arXiv subjects

Kenji Nagata

Publications and source records attributed to Kenji Nagata.

At least 19 recordsLinked to original sources

arXiv2026

Automatic Termination Strategy of Inelastic Neutron-scattering Measurement Using Bayesian Optimization for Bin-width Selection

Currently, an excessive amount of event data is being obtained in four-dimensional inelastic neutron-scattering experiments. A method for automatic bin-width optimization of multidimensional histograms has been developed and recently validated on real inelastic neutron-scattering data. However, measuring beyond the equipment resolution leads to inefficient use of valuable beam time. To improve experimental efficiency, an automatic termination strategy is essential. We propose a Bayesian-optimization-based method to compute a stopping criterion that can support online decisions on whether to continue or terminate an experiment. In the proposed method, the bin-width optimization is performed using Bayesian optimization to efficiently compute the optimal bin widths. The experiment is terminated when the optimal bin widths become smaller than the target resolutions. In numerical experiments using real inelastic neutron-scattering data, the optimal bin widths decrease as the number of events increases. Even the optimal bin widths for data downsampled to 1/5 are comparable with the resolutions limited by the sample size, choppers, and so on. This implies excessive measurement of the inelastic neutron experiments for the moment. Moreover, we found that Bayesian optimization can reduce the search cost to approximately 10% of an exhaustive search in our numerical experiments.

physics.data-an↗

arXiv2025

Bayesian sparse modeling for interpretable prediction of hydroxide ion conductivity in anion-conductive polymer membranes

Anion-conductive polymer membranes have attracted considerable attention as solid electrolytes for alkaline fuel cells and electrolysis cells. Their hydroxide ion conductivity varies depending on factors such as the type and distribution of quaternary ammonium groups, as well as the structure and connectivity of hydrophilic and hydrophobic domains. In particular, the size and connectivity of hydrophilic domains significantly influence the mobility of hydroxide ions; however, this relationship has remained largely qualitative. In this study, we calculated the number of key constituent elements in the hydrophilic and hydrophobic units based on the copolymer composition, and investigated their relationship with hydroxide ion conductivity by using Bayesian sparse modeling. As a result, we successfully identified composition-derived features that are critical for accurately predicting hydroxide ion conductivity.

cond-mat.soft↗

arXiv2025

Sequential Exchange Monte Carlo: A Sampling Method for Bayesian Data Analysis without Parameter Tuning

Bayesian data analysis is widely used across many disciplines, and representative examples in materials science include spectral analysis and sparse modeling. In such applications, the underlying models often become complex and yield multimodal posterior distributions, making efficient sampling from multimodal distributions essential. Replica exchange Monte Carlo has been commonly employed for this purpose; however, its performance strongly depends on difficult parameter tuning, such as the design of the inverse temperature. In this study, we comparatively investigate sampling algorithms that require fewer tuning parameters for Bayesian data analysis in materials science. Specifically, we compare three approaches: non-reversible parallel tempering (NRPT), sequential Monte Carlo samplers (SMCS), and a newly proposed method, sequential exchange Monte Carlo (SEMC). Our results indicate that NRPT can require computational time for parameter tuning, while SMCS requires careful adjustment of the number of MCMC steps at each temperature level. In contrast, SEMC achieves robust convergence across a range of problem settings without additional tuning, demonstrating its practicality for Bayesian inference.

cs.IT↗

arXiv2025

Rapid, Comprehensive Search of Crystalline Phases from X-ray Diffraction in Seconds via GPU-Accelerated Bayesian Variational Inference

In analysis of X-ray diffraction data, identifying the crystalline phase is important for interpreting the material. The typical method is identifying the crystalline phase from the coincidence of the main diffraction peaks. This method identifies crystalline phases by matching them as individual crystalline phases rather than as combinations of crystalline phases, in the same way as the greedy method. If multiple candidates are obtained, the researcher must subjectively select the crystalline phases. Thus, the identification results depend on the researcher's experience and knowledge of materials science. To solve this problem, we have developed a Bayesian estimation method to identify the combination of crystalline phases, taking the entire profile into account. This method estimates the Bayesian posterior probability of crystalline phase combinations by performing an approximate exhaustive search of all possible combinations. It is a method for identifying crystalline phases that takes into account all peak shapes and phase combinations. However, it takes a few hours to obtain the analysis results. The aim of this study is to develop a Bayesian method for crystalline phase identification that can provide results in seconds, which is a practical calculation time. We introduce variational sparse estimation and GPU computing. Our method is able to provide results within 10 seconds even when analysing $2^{50}$ candidate crystalline phase combinations. Furthermore, the crystalline phases identified by our method are consistent with the results of previous studies that used a high-precision algorithm.

cond-mat.mtrl-sci↗

arXiv2024

Mesoscopic Bayesian Inference by Solvable Models

The rapid advancement of data science and artificial intelligence has affected physics in numerous ways, including the application of Bayesian inference, setting the stage for a revolution in research methodology. Our group has proposed Bayesian measurement, a framework that applies Bayesian inference to measurement science with broad applicability across various natural sciences. This framework enables the determination of posterior probability distributions of system parameters, model selection, and the integration of multiple measurement datasets. However, applying Bayesian measurement to real data analysis requires a more sophisticated approach than traditional statistical methods like Akaike information criterion (AIC) and Bayesian information criterion (BIC), which are designed for an infinite number of measurements $N$. Therefore, in this paper, we propose an analytical theory that explicitly addresses the case where $N$ is finite in the linear regression model. We introduce $O(1)$ mesoscopic variables for $N$ observation noises. Using this mesoscopic theory, we analyze the three core principles of Bayesian measurement: parameter estimation, model selection, and measurement integration. Furthermore, by introducing these mesoscopic variables, we demonstrate that the difference in free energies, critical for both model selection and measurement integration, can be analytically reduced by two mesoscopic variables of $N$ observation noises. This provides a deeper qualitative understanding of model selection and measurement integration and further provides deeper insights into actual measurements for nonlinear models. Our framework presents a novel approach to understanding Bayesian measurement results.

physics.data-an↗

arXiv2024

Algebraic Geometrical Analysis of Metropolis Algorithm When Parameters Are Non-identifiable

The Metropolis algorithm is one of the Markov chain Monte Carlo (MCMC) methods that realize sampling from the target probability distribution. In this paper, we are concerned with the sampling from the distribution in non-identifiable cases that involve models with Fisher information matrices that may fail to be invertible. The theoretical adjustment of the step size, which is the variance of the candidate distribution, is difficult for non-identifiable cases. In this study, to establish such a principle, the average acceptance rate, which is used as a guideline to optimize the step size in the MCMC method, was analytically derived in non-identifiable cases. The optimization principle for the step size was developed from the viewpoint of the average acceptance rate. In addition, we performed numerical experiments on some specific target distributions to verify the effectiveness of our theoretical results.

math.ST↗

arXiv2024

Bayesian Inference for Small-Angle Scattering Data II: Core-Shell Samples

Small-angle scattering (SAS) techniques, which utilize neutrons and X-rays, are employed in various scientific fields, including materials science, biochemistry, and polymer physics. During the analysis of SAS data, model parameters that contain information about the sample are estimated by fitting the observational data to a model of sample. Previous research has demonstrated the effectiveness of Bayesian inference in analyzing SAS data using a sphere model. However, compared with the sphere model, the core-shell model, which represents functional nanoparticles, offers higher application potential and greater analytical value. Therefore, in this study, we propose an analytical method for the more complex and practical core-shell model based on Bayesian inference. Through numerical experiments, we evaluated the performance of this method under different conditions, including measurement times, number of data points, and differences in scattering length density. As a result, we clarify the conditions under which accurate estimations are possible.

physics.app-ph↗

arXiv2024

Basis Function Dependence of Estimation Precision for Synchrotron-Radiation-Based M\"ossbauer Spectroscopy

M\"ossbauer spectroscopy is a technique employed to investigate the microscopic properties of materials using transitions between energy levels in the nuclei. Conventionally, in synchrotron-radiation-based M\"ossbauer spectroscopy, the measurement window is decided by the researcher heuristically, although this decision has a significant impact on the shape of the measurement spectra. In this paper, we propose a method for evaluating the precision of the spectral position by introducing Bayesian estimation. The proposed method makes it possible to select the best measurement window by calculating the precision of M\"ossbauer spectroscopy from the data. Based on the results, the precision of the M\"ossbauer center shifts improved by more than three times compared with the results achieved with the conventional simple fitting method using the Lorentzian function.

physics.comp-ph↗

arXiv2024

Rapid and Robust construction of an ML-ready peak feature table from X-ray diffraction data using Bayesian peak-top fitting

To advance the development of materials through data-driven scientific methods, appropriate methods for building machine learning (ML)-ready feature tables from measured and computed data must be established. In materials development, X-ray diffraction (XRD) is an effective technique for analysing crystal structures and other microstructural features that have information that can explain material properties. Therefore, the fully automated extraction of peak features from XRD data without the bias of an analyst is a significant challenge. This study aimed to establish an efficient and robust approach for constructing peak feature tables that follow ML standards (ML-ready) from XRD data. We challenge peak feature extraction in the situation where only the peak function profile is known a priori, without knowledge of the measurement material or crystal structure factor. We utilized Bayesian estimation to extract peak features from XRD data and subsequently performed Bayesian regression analysis with feature selection to predict the material property. The proposed method focused only on the tops of peaks within localized regions of interest (ROIs) and extracted peak features quickly and accurately. This process facilitated the rapid extracting of major peak features from the XRD data and the construction of an ML-ready feature table. We then applied Bayesian linear regression to the maximum energy product $(BH)_{max}$, using the extracted peak features as the explanatory variable. The outcomes yielded reasonable and robust regression results. Thus, the findings of this study indicated that \textit{004} peak height and area were important features for predicting $(BH)_{max}$.

cond-mat.mtrl-sci↗

arXiv2024

Quantitative Selection of Sample Structures in Small-Angle Scattering Using Bayesian Methods

Small-angle scattering (SAS) is a key experimental technique for analyzing nano-scale structures in various materials.In SAS data analysis, selecting an appropriate mathematical model for the scattering intensity is critical, as it generates a hypothesis of the structure of the experimental sample. Traditional model selection methods either rely on qualitative approaches or are prone to overfitting.This paper introduces an analytical method that applies Bayesian model selection to SAS measurement data, enabling a quantitative evaluation of the validity of mathematical models.We assess the performance of our method through numerical experiments using artificial data for multicomponent spherical materials, demonstrating that our proposed method analysis approach yields highly accurate and interpretable results.We also discuss the ability of our method to analyze a range of mixing ratios and particle size ratios for mixed components, along with its precision in model evaluation by the degree of fitting.Our proposed method effectively facilitates quantitative analysis of nano-scale sample structures in SAS, which has traditionally been challenging, and is expected to significantly contribute to advancements in a wide range of fields.

physics.data-an↗

arXiv2023

Bayesian inference to identify crystalline structures for XRD

Crystalline phase structure is essential for understanding the performance and properties of a material. Therefore, this study identified and quantified the crystalline phase structure of a sample based on the diffraction pattern observed when the crystalline sample was irradiated with electromagnetic waves such as X-rays. Conventional analysis necessitates experienced and knowledgeable researchers to shorten the list from many candidate crystalline phase structures. However, the Conventional diffraction pattern analysis is highly analyst-dependent and not objective. Additionally, there is no established method for discussing the confidence intervals of the analysis results. Thus, this study aimed to establish a method for automatically inferring crystalline phase structures from diffraction patterns using Bayesian inference. Our method successfully identified true crystalline phase structures with a high probability from 50 candidate crystalline phase structures. Further, the mixing ratios of selected crystalline phase structures were estimated with a high degree of accuracy. This study provided reasonable results for well-crystallized samples that clearly identified the crystalline phase structures.

cond-mat.mtrl-sci↗

arXiv2023

Bayesian Inference for Small-Angle Scattering Data

In this paper, we propose a method for estimating model parameters using Small-Angle Scattering (SAS) data based on the Bayesian inference. Conventional SAS data analyses involve processes of manual parameter adjustment by analysts or optimization using gradient methods. These analysis processes tend to involve heuristic approaches and may lead to local solutions.Furthermore, it is difficult to evaluate the reliability of the results obtained by conventional analysis methods. Our method solves these problems by estimating model parameters as probability distributions from SAS data using the framework of the Bayesian inference. We evaluate the performance of our method through numerical experiments using artificial data of representative measurement target models.From the results of the numerical experiments, we show that our method provides not only high accuracy and reliability of estimation, but also perspectives on the transition point of estimability with respect to the measurement time and the lower bound of the angular domain of the measured data.

stat.ME↗

arXiv2023

Sequential Experimental Design for Spectral Measurement: Active Learning Using a Parametric Model

In this study, we demonstrate a sequential experimental design for spectral measurements by active learning using parametric models as predictors. In spectral measurements, it is necessary to reduce the measurement time because of sample fragility and high energy costs. To improve the efficiency of experiments, sequential experimental designs are proposed, in which the subsequent measurement is designed by active learning using the data obtained before the measurement. Conventionally, parametric models are employed in data analysis; when employed for active learning, they are expected to afford a sequential experimental design that improves the accuracy of data analysis. However, due to the complexity of the formulas, a sequential experimental design using general parametric models has not been realized. Therefore, we applied Bayesian inference-based data analysis using the exchange Monte Carlo method to realize a sequential experimental design with general parametric models. In this study, we evaluated the effectiveness of the proposed method by applying it to Bayesian spectral deconvolution and Bayesian Hamiltonian selection in X-ray photoelectron spectroscopy. Using numerical experiments with artificial data, we demonstrated that the proposed method improves the accuracy of model selection and parameter estimation while reducing the measurement time compared with the results achieved without active learning or with active learning using the Gaussian process regression.

cs.LG↗

arXiv2023

Bayesian Inference of Absorption Spectra Based on Binomial Distribution

In this paper, we propose a Bayesian spectral deconvolution method for absorption spectra. In conventional analysis, the noise mechanism of absorption spectral data is never considered appropriately. In that analysis, the least-squares method, which assumes Gaussian noise from the perspective of Bayesian statistics, is frequently used. Since Bayesian inference is possible by introducing an appropriate noise model for the data, we consider the absorption process of a single photon to be a Bernoulli trial and develop a Bayesian spectral deconvolution method based on binomial distribution. We have evaluated our method on artificial data under several conditions by numerical experiments. The results show that our method not only allows us to estimate parameters with high accuracy from absorption spectral data, but also to infer them even from absorption spectral data with large absorption rates where the spectral structure is flattened, which was previously impossible to analyze.

stat.ME↗

arXiv2022

Intrinsic regularization effect in Bayesian nonlinear regression scaled by observed data

Occam's razor is a guiding principle that models should be simple enough to describe observed data. While Bayesian model selection (BMS) embodies it by the intrinsic regularization effect (IRE), how observed data scale the IRE has not been fully understood. In the nonlinear regression with conditionally independent observations, we show that the IRE is scaled by observations' fineness, defined by the amount and quality of observed data. We introduce an observable that quantifies the IRE, referred to as the Bayes specific heat, inspired by the correspondence between statistical inference and statistical physics. We derive its scaling relation to observations' fineness. We demonstrate that the optimal model chosen by the BMS changes at critical values of observations' fineness, accompanying the IRE's variation. The changes are from choosing a coarse-grained model to a fine-grained one as observations' fineness increases. Our findings expand an understanding of BMS's typicality when observed data are insufficient.

physics.data-an↗

arXiv2022

Bayesian Spectral Deconvolution of X-Ray Absorption Near Edge Structure Discriminating High- and Low-Energy Domains

In this paper, we propose a Bayesian spectral deconvolution considering the properties of peaks in different energy domains. Bayesian spectral deconvolution regresses spectral data into the sum of multiple basis functions. Conventional methods use a model that treats all peaks equally. However, in X-ray absorption near edge structure (XANES) spectra, the properties of the peaks differ depending on the energy domain, and the specific energy domain of XANES is essential in condensed matter physics. We propose a model that discriminates between the low- and high-energy domains. We also propose a prior distribution that reflects the physical properties. We compare the conventional and proposed models in terms of computational efficiency, estimation accuracy, and model evidence. We demonstrate that our method effectively estimates the number of transition components in the important energy domain, on which the material scientists focus for mapping the electronic transition analysis by first-principles simulation.

stat.ME↗

arXiv2022

Bayesian Inference on Hamiltonian Selections for Mössbauer Spectroscopy

Mössbauer spectroscopy, which provides knowledge related to electronic states in materials, has been applied to various fields such as condensed matter physics and material sciences. In conventional spectral analyses based on least-square fitting, hyperfine interactions in materials have been determined from the shape of observed spectra. In conventional spectral analyses, it is difficult to discuss the validity of the hyperfine interactions and the estimated values. We propose a spectral analysis method based on Bayesian inference for the selection of hyperfine interactions and the estimation of Mössbauer parameters. An appropriate Hamiltonian has been selected by comparing Bayesian free energy among possible Hamiltonians. We have estimated the Mössbauer parameters and evaluated their estimated values by calculating the posterior distribution of each Mössbauer parameter with confidence intervals. We have also discussed the accuracy of the spectral analyses to elucidate the noise intensity dependence of numerical experiments.

physics.comp-ph↗

arXiv2020

Fast Bayesian Deconvolution using Simple Reversible Jump Moves

We propose a Markov chain Monte Carlo-based deconvolution method designed to estimate the number of peaks in spectral data, along with the optimal parameters of each radial basis function. Assuming cases where the number of peaks is unknown, and a sweep simulation on all candidate models is computationally unrealistic, the proposed method efficiently searches over the probable candidates via trans-dimensional moves assisted by annealing effects from replica exchange Monte Carlo moves. Through simulation using synthetic data, the proposed method demonstrates its advantages over conventional sweep simulations, particularly in model selection problems. Application to a set of olivine reflectance spectral data with varying forsterite and fayalite mixture ratios reproduced results obtained from previous mineralogical research, indicating that our method is applicable to deconvolution on real data sets.

stat.ME↗