Monte Carlo Algorithm Research Articles

A Method of Rapidly Deriving Late-type Contact Binary Parameters and Its Application in the Catalina Sky Survey

With the continuous development of large optical surveys, a large number of light curves of late-type contact binary systems (CBs) have been released. Deriving parameters for CBs using the the Wilson–Devinney program and the PHOEBE program poses a challenge. Therefore, this study developed a method for rapidly deriving light curves based on the Neural Networks model combined with the Hamiltonian Monte Carlo (HMC) algorithm (NNHMC). The neural network was employed to establish the mapping relationship between the parameters and the pregenerated light curves by the PHOEBE program, and the HMC algorithm was used to obtain the posterior distribution of the parameters. The NNHMC method was applied to a large contact binary sample from the Catalina Sky Survey, and a total of 19,104 late-type contact binary parameters were derived. Among them, 5172 have an inclination greater than 70° and a temperature difference less than 400 K. The obtained results were compared with the previous studies for 30 CBs, and there was an essentially consistent goodness-of-fit (R 2) distribution between them. The NNHMC method possesses the capability to simultaneously derive parameters for a vast number of targets. Furthermore, it can provide an extremely efficient tool for the rapid derivation of parameters in future sky surveys involving large samples of CBs.

Eyes on me: how social media use is associated with urban Chinese adolescents' concerns about their physical appearance.

Social media usage carries risks of negative impacts on one's perception of physical attractiveness, especially among adolescents who are developing their self-image. These findings suggest that targeted interventions focusing on attention-seeking behaviors may be effective in addressing appearance-related anxieties among adolescents. We employed Bayesian analysis with Markov Chain Monte Carlo algorithms on survey data from 11,926 middle school students in China. Our findings indicate that while the amount of daily social media usage does not significantly correlate with appearance concerns, the desire for social media attention through interactions such as liking, commenting, and sharing shows a clear positive association. Female adolescents exhibit a higher degree of concern about their physical appearance compared to males. Additionally, behaviors aimed at improving perceived physical attractiveness, such as exercising and using skin-whitening products, are positively associated with increased appearance concerns. These findings suggest that targeted interventions focusing on attention-seeking behaviors may be effective in addressing appearance-related anxieties among adolescents.

Bayesian regression modeling and inference of energy efficiency data: the effect of collinearity and sensitivity analysis

The majority of research predicted heating demand using linear regression models, but they did not give current building features enough context. Model problems such as Multicollinearity need to be checked and appropriate features must be chosen based on their significance to produce accurate load predictions and inferences. Numerous building energy efficiency features correlate with each other and with heating load in the energy efficiency dataset. The standard Ordinary Least Square regression has a problem when the dataset shows Multicollinearity. Bayesian supervised machine learning is a popular method for parameter estimation and inference when frequentist statistical assumptions fail. The prediction of the heating load as the energy efficiency output with Bayesian inference in multiple regression with a collinearity problem needs careful data analysis. The parameter estimates and hypothesis tests were significantly impacted by the Multicollinearity problem that occurred among the features in the building energy efficiency dataset. This study demonstrated several shrinkage and informative priors on likelihood in the Bayesian framework as alternative solutions or remedies to reduce the collinearity problem in multiple regression analysis. This manuscript tried to model the standard Ordinary Least Square regression and four distinct Bayesian regression models with several prior distributions using the Hamiltonian Monte Carlo algorithm in Bayesian Regression Modeling using Stan and the package used to fit linear models. Several model comparison and assessment methods were used to select the best-fit regression model for the dataset. The Bayesian regression model with weakly informative prior is the best-fitted model compared to the standard Ordinary Least Squares regression and other Bayesian regression models with shrinkage priors for collinear energy efficiency data. The numerical findings of collinearity were checked using variance inflation factor, estimates of regression coefficient and standard errors, and sensitivity of priors and likelihoods. It is suggested that applied research in science, engineering, agriculture, health, and other disciplines needs to check the Multicollinearity effect for regression modeling for better estimation and inference.

Revisiting kinetic Monte Carlo algorithms for time-dependent processes: From open-loop control to feedback control.

Simulating stochastic systems with feedback control is challenging due to the complex interplay between the system's dynamics and the feedback-dependent control protocols. We present a single-step-trajectory probability analysis to time-dependent stochastic systems. Based on this analysis, we revisit several time-dependent kinetic Monte Carlo (KMC) algorithms designed for systems under open-loop-control protocols. Our analysis provides a unified alternative proof to these algorithms, summarized into a pedagogical tutorial. Moreover, with the trajectory probability analysis, we present a novel feedback-controlled KMC algorithm that accurately captures the dynamics systems controlled by an external signal based on the measurements of the system's state. Our method correctly captures the system dynamics and avoids the artificial Zeno effect that arises from incorrectly applying the direct Gillespie algorithm to feedback-controlled systems. This work provides a unified perspective on existing open-loop-control KMC algorithms and also offers a powerful and accurate tool for simulating stochastic systems with feedback control.

Variable-order fractional diffusion: Physical interpretation and simulation within the multiple trapping model

The physical interpretation of a variable-order fractional diffusion equation within the framework of the multiple trapping model is presented. This interpretation enables the development of a numerical Monte Carlo algorithm to solve the associated subdiffusion equation. An important feature of the model is variation in energy density of localized states, when the detailed balance condition between localized and mobile particles is satisfied. The variable order anomalous diffusion equations under consideration can be applied to the description of transient subdiffusion in inhomogeneous materials, the order of which depends on the considered spatial and/or time scale. Examples of numerical solutions for different situations are demonstrated. Considering variable-order fractional drift, we calculate and analyze the transient current curves of the time-of-flight method for samples with varying density of localized states.

Reconstruction of gene regulatory networks for Caenorhabditis elegans using tree-shaped gene expression data.

Constructing gene regulatory networks is a widely adopted approach for investigating gene regulation, offering diverse applications in biology and medicine. A great deal of research focuses on using time series data or single-cell RNA-sequencing data to infer gene regulatory networks. However, such gene expression data lack either cellular or temporal information. Fortunately, the advent of time-lapse confocal laser microscopy enables biologists to obtain tree-shaped gene expression data of Caenorhabditis elegans, achieving both cellular and temporal resolution. Although such tree-shaped data provide abundant knowledge, they pose challenges like non-pairwise time series, laying the inaccuracy of downstream analysis. To address this issue, a comprehensive framework for data integration and a novel Bayesian approach based on Boolean network with time delay are proposed. The pre-screening process and Markov Chain Monte Carlo algorithm are applied to obtain the parameter estimates. Simulation studies show that our method outperforms existing Boolean network inference algorithms. Leveraging the proposed approach, gene regulatory networks for five subtrees are reconstructed based on the real tree-shaped datatsets of Caenorhabditis elegans, where some gene regulatory relationships confirmed in previous genetic studies are recovered. Also, heterogeneity of regulatory relationships in different cell lineage subtrees is detected. Furthermore, the exploration of potential gene regulatory relationships that bear importance in human diseases is undertaken. All source code is available at the GitHub repository https://github.com/edawu11/BBTD.git.

Robust self-assembly of nonconvex shapes in two dimensions.

We present fast simulation methods for the self-assembly of complex shapes in two dimensions. The shapes are modeled via a general boundary curve and interact via a standard volume term promoting overlap and an interpenetration penalty. To efficiently realize the Gibbs measure on the space of possible configurations we employ the hybrid Monte Carlo algorithm together with a careful use of signed distance functions for energy evaluation. Motivated by the self-assembly of identical coat proteins of the tobacco mosaic virus which assemble into a helical shell, we design a nonconvex two-dimensional model shape and demonstrate its robust self-assembly into a unique final state. Our numerical experiments reveal certain essential prerequisites for this self-assembly process: blocking and matching (i.e., local repulsion and attraction) of different parts of the boundary, and nonconvexity and handedness of the shape.

Monte Carlo algorithm for spin foam intertwiners

Monte Carlo algorithm for spin foam intertwiners

Covariance-based MCMC for high-dimensional Bayesian updating with Sequential Monte Carlo

Sequential Monte Carlo (SMC) is a reliable method to generate samples from the posterior parameter distribution in a Bayesian updating context. The method samples a series of distributions sequentially, which start from the prior distribution and gradually approach the posterior distribution. Sampling from the distribution sequence is performed through application of a resample-move scheme, whereby the move step is performed using a Markov Chain Monte Carlo (MCMC) algorithm. The preconditioned Crank–Nicolson (pCN) is a popular choice for the MCMC step in high dimensional Bayesian updating problems, since its performance is invariant to the dimension of the prior distribution. This paper proposes two other SMC variants that use covariance information to inform the MCMC distribution proposals and compares their performance to the one of pCN-based SMC. Particularly, a variation of the pCN algorithm that employs covariance information, and the principle component Metropolis Hastings algorithm are considered. These algorithms are combined with an intermittent and recursive updating scheme of the target distribution covariance matrix based on the current MCMC progress. We test the performance of the algorithms in three numerical examples; a two dimensional algebraic example, the estimation of the flexibility of a cantilever beam and the estimation of the hydraulic conductivity field of an aquifer. The results show that covariance-based MCMC algorithms are capable of producing smaller errors in parameter mean and variance and better estimates of the model evidence compared to the pCN approach.

Bayesian Estimation of the Semiparametric Spatial Lag Model

This paper proposes a semiparametric spatial lag model and develops a Bayesian estimation method for this model. In the estimation of the model, the paper combines Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm, random walk Metropolis sampler, and Gibbs sampling techniques to sample all the parameters. The paper conducts numerical simulations to validate the proposed Bayesian estimation theory using a numerical example. The simulation results demonstrate satisfactory estimation performance of the parameter part and the fitting performance of the nonparametric function under different spatial weight matrix settings. Furthermore, the paper applies the constructed model and its estimation method to an empirical study on the relationship between economic growth and carbon emissions in China, illustrating the practical application value of the theoretical results.

The Bellman equation and optimal local flipping strategies for kinetic Ising models

There is a deep connection between thermodynamics, information and work extraction. Ever since the birth of thermodynamics, various types of Maxwell demons have been introduced in order to deepen our understanding of the second law. Thanks to them, it has been shown that there is a deep connection between thermodynamics and information, and between information and work in a thermal system. In this paper we study the problem of energy extraction from a thermodynamic system satisfying detailed balance by an agent with perfect information, e.g. one that has an optimal strategy, given by the solution of the Bellman equation, in the context of Ising models. We call these agents kobolds, in contrast to Maxwell’s demons which do not necessarily need to satisfy detailed balance. This is in stark contrast with typical Monte Carlo algorithms, which choose an action at random at each time step. It is thus natural to compare the behavior of these kobolds to a Metropolis algorithm. For various Ising models, we study numerically and analytically the properties of the optimal strategies, showing that there is a transition in the behavior of the kobold as a function of the parameter characterizing its strategy.

Computing macroscopic reaction rates in reaction-diffusion systems using Monte Carlo simulations.

Stochastic reaction-diffusion models are employed to represent many complex physical, biological, societal, and ecological systems. The macroscopic reaction rates describing the large-scale, long-time kinetics in such systems are effective, scale-dependent renormalized parameters that need to be either measured experimentally or computed by means of a microscopic model. In a Monte Carlo simulation of stochastic reaction-diffusion systems, microscopic probabilities for specific events to happen serve as the input control parameters. To match the results of any computer simulation to observations or experiments carried out on the macroscale, a mapping is required between the microscopic probabilities that define the Monte Carlo algorithm and the macroscopic reaction rates that are experimentally measured. Finding the functional dependence of emergent macroscopic rates on the microscopic probabilities (subject to specific rules of interaction) is a very difficult problem, and there is currently no systematic, accurate analytical way to achieve this goal. Therefore, we introduce a straightforward numerical method of using lattice Monte Carlo simulations to evaluate the macroscopic reaction rates by directly obtaining the count statistics of how many events occur per simulation time step. Our technique is first tested on well-understood fundamental examples, namely, restricted birth processes, diffusion-limited two-particle coagulation, and two-species pair annihilation kinetics. Next we utilize the thus gained experience to investigate how the microscopic algorithmic probabilities become coarse-grained into effective macroscopic rates in more complex model systems such as the Lotka-Volterra model for predator-prey competition and coexistence, as well as the rock-paper-scissors or cyclic Lotka-Volterra model and its May-Leonard variant that capture population dynamics with cyclic dominance motifs. Thereby we achieve a more thorough and deeper understanding of coarse graining in spatially extended stochastic reaction-diffusion systems and the nontrivial relationships between the associated microscopic and macroscopic model parameters, with a focus on ecological systems. The proposed technique should generally provide a useful means to better fit Monte Carlo simulation results to experimental or observational data.

An optimization framework with dimensionality reduction using Markov Chain Monte Carlo and genetic algorithms for groundwater potential assessment

Limited samples and high-dimensional feature spaces often hinder the accuracy of machine learning (ML) models in regional groundwater potential assessment (GPA). This study proposes a novel framework, the GPA with Dimensionality Optimization (GPADO), that optimizes feature dimension reduction to enhance prediction performance. Taking the Jianghan Basin as an example, data on nine continuous variables and five categorical variables influencing the region's GPA were gathered, expanding the feature set to 37 through One-hot encoding for categorical variables. Three scenarios were devised to assess prediction outcomes following various dimensionality reduction approaches. Comparative analysis revealed that a hybrid dimension reduction method, incorporating both continuous and categorical variables, yielded the highest validation set accuracy. Consequently, genetic algorithm and Markov Chain Monte Carlo methods were employed to determine the optimal solution and uncertainties associated with four unknown parameters: the chosen dimension reduction method for continuous and categorical variables, and the number of dimensions retained. Results indicated that utilizing singular value decomposition to reduce categorical variables to three dimensions, coupled with principal component analysis reducing continuous variables to three dimensions, produced the highest model validation accuracy of 0.834 within the GPADO framework. This optimal configuration facilitated automated ML training, resulting in a final validation set accuracy of 0.851 and a test set accuracy of 0.836. The resulting model provided a more precise spatial distribution of groundwater potential and demonstrated the GPADO framework's effectiveness in improving GPA accuracy, particularly in data-scarce regions. The GPADO framework offers a valuable approach for enhancing GPA studies.

Research on Ice Load Optimization based on Monte Carlo Algorithm and Finite Element Analysis

Research on Ice Load Optimization based on Monte Carlo Algorithm and Finite Element Analysis

Evolution of level population in Ar interacting with XFEL pulses: impact of resonant absorptions

Theoretical exploration of the population dynamics at fine-structure levels of Ar atoms interacting with ultrafast ultraintense x-ray free electron laser (XFEL) pulses is conducted. A time-dependent rate equation based on a detailed-level accounting approach is applied for tracking population levels, encompassing microscopic atomic processes such as photoexcitation, radiative decay, photoionization and Auger decay. A Monte Carlo algorithm is implemented to solve large-scale rate equations efficiently. The primary investigation centers on generating Ar17+ through resonant absorption by the second-harmonic radiation of the x-ray pulse. The calculated population ratios of Ar17+ to Ar16+ align well with the experimental measurements (LaForge et al 2021 Phys. Rev. Lett. 127 213202). In comparison to the transition energy of the strongest line, (1s2)0→(1s1/22p3/2)1 of Ar16+, there is a distinct ∼25 eV red shift in the peak ratio, which is attributed to the presence of intricate resonant channels in the lower ionization stages. The results demonstrate the sensitivity of the population ratio Ar17+/Ar16+ to the laser pulse parameters such as x-ray pulse duration, bandwidth and the contribution of second-harmonic radiation, indicating their potential as diagnostic tools in future experiments.

Deep network embedding with dimension selection

Network embedding is a general-purpose machine learning technique that converts network data from non-Euclidean space to Euclidean space, facilitating downstream analyses for the networks. However, existing embedding methods are often optimization-based, with the embedding dimension determined in a heuristic or ad hoc way, which can cause potential bias in downstream statistical inference. Additionally, existing deep embedding methods can suffer from a nonidentifiability issue due to the universal approximation power of deep neural networks. We address these issues within a rigorous statistical framework. We treat the embedding vectors as missing data, reconstruct the network features using a sparse decoder, and simultaneously impute the embedding vectors and train the sparse decoder using an adaptive stochastic gradient Markov chain Monte Carlo (MCMC) algorithm. Under mild conditions, we show that the sparse decoder provides a parsimonious mapping from the embedding space to network features, enabling effective selection of the embedding dimension and overcoming the nonidentifiability issue encountered by existing deep embedding methods. Furthermore, we show that the embedding vectors converge weakly to a desired posterior distribution in the 2-Wasserstein distance, addressing the potential bias issue experienced by existing embedding methods. This work lays down the first theoretical foundation for network embedding within the framework of missing data imputation.

Irreversible MonteCarlo Algorithms for Hard Disk Glasses: From Event-Chain to Collective Swaps.

Equilibrium sampling of the configuration space in disordered systems requires algorithms that bypass the glassy slowing down of the physical dynamics. Irreversible MonteCarlo algorithms breaking detailed balance successfully accelerate sampling in some systems. We first implement an irreversible event-chain MonteCarlo algorithm in a model of continuously polydisperse hard disks. The effect of collective translational moves marginally affects the dynamics and results in a modest speedup that decreases with density. We then propose an irreversible algorithm performing collective particle swaps which outperforms all known MonteCarlo algorithms. We show that these collective swaps can also be used to prepare very dense jammed packings of disks.

Influence of corrugated tube structure and flow rate on the hydrogen absorption performance of metal hydride reactor and structural optimization

The metal hydride bed (MHB) reactor is an effective instrument for storing hydrogen. However, thermal stress causes the cooling tube expansion inside the MHB. The long-term effects will lead to the failure of the cooling tube. To absorb the thermal stress and reduce the deformation of the cooling tubes, this article establishes an MHB reactor with corrugated cooling tubes to study its hydrogen absorption performance. The results prove that some parameters are adversarial and flow rate patterns are complex (such as extreme flow rate and insufficient flow rate) in the hydrogen absorption process of the corrugated tube MHB reactor, which makes it impossible to optimize the structure of the corrugated tube through the gradient method. Under the condition of a fixed corrugated tube volume of 3×10−6m3 and a cooling water volumetric flow rate of 0.5×10−4m3/s, the structural parameters of the corrugated tube are optimized by the Monte Carlo algorithm. According to the optimized results (N=8, ro=4.25 mm, ri=3.98 mm, do=3.17 mm, di=4.33 mm), the hydrogen absorption efficiency of the corrugated tube MHB reactor (reaction fraction 0.758) is 1.36 times that of the straight tube (reaction fraction 0.557) at 560 s. Thus, the corrugated tube can reduce thermal stress and improve the heat transfer effect. This research is beneficial in improving long-term stability, enhancing operational efficiency, and reducing the volume and weight of large MHB reactors.

Efficient determination of free energies of non-ideal solid solutions via hybrid Monte Carlo simulations

Predicting the phase diagram of solid solutions is crucial for understanding their physical behavior under various conditions and at different compositions. However, conventional sampling methods face challenges in efficiently addressing configurational and vibrational disorder for substitutional solid solutions. Additionally, a persistent obstacle has been the lack of a robust theoretical approach for determining the free energy of interstitial solid solutions characterized by the fluid-like diffusion of interstitial species. The method presented in this paper overcomes both hurdles by coupling thermodynamic integration with hybrid Monte Carlo algorithms. We validate the accuracy of the method by computing the free energies of iron alloys described by a Lennard-Jones potential. We also showcase its efficiency by determining the phase diagram of the MgO-CaO system, described by a machine-learning interatomic potential. The high efficiencies achieved with this method pave the way to the determination of the free energies of solid solutions with ab initio accuracy.

Refining tomography with generative neural networks trained from geodynamics

SUMMARY Inverse problems occur in many fields of geophysics, wherein surface observations are used to infer the internal structure of the Earth. Given the non-linearity and non-uniqueness inherent in these problems, a standard strategy is to incorporate a priori information regarding the unknown model. Sometimes a solution is obtained by imposing that the inverted model remains close to a reference model and with smooth lateral variations (e.g. a correlation length or a minimal wavelength are imposed). This approach forbids the presence of strong gradients or discontinuities in the recovered model. Admittedly, discontinuities, such as interfaces between layers, or shapes of geological provinces or of geological objects such as slabs can be a priori imposed or even suggested by the data themselves. This is however limited to a small set of possible constraints. For example, it would be very challenging and computationally expensive to perform a tomographic inversion where the subducting slabs would have possible top discontinuities with unknown shapes. The problem seems formidable because one cannot even imagine how to sample the prior space: is each specific slab continuous or broken into different portions having their own interfaces? No continuous set of parameters seems to describe all the possible interfaces that we could consider. To circumvent these questions, we propose to train a Generative Adversarial neural Network (GAN) to generate models from a geologically plausible prior distribution obtained from geodynamic simulations. In a Bayesian framework, a Markov chain Monte Carlo algorithm is used to sample the low-dimensional model space depicting the ensemble of potential geological models. This enables the integration of intricate a priori information, parametrized within a low-dimensional model space conducive to efficient sampling. The application of this approach is demonstrated in the context of a downscaling problem, where the objective is to infer small-scale geological structures from a smooth seismic tomographic image.