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Monte Carlo evaluation of the continuum limit of the two-point function of two Euclidean Higgs real scalar fields subject to affine quantization

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Physical Review D 2021年第5期104卷 054514-054514页

作者： Riccardo Fantoni John R. Klauder Università di Trieste Dipartimento di Fisica strada Costiera 11 34151 Grignano (Trieste) Italy Department of Physics and Department of Mathematics University of Florida Gainesville Florida 32611-8440 USA

We study canonical and affine versions of the quantized covariant Euclidean Higgs scalar field-theory for two real fields on four dimensional lattices through the Monte Carlo method. We calculate the two-point functio... 详细信息

关键词： Quantum field theory metropolis algorithm Path-integral Monte Carlo

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One-dimensional Monte Carlo dynamics at zero temperature

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JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL 2021年第48期54卷 485001-485001页

作者： Chepelianskii, Alexei D. Majumdar, Satya N. Schawe, Hendrik Trizac, Emmanuel Univ Paris Saclay CNRS Lab Phys Solides F-91405 Orsay France Univ Paris Saclay CNRS LPTMS F-91405 Orsay France CY Cergy Paris Univ CNRS LPTM UMR 8089 F-95000 Cergy France

We investigate, both analytically and with numerical simulations, a Monte Carlo dynamics at zero temperature, where a random walker evolving in continuous space and discrete time seeks to minimize its potential energy, by decreasing this quantity at each jump. The resulting dynamics is universal in the sense that it does not depend on the underlying potential energy landscape, as long as it admits a unique minimum;furthermore, the long time regime does not depend on the details of the jump distribution, but only on its behavior for small jumps. We work out the scaling properties of this dynamics, as embodied by the walker probability density. Our analytical predictions are in excellent agreement with direct Monte Carlo simulations.

关键词： Monte Carlo metropolis algorithm Markov chains

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Simulating Yang-Mills theories with a complex coupling

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Physical Review D 2021年第9期103卷 094505-094505页

作者： Jan M. Pawlowski Manuel Scherzer Christian Schmidt Felix P. G. Ziegler Felix Ziesché Institut für Theoretische Physik Universität Heidelberg Philosophenweg 16 D-69120 Heidelberg Germany ExtreMe Matter Institute EMMI GSI Planckstraße 1 D-64291 Darmstadt Germany Fakultät für Physik Universität Bielefeld Postfach 100131 D-33501 Bielefeld Germany CP3-Origins and Danish IAS Department of Mathematics and Computer Science University of Southern Denmark Campusvej 55 5230 Odense M Denmark

We propose a novel simulation strategy for Yang-Mills theories with a complex coupling, based on the Lefschetz thimble decomposition. We envisage that the approach developed in the present work can also be adapted to QCD at finite density and real-time simulations. Simulations with Lefschetz thimbles offer a potential solution to sign problems in Monte Carlo calculations within many different models with complex actions. We discuss the structure of generalized Lefschetz thimbles for pure Yang-Mills theories with a complex gauge coupling β and show how to incorporate the gauge orbits. We propose to simulate such theories on the union of the tangential manifolds to the relevant Lefschetz thimbles attached to the critical manifolds of the Yang-Mills action. We demonstrate our algorithm on a (1+1)-dimensional U(1) model and discuss how, starting from the main thimble result, successive subleading thimbles can be taken into account via a reweighting approach. While we face a residual sign problem, our novel approach performs exponentially better than the standard reweighting approach.

关键词： Finite temperature field theory Lattice QCD Lattice gauge theory Non-Abelian gauge theories Path integrals Quantum field theory Geometry Lattice field theory metropolis algorithm Real & complex analysis Topology

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Bayes analysis of some important lifetime models using MCMC based approaches when the observations are left truncated and right censored

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RELIABILITY ENGINEERING & SYSTEM SAFETY 2021年 214卷 107747-107747页

作者： Ranjan, Rakesh Sen, Rijji Upadhyay, Satyanshu K. Banaras Hindu Univ DST Ctr Interdisciplinary Math Sci Varanasi Uttar Pradesh India Calcutta Univ Behala Coll Dept Stat Kolkata W Bengal India Banaras Hindu Univ Dept Stat Varanasi Uttar Pradesh India

The paper considers the Bayes analysis of important lifetime models such as the Weibull, the gamma, and the lognormal distributions when the available data are left truncated and right-censored. Weakly informative prior distributions are employed for the purpose. Two well-known Markov chain Monte Carlo based approaches, namely, the metropolis algorithm and the Hamiltonian Monte Carlo technique are used to draw samples from analytically intractable posterior distributions. Besides, the paper does a comparative study of the three entertained models using Bayes factor. The paper has considered calculating the marginal likelihood using bridge sampler algorithm for evaluating the necessary Bayes factor. Finally, a numerical illustration based on a real dataset compares the two algorithms and draws relevant conclusions appropriately.

关键词： Left truncated right censored data Weibull distribution Gamma distribution Lognormal distribution Weakly informative prior metropolis algorithm Hamiltonian Monte Carlo Bayes factor Bridge sampling

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Modelling Dengue Fever Epidemics in Jakarta

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International Journal of Applied and Computational Mathematics 2020年第3期6卷 1-25页

作者： Schäfer, Moritz Götz, Thomas Mathematical Institute University Koblenz-Landau Universitätsstraße 1 Koblenz 56070 Germany

This article thematizes the qualitative estimation of transmission dynamics of Dengue fever. At first, a single-compartment vector-host model for the total infective cases in one homogeneous area has been set up and simplified using a steady-state approximation. Seasonality has been considered in the transmission parameter which is modelled by a Fourier sum. The equilibria of the model and their stability as well as the computation of the basic reproductive number are presented. As a modification, models considering a segmenting of the area in separate districts and their inter-district mobility have been set up, both with and without dependence of the disease transmission parameters on the district. Those have also been analysed in terms of equilibria and stability. Parameter estimation on available Dengue data from Jakarta in the time interval of 2008–2016 using the metropolis algorithm has been done. L₁ and L₂ comparisons show that using the multi-patch model with district-dependent parameters a decent approximation to the infection data is possible. © 2020, Springer Nature India Private Limited.

关键词： Basic reproductive number Dengue fever Epidemiological model metropolis algorithm ODE system

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Unbiased Monte Carlo cluster updates with autoregressive neural networks

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Physical Review Research 2021年第4期3卷 L042024-L042024页

作者： Dian Wu Riccardo Rossi Giuseppe Carleo Institute of Physics École Polytechnique Fédérale de Lausanne (EPFL) Lausanne CH-1015 Switzerland

Efficient sampling of complex high-dimensional probability distributions is a central task in computational science. Machine learning methods like autoregressive neural networks, used with Markov chain Monte Carlo sampling, provide good approximations to such distributions but suffer from either intrinsic bias or high variance. In this Letter, we propose a way to make this approximation unbiased and with low variance. Our method uses physical symmetries and variable-size cluster updates which utilize the structure of autoregressive factorization. We test our method for first- and second-order phase transitions of classical spin systems, showing its viability for critical systems and in the presence of metastable states.

关键词： Frustrated magnetism Artificial neural networks Classical spin models Machine learning metropolis algorithm Monte Carlo methods Variational approach

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Early dark energy resolution to the Hubble tension in light of weak lensing surveys and lensing anomalies

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Physical Review D 2021年第6期103卷 063502-063502页

作者： Riccardo Murgia Guillermo F. Abellán Vivian Poulin Laboratoire Univers & Particules de Montpellier (LUPM) CNRS & Université de Montpellier (UMR-5299) Place Eugène Bataillon F-34095 Montpellier Cedex 05 France

A constant early dark energy (EDE) component contributing a fraction fEDE(zc)∼10% of the energy density of the universe around zc≃3500 and diluting as or faster than radiation afterwards, can provide a simple resolution to the Hubble tension, the ∼5σ discrepancy—in the ΛCDM context—between the H0 value derived from early- and late-universe observations. However, it has been pointed out that including Large-Scale Structure (LSS) data, which are in ∼3σ tension with ΛCDM and EDE cosmologies, might break some parameter degeneracy and alter these conclusions. We reassess the viability of the EDE against a host of high- and low-redshift measurements, by combining LSS observations from recent weak lensing (WL) surveys with CMB, baryon acoustic oscillation (BAO), growth function (FS) and Supernova Ia (SNIa) data. Introducing a model whose only parameter is fEDE(zc), we report in agreement with past work a ∼2σ preference for nonzero fEDE(zc) from Planck CMB data alone, while the tension with the local H0 measurement from sh0es is reduced below 2σ. Adding BAO, FS and SNIa does not affect this conclusion, while the inclusion of a prior on H0 from sh0es increase the preference for EDE over ΛCDM to the ∼3.6σ level. After checking the EDE nonlinear matter power spectrum as predicted by standard semi-analytical algorithms via a dedicated set of N-body simulations, we test the 1-parameter EDE cosmology against WL data. We find that it does not significantly worsen the fit to the S8 measurement as compared to ΛCDM, and that current WL observations do not exclude the EDE resolution to the Hubble tension. We also caution against the interpretation of constraints obtained from combining statistically inconsistent datasets within the ΛCDM cosmology. In light of the CMB lensing anomalies, we show that the lensing-marginalized CMB data also favor nonzero fEDE(zc) at ∼2σ, predicts H0 in 1.4σ agreement with sh0es and S8 in 1.5σ and 0.8σ agreement with kids-viking and des respectively. There

关键词： Axions Cosmic microwave background Cosmological parameters Cosmology Dark energy Evolution of the Universe Large scale structure of the Universe Astrophysical & cosmological simulations metropolis algorithm Monte Carlo methods Numerical simulations in gravitation & astrophysics

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Efficient modeling of trivializing maps for lattice ϕ4 theory using normalizing flows: A first look at scalability

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Physical Review D 2021年第9期104卷 094507-094507页

作者： Luigi Del Debbio Joe Marsh Rossney Michael Wilson Higgs Centre for Theoretical Physics School of Physics and Astronomy The University of Edinburgh Edinburgh EH9 3FD United Kingdom

General-purpose Markov chain Monte Carlo sampling algorithms suffer from a dramatic reduction in efficiency as the system being studied is driven toward a critical point through, for example, taking the continuum limit. Recently, a series of seminal studies suggested that normalizing flows—a class of deep generative models—can form the basis of a sampling strategy that does not suffer from this “critical slowing down.” The central idea is to use machine learning techniques to build (approximate) trivializing maps, i.e., field transformations that map the theory of interest into a “simpler” theory in which the degrees of freedom decouple. These trivializing maps provide a representation of the theory in which all its nontrivial aspects are encoded within an invertible transformation to a set of field variables whose statistical weight in the path integral is given by a distribution from which sampling is easy. No separate process is required to generate training data for such models, and convergence to the desired distribution is guaranteed through a reweighting procedure such as a metropolis test. From a theoretical perspective, this approach has the potential to become more efficient than traditional sampling since the statistical efficiency of the sampling algorithm is decoupled from the correlation length of the system. The caveat to all of this is that, somehow, the costs associated with the highly nontrivial task of sampling from the path integral of an interacting field theory are transferred to the training of a model to perform this transformation. In a proof-of-principle demonstration on two-dimensional ϕ4 theory, Albergo, Kanwar, and Shanahan [Phys. Rev. D 100, 034515 (2019)] modeled the trivializing map as a sequence of pointwise affine transformations. We pick up this thread, with the aim of quantifying how well we can expect this approach to scale as we increase the number of degrees of freedom in the system. We make several modifications to the origina

关键词： Lattice field theory metropolis algorithm

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Inferring microscale properties of interacting systems from macroscale observations

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Physical Review Research 2021年第4期3卷 043074-043074页

作者： Nazareno Campioni Dirk Husmeier Juan Morales Jennifer Gaskell Colin J. Torney School of Mathematics & Statistics University of Glasgow University Avenue Glasgow G12 8QQ United Kingdom Grupo de Ecología Cuantitativa INIBIOMA-CONICET Universidad Nacional del Comahue Quintral 1250 CP: 8400 San Carlos de Bariloche Río Negro Argentina

Emergent dynamics of complex systems are observed throughout nature and society. The coordinated motion of bird flocks, the spread of opinions, fashions and fads, or the dynamics of an epidemic, are all examples of complex macroscale phenomena that arise from fine-scale interactions at the individual level. In many scenarios, observations of the system can only be made at the macroscale, while we are interested in creating and fitting models of the microscale dynamics. This creates a challenge for inference as a formal mathematical link between the microscale and macroscale is rarely available. Here, we develop an inferential framework that bypasses the need for a formal link between scales and instead uses sparse Gaussian process regression to learn the drift and diffusion terms of an empirical Fokker-Planck equation, which describes the time evolution of the probability density of a macroscale variable. This gives us access to the likelihood of the microscale properties of the physical system and a second Gaussian process is then used to emulate the log-likelihood surface, allowing us to define a fast, adaptive MCMC sampler, which iteratively refines the emulator when needed. We illustrate the performance of our method by applying it to a simple model of collective motion.

关键词： Diffusion Patterns in complex systems Random walks Stochastic inference Stochastic processes Self-propelled particles Coarse graining Fokker–Planck equation Markovian processes metropolis algorithm Monte Carlo methods

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Normalizing flows and the real-time sign problem

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Physical Review D 2021年第11期103卷 114509-114509页

作者： Scott Lawrence Yukari Yamauchi Department of Physics University of Colorado Boulder Colorado 80309 USA Department of Physics University of Maryland College Park Maryland 20742 USA

Normalizing flows have recently been applied to the problem of accelerating Markov chains in lattice field theory. We propose a generalization of normalizing flows that allows them to applied to theories with a sign problem. These complex normalizing flows are closely related to contour deformations (i.e., the generalized Lefschetz thimble method), which been applied to sign problems in the past. We discuss the question of the existence of normalizing flows; they do not exist in the most general case, but we argue that exact normalizing flows are likely to exist for many physically interesting problems, including cases where the Lefschetz thimble decomposition has an intractable sign problem. Finally, normalizing flows can be constructed in perturbation theory. We give numerical results on their effectiveness across a range of couplings for the Schwinger-Keldysh sign problem associated to a real scalar field in 0+1 dimensions.

关键词： Ab initio calculations Lattice field theory metropolis algorithm

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