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Machine learning of explicit order parameters: From the Ising model to SU(2) lattice gauge theory

Physical Review B 2017年第18期96卷 184410-184410页

作者： Sebastian J. Wetzel Manuel Scherzer Institut für Theoretische Physik Universität Heidelberg Philosophenweg 16 69120 Heidelberg Germany

We present a solution to the problem of interpreting neural networks classifying phases of matter. We devise a procedure for reconstructing the decision function of an artificial neural network as a simple function of the input, provided the decision function is sufficiently symmetric. In this case one can easily deduce the quantity by which the neural network classifies the input. The method is applied to the Ising model and SU(2) lattice gauge theory. In both systems we deduce the explicit expressions of the order parameters from the decision functions of the neural networks. We assume no prior knowledge about the Hamiltonian or the order parameters except Monte Carlo–sampled configurations.

关键词： Classical statistical mechanics Gauge theories Machine learning Order parameters Phase transitions Heatbath algorithm Ising model Lattice gauge theory metropolis algorithm Monte Carlo methods Simulated annealing

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Electrophoresis of topologically nontrivial macromolecules: Mathematical and computational studies

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INTERNATIONAL JOURNAL OF MODERN PHYSICS C 1996年第2期7卷 217-271页

作者： Lim, HA Bioinformatics HYSEQ Inc. 670 Almanor Avenue Sunnyvale California 94086 USA

Mathematical and numerical models for studying the electrophoresis of topologically nontrivial molecules in two and three dimensions are presented. The molecules are modeled as polygons residing on a square lattice and a cubic lattice whereas the electrophoretic media of obstacle network are simulated by removing vertices from the lattices at random. The dynamics of the polymeric molecules are modeled by configurational readjustments of segments of the polygons. Configurational readjustments arise from thermal fluctuations and they correspond to piecewise reptation in the simulations. A metropolis algorithm is introduced to simulate these dynamics, and the algorithms are proven to be reversible and ergodic. Monte Carlo simulations of steady field random obstacle electrophoresis are performed and the results are presented.

关键词： DNA electrophoresis knot macromolecules metropolis algorithm Monte Carlo simulation self-avoiding walk

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Revealing a deep connection between factorization and saturation: New insight into modeling high-energy proton-proton and nucleus-nucleus scattering in the EPOS4 framework

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Physical Review C 2023年第6期108卷 064903-064903页

作者： K. Werner SUBATECH Nantes University IN2P3/CNRS IMT Atlantique 44300 Nantes France

It is known that multiple partonic scatterings in high-energy proton-proton (pp) collisions must happen in parallel. However, a rigorous parallel scattering formalism, taking energy sharing properly into account, fails to reproduce factorization, which on the other hand is the basis of almost all pp event generators. In addition, binary scaling in nuclear scatterings is badly violated. These problems are usually “solved” by simply not considering strictly parallel scatterings, which is not a solution. I will report on new ideas (leading to EPOS4), which allow recovering perfectly factorization, and also binary scaling in AA collisions, in a rigorous unbiased parallel scattering formalism. In this new approach, dynamical saturation scales play a crucial role, and this seems to be the missing piece needed to reconcile parallel scattering with factorization. From a practical point of view, one can compute within the EPOS4 framework parton distribution functions (EPOS PDFs) and use them to compute inclusive pp cross sections. So, for the first time, one may compute inclusive jet production (for heavy or light flavors) at very high transverse momentum (pt) and at the same time in the same formalism study flow effects at low pt in high-multiplicity pp events, making EPOS4 a full-scale “general purpose event generator”. I discuss applications, essentially multiplicity dependencies (of particle ratios, mean pt, charm production) which are very strongly affected by the saturation issues discussed in this paper.

关键词： Relativistic heavy-ion collisions Relativistic multiple-particle dynamics metropolis algorithm Monte Carlo methods S-matrix method in transport

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Polarizability of electrically induced magnetic vortex plasma

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Physical Review B 2017年第19期95卷 195136-195136页

作者： P. I. Karpov S. I. Mukhin Department of Theoretical Physics and Quantum Technologies National University of Science and Technology MISiS Leninski Avenue 4 119991 Moscow Russia

Electric field control of magnetic structures, particularly topological defects in magnetoelectric materials, has drawn a great deal of attention in recent years, which has led to experimental success in creation and manipulation by an electric field of single magnetic defects, such as domain walls and skyrmions. In this work we explore a scenario of electric field creation of another type of topological defect, magnetic vortices and antivortices, which are characteristic of materials with easy-plane (XY) symmetry. Each magnetic (anti)vortex in magnetoelectric materials (such as type-II multiferroics) possesses a quantized magnetic and an electric charge, where the former is responsible for interaction between vortices and the latter couples the vortices to an electric field. This property of magnetic vortices opens a peculiar possibility of creation of magnetic vortex plasma by nonuniform electric fields. We show that the electric field, created by a cantilever tip, produces a “magnetic atom” with a localized spatially ordered spot of vortices (“nucleus” of the atom) surrounded by antivortices (“electronic shells”). We analytically find the vortex density distribution profile and temperature dependence of polarizability of this structure and confirm it numerically. We show that electric polarizability of the “magnetic atom” depends on temperature as α∼1/T1−η (η>0), which is consistent with Euclidean random matrix theory prediction.

关键词： Dzyaloshinskii-Moriya interaction Helicoidal magnetic texture Magnetic vortices Magnetoelectric effect XY model Helimagnets Multiferroics Multilayer thin films metropolis algorithm Micromagnetic modeling Simulated annealing

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A Novel Hybrid MCMC Method for Interval-Censored Data

A Novel Hybrid MCMC Method for Interval-Censored Data

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The 2010 International Conference on Computer Application and System Modeling(2010计算机应用与系统建模国际会议 ICCASM 2010)

作者： Guoqing Zheng Jinshan Liu Guoquan Zhang Dept of Mathematics South China Agricultural University Guangzhou China

ISBN: (纸本)9781424472352

Interval-censored data analysis is a hot topic in biomedical statistics and survival analysis and draws much research interest. There are several methods existing in the literature to approach interval-censored data, for example, the Non-Parametric Maximum Likelihood Estimator (NPMLE), the Momentum Estimator, and the generalized log-rank test. Markov chain Monte Carlo (MCMC) methods provides an alternative and prospective solution to this problem due to its generality and simplicity. To avoid random walk behavior, Hybrid Monte Carlo Markov chain (HMCMC) methods introduce an auxiliary momentum vector and implement Hamiitonian dynamics where the potential function is the target density. In this paper, a novel HMCMC schema that combines the Hamiitonian method and the Gibbs sampling is set forth. The new algorithm is then adopted to parameter estimation of interval-censored data. Numerical experiments demonstrate that the new HMCMC schema outperforms other methods not only in accuracy of parameters estimation, but also in computational efficiency.

关键词： interval-censored data markov chain monte carlo hamiitonian method hybrid mcmc gibbs sampling metropolis algorithm

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Monte Carlo Simulations

Monte Carlo Simulations

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作者： David J. Earl Michael W. Deem

A description of Monte Carlo methods for simulation of proteins is given. Advantages and disadvantages of the Monte Carlo approach are presented. The theoretical basis for calculating equilibrium properties of biological molecules by the Monte Carlo method is presented. Some of the standard and some of the more recent ways of performing Monte Carlo on proteins are presented. A discussion of the estimation of errors in properties calculated by Monte Carlo is given. less

关键词： Monte Carlo Simulations Monte Carlo Markov chain metropolis algorithm Protein simulation Stochastic methods

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A PROBABILITY INEQUALITY FOR THE OCCUPATION MEASURE OF A REVERSIBLE MARKOV CHAIN

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ANNALS OF APPLIED PROBABILITY 1995年第1期5卷 37-43页

作者： Dinwoodie, I. H. Tulane Univ Dept Math New Orleans LA 70118 USA

A bound is given for a reversible Markov chain on the probability that the occupation measure of a set exceeds the stationary probability of the set by a positive quantity.

关键词： Markov chain occupation measure expander graphs metropolis algorithm

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Synchronous relaxation for parallel Ising spin simulations 01

Synchronous relaxation for parallel Ising spin simulations

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Proceedings of the fifteenth workshop on Parallel and distributed simulation

作者： Boris Lubachevsky Alan Weiss Bell Labs 600 Mountain Avenue Murray Hill New Jersey

ISBN: (纸本)9780769511047

A new parallel algorithm for simulating Ising spin systems is presented. The sequential prototype is the n-fold way algorithm [2], which is efficient but is hard to parallelize using conservative methods. Our parallel algorithm is optimistic. Unlike other optimistic algorithms, e.g., Time Warp, our algorithm is synchronous. It also belongs to the class of simulations known as “relaxation” [3]; hence it is named “synchronous relaxation.” We derive performance guarantees for this algorithm. If N is the number of PEs, then under weak assumptions we show that the number of correct events processed per unit of time is, on average, at least of order N/ log N. All communication delays, processing time, and busy waits are taken into account.

关键词： metropolis algorithm conservative simulation optimistic simulation computational physics

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SU(4) Heisenberg model on the honeycomb lattice with exchange-frustrated perturbations: Implications for twistronics and Mott insulators

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Physical Review B 2019年第20期100卷 205131-205131页

作者： W. M. H. Natori R. Nutakki R. G. Pereira E. C. Andrade Instituto de Física de São Carlos Universidade de São Paulo São Carlos São Paulo 13560-970 CP 369 Brazil Blackett Laboratory Imperial College London London SW7 2AZ United Kingdom Department of Physics University of Bath Claverton Down Bath BA2 7AY United Kingdom International Institute of Physics and Departamento de Física Teórica e Experimental Universidade Federal do Rio Grande do Norte Natal Rio Grande do Norte 59078-970 Brazil

The SU(4)-symmetric spin-orbital model on the honeycomb lattice was recently studied in connection to correlated insulators such as the eg Mott insulator Ba3CuSb2O9 and the insulating phase of magic-angle twisted bilayer graphene at quarter filling. Here we provide a unified discussion of these systems by investigating an extended model that includes the effects of Hund's coupling and anisotropic, orbital-dependent exchange interactions. Using a combination of mean-field theory, linear flavor-wave theory, and variational Monte Carlo, we show that this model harbors a quantum spin-orbital liquid over a wide parameter regime around the SU(4)-symmetric point. For large Hund's coupling, a ferromagnetic antiferro-orbital ordered state appears, while a valence-bond crystal combined with a vortex orbital state is stabilized by dominant orbital-dependent exchange interactions.

关键词： Quantum spin liquid Graphene Honeycomb lattice Magnetic insulators Heisenberg model Holstein-Primakoff method metropolis algorithm Spin lattice models Variational approach

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Comparison between Bayesian Method and LSE in Estimating MTBF of NC Machine Tools

Comparison between Bayesian Method and LSE in Estimating MTB...

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International Conference on Computer Science and Mechanical Automation

作者： Yingnan KAN Xiaocui ZHU Lihui WANG Binbin XU Zhaojun YANG Hongzhou LI College of Mechanical Science and Engineering Jilin University

ISBN: (纸本)9781467391672

Aiming at the large bias of LSE (Least Squares Estimation) in estimating MTBF (mean time between failures) under a small sample of data, a Bayesian MTBF estimating method is proposed for NC (numerical control) machine tools. To solve difficulty in directly presenting the prior distributions of Weibull parameters, an expert-judgment method which incorporates prior information is developed to indirectly obtain Weibull parameters' prior distributions. Aiming at the problem that analytic solutions to Weibull parameters' posterior distributions and estimators are impossible to obtain, a metropolis algorithm is developed. The iteration procedure of the algorithm is presented;the posterior distribution of each parameter is simulated;and the parameter estimators and MTBF are obtained. Given the actual MTBF as standard value, the proposed method and LSE are applied to the same real case respectively. The results indicate that when sample size n≤10, relative errors of the proposed method lie between 4.43% and 7.19%, which are smaller than those of LSE. The proposed Bayesian MTBF estimating method is better than LSE and suitable for NC machine tools under small samples.

关键词： LSE MTBF NC machine tools Small sample Bayes metropolis algorithm

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