating random walk (FRW) algorithm for the solution of the nonlinear Poisson-Boltzmann (NPB) equation. Historically, the FRW method has not been applied efficiently to the solution of the NPB equation which can be attributed to the absence of analytical expressions for volumetric Green's functions. stochastic approaches to solving nonlinear equations (in particular the NPB equation) that have been suggested in literature involve an iterative solution of a series of linear problems. As a result, previous applications of the FRW method have examined only the linearized Poisson-Boltzmann equation. In our proposed approach, an approximate (yet accurate) expression for the Green's function for the nonlinear problem is obtained through perturbation theory, which gives rise to an integral formulation that is valid for the entire nonlinear problem. As a result, our algorithm does not have any iteration steps, and thus has a lower computational cost. A unique advantage of the FRW method is that it requires no discretization of either the volume or the surface of the problem domains. Furthermore, each random walk is independent, so that the computational procedure is highly parallelizable. In previously published work, we have presented the fundamentals of our algorithm and in this paper we report the parallelization of this algorithm in two dimensions. The solution of the NPB equation has many interesting applications, including the modeling of plasma discharges, semiconductor device modeling and the modeling of biomolecules.

关键词： Monte Carlo random walk stochastic algorithm nonlinear Poisson-Boltzmann equation modeling of plasma sheaths semiconductor device modeling modeling of biomolecular structure and dynamics

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