arXiv subjects

Yoh-ichi Mototake

Publications and source records attributed to Yoh-ichi Mototake.

14 recordsLinked to original sources

arXiv2026

Dynamics-Based Intrinsic Signal Model for High-Dimensional, Small-Sample Data

Signal extraction is difficult when the number of variables $N$ is much larger than the number of observations $M$. We address this problem under the working hypothesis that an empirical dataset consists of states sampled from underlying multivariate dynamics. Instead of treating the $M$ observations as points in an $N$-dimensional variable space, we treat the $N$ variables as points in an $M$-dimensional sample-coordinate space, interpreted as an effective time-delay coordinate space of the latent dynamics. This representation allows a large $N$ to provide many points for estimating the variable distribution even when $M$ is small. Transposed singular value decomposition (SVD) and the unsupervised feature-selection method of Taguchi are used to extract variable-side deviations from an estimated Gaussian background as signal candidates. As $M$ is reduced, the effective separation between sampled states increases; contributions from finite-correlation components are expected to decay, whereas sufficiently long-correlation components can persist toward the small-sample limit. We define these persistent components as intrinsic signals and estimate them by extrapolation toward $M=0$. We first tested the method on high-dimensional, small-sample data explicitly generated by a randomised coupling strength globally coupled map (RCS-GCM), for which the long- and short-correlation components were known. The extracted intrinsic signals corresponded to the known long-correlation variables. We then applied the method to The Cancer Genome Atlas (TCGA) pan-kidney gene-expression data, which are not ordinarily treated as data explicitly generated by a dynamical system. Using an SVD component associated with the pathologic-M category, variable-side signal components were extracted from the 20,531-dimensional data even under small-sample conditions.

physics.data-an↗

arXiv2026

Integrating Bayesian Spectral Deconvolution and Expert Scientific Reasoning for Robust Peak Estimation

Spectral deconvolution is essential for extracting peak structures that encode material properties and chemical structures, but conventional automated methods often fail when spectra contain high-intensity noise or unknown background components. In practice, scientists rarely interpret spectra in isolation. Instead, they identify physically meaningful peaks by relating spectral structures to auxiliary information such as physical-property values, chemical structures, and trends across related measurements. Here, we propose a Bayesian framework that integrates spectral deconvolution with a model of expert scientific reasoning. In this work, expert scientific reasoning refers to the practice of evaluating candidate spectral structures by their consistency with independently measured physical-property values, rather than to manual expert intervention during inference. We formalize this reasoning as a physical-property regression layer, implemented using Gaussian process regression, and couple it with Bayesian spectral deconvolution. By averaging the physical-property likelihood over posterior predictive spectra inferred from Bayesian spectral deconvolution, the proposed method selects spectral models according to the consistency between inferred spectral structures and physical-property information. We validate the framework using synthetic spectra with high-intensity noise or unknown backgrounds and infrared spectra of poly(lactic acid). The method recovers physically meaningful peak structures that conventional Bayesian spectral deconvolution misses or misidentifies from spectra alone, including weak peaks in poly(lactic acid) IR spectra related to measured degradation rates. These results demonstrate that integrating expert scientific reasoning with Bayesian spectral deconvolution enables robust peak estimation under conditions where spectrum-only inference is unreliable.

physics.data-an↗

arXiv2026

Unsupervised feature selection using Bayesian Tucker decomposition

In this paper, we proposed Bayesian Tucker decomposition (BTuD) in which residual is supposed to obey Gaussian distribution analogous to linear regression. Although we have proposed an algorithm to perform the proposed BTuD, the conventional higher-order orthogonal iteration can generate Tucker decomposition consistent with the present implementation. Using the proposed BTuD, we can perform unsupervised feature selection successfully applied to various synthetic datasets, global coupled maps with randomized coupling strength, and gene expression profiles. Thus we can conclude that our newly proposed unsupervised feature selection method is promising. In addition to this, BTuD based unsupervised FE is expected to coincide with TD based unsupervised FE that were previously proposed and successfully applied to a wide range of problems.

stat.ML↗

arXiv2025

Uncertainties in Physics-informed Inverse Problems: The Hidden Risk in Scientific AI

Physics-informed machine learning (PIML) integrates partial differential equations (PDEs) into machine learning models to solve inverse problems, such as estimating coefficient functions (e.g., the Hamiltonian function) that characterize physical systems. This framework enables data-driven understanding and prediction of complex physical phenomena. While coefficient functions in PIML are typically estimated on the basis of predictive performance, physics as a discipline does not rely solely on prediction accuracy to evaluate models. For example, Kepler's heliocentric model was favored owing to small discrepancies in planetary motion, despite its similar predictive accuracy to the geocentric model. This highlights the inherent uncertainties in data-driven model inference and the scientific importance of selecting physically meaningful solutions. In this paper, we propose a framework to quantify and analyze such uncertainties in the estimation of coefficient functions in PIML. We apply our framework to reduced model of magnetohydrodynamics and our framework shows that there are uncertainties, and unique identification is possible with geometric constraints. Finally, we confirm that we can estimate the reduced model uniquely by incorporating these constraints.

physics.comp-ph↗

arXiv2024

Procedure to Reveal the Mechanism of Pattern Formation Process by Topological Data Analysis

Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics does not agree one-to-one, and the physical interpretation of the TDA features needs to be set appropriately according to the phenomenon to be analyzed. In this study, we propose an analytical procedure to physically interpret pattern dynamics through TDA and machine learning techniques. The proposed procedure was applied to the process of magnetic domain pattern formation to quantify non-trivial domain pattern classifications and reveal the nature of the underlying dynamics. On the basis of these findings, we also propose a candidate reduction model to understand the nature of magnetic domain formation.

nlin.PS↗

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

Autoregressive with Slack Time Series Model for Forecasting a Partially-Observed Dynamical Time Series

This study delves into the domain of dynamical systems, specifically the forecasting of dynamical time series defined through an evolution function. Traditional approaches in this area predict the future behavior of dynamical systems by inferring the evolution function. However, these methods may confront obstacles due to the presence of missing variables, which are usually attributed to challenges in measurement and a partial understanding of the system of interest. To overcome this obstacle, we introduce the autoregressive with slack time series (ARS) model, that simultaneously estimates the evolution function and imputes missing variables as a slack time series. Assuming time-invariance and linearity in the (underlying) entire dynamical time series, our experiments demonstrate the ARS model's capability to forecast future time series. From a theoretical perspective, we prove that a 2-dimensional time-invariant and linear system can be reconstructed by utilizing observations from a single, partially observed dimension of the system.

stat.ME↗

arXiv2023

Quantifying physical insights cooperatively with exhaustive search for Bayesian spectroscopy of X-ray photoelectron spectra

We analyzed the X-ray photoemission spectra (XPS) of carbon 1s states in graphene and oxygen-intercalated graphene grown on SiC(0001) using Bayesian spectroscopy. To realize highly accurate spectral decomposition of the XPS spectra, we proposed a framework for discovering physical constraints from the absence of prior quantified physical knowledge, in which we designed the prior probabilities based on the found constraints and the physically required conditions. This suppresses the exchange of peak components during replica exchange Monte Carlo iterations and makes possible to decompose XPS in the case where a reliable structure model or a presumable number of components is not known. As a result, we have successfully decomposed XPS of one monolayer (1ML), two monolayers (2ML), and quasi-freestanding 2ML (qfs-2ML) graphene samples deposited on SiC substrates with the meV order precision of the binding energy, in which the posterior probability distributions of the binding energies were obtained distinguishably between the different components of buffer layer even though they are observed as hump and shoulder structures because of their overlapping.

cond-mat.mtrl-sci↗

arXiv2022

Quantitative Prediction of Fracture Toughness $(K_{{\rm I}c})$ of Polymer by Fractography Using Deep Neural Networks

Fracture surfaces provide various types of information about fracture. The fracture toughness $K_{{\rm I}c}$, which represents the resistance to fracture, can be estimated using the three-dimensional (3D) information of a fracture surface, i.e., its roughness. However, this is time-consuming and expensive to obtain the 3D information of a fracture surface; thus, it is desirable to estimate $K_{{\rm I}c}$ from a two-dimensional (2D) image, which can be easily obtained. In recent years, methods of estimating a 3D structure from its 2D image using deep learning have been rapidly developed. In this study, we propose a framework for fractography that directly estimates $K_{{\rm I}c}$ from a 2D fracture surface image using deep neural networks (DNNs). Typically, image recognition using a DNN requires a tremendous amount of image data, which is difficult to acquire for fractography owing to the high experimental cost. To compensate for the limited data, in this study, we used the transfer learning (TL) method, and constructed high-performance prediction models even with a small dataset by transferring machine learning models trained using other large datasets. We found that the regression model obtained using our proposed framework can predict $K_{{\rm I}c}$ in the range of approximately 1-5 [MPa$\sqrt{m}$] with a standard deviation of the estimation error of approximately $\pm$0.37 [MPa$\sqrt{m}$]. The present results demonstrate that the DNN trained with TL opens a new route for quantitative fractography by which parameters of fracture process can be estimated from a fracture surface even with a small dataset. The proposed framework also enables the building of regression models in a few hours. Therefore, our framework enables us to screen a large number of image datasets available in the field of materials science and find candidates that are worth expensive machine learning analysis.

cond-mat.mtrl-sci↗

arXiv2020

Interpretable Conservation Law Estimation by Deriving the Symmetries of Dynamics from Trained Deep Neural Networks

Understanding complex systems with their reduced model is one of the central roles in scientific activities. Although physics has greatly been developed with the physical insights of physicists, it is sometimes challenging to build a reduced model of such complex systems on the basis of insights alone. We propose a novel framework that can infer the hidden conservation laws of a complex system from deep neural networks (DNNs) that have been trained with physical data of the system. The purpose of the proposed framework is not to analyze physical data with deep learning, but to extract interpretable physical information from trained DNNs. With Noether's theorem and by an efficient sampling method, the proposed framework infers conservation laws by extracting symmetries of dynamics from trained DNNs. The proposed framework is developed by deriving the relationship between a manifold structure of time-series dataset and the necessary conditions for Noether's theorem. The feasibility of the proposed framework has been verified in some primitive cases for which the conservation law is well known. We also apply the proposed framework to conservation law estimation for a more practical case that is a large-scale collective motion system in the metastable state, and we obtain a result consistent with that of a previous study.

physics.data-an↗

arXiv2019

Semi-flat minima and saddle points by embedding neural networks to overparameterization

We theoretically study the landscape of the training error for neural networks in overparameterized cases. We consider three basic methods for embedding a network into a wider one with more hidden units, and discuss whether a minimum point of the narrower network gives a minimum or saddle point of the wider one. Our results show that the networks with smooth and ReLU activation have different partially flat landscapes around the embedded point. We also relate these results to a difference of their generalization abilities in overparameterized realization.

cs.LG↗

arXiv2018

Bayesian Spectral Deconvolution Based on Poisson Distribution: Bayesian Measurement and Virtual Measurement Analytics (VMA)

In this paper, we propose a new method of Bayesian measurement for spectral deconvolution, which regresses spectral data into the sum of unimodal basis function such as Gaussian or Lorentzian functions. Bayesian measurement is a framework for considering not only the target physical model but also the measurement model as a probabilistic model, and enables us to estimate the parameter of a physical model with its confidence interval through a Bayesian posterior distribution given a measurement data set. The measurement with Poisson noise is one of the most effective system to apply our proposed method. Since the measurement time is strongly related to the signal-to-noise ratio for the Poisson noise model, Bayesian measurement with Poisson noise model enables us to clarify the relationship between the measurement time and the limit of estimation. In this study, we establish the probabilistic model with Poisson noise for spectral deconvolution. Bayesian measurement enables us to perform virtual and computer simulation for a certain measurement through the established probabilistic model. This property is called "Virtual Measurement Analytics(VMA)" in this paper. We also show that the relationship between the measurement time and the limit of estimation can be extracted by using the proposed method in a simulation of synthetic data and real data for XPS measurement of MoS$_2$.

eess.SP↗

arXiv2018

Bayesian Hamiltonian Selection in X-ray Photoelectron Spectroscopy

Core-level X-ray photoelectron spectroscopy (XPS) is a useful measurement technique for investigating the electronic states of a strongly correlated electron system. Usually, to extract physical information of a target object from a core-level XPS spectrum, we need to set an effective Hamiltonian by physical consideration so as to express complicated electron-to-electron interactions in the transition of core-level XPS, and manually tune the physical parameters of the effective Hamiltonian so as to represent the XPS spectrum. Then, we can extract physical information from the tuned parameters. In this paper, we propose an automated method for analyzing core-level XPS spectra based on the Bayesian model selection framework, which selects the effective Hamiltonian and estimates its parameters automatically. The Bayesian model selection, which often has a large computational cost, was carried out by the exchange Monte Carlo sampling method. By applying our proposed method to the 3$d$ core-level XPS spectra of Ce and La compounds, we confirmed that our proposed method selected an effective Hamiltonian and estimated its parameters appropriately; these results were consistent with conventional knowledge obtained from physical studies. Moreover, using our proposed method, we can also evaluate the uncertainty of its estimation values and clarify why the effective Hamiltonian was selected. Such information is difficult to obtain by the conventional analysis method.

cond-mat.str-el↗

arXiv2018

Finding Continuity and Discontinuity in Fish Schools via Integrated Information Theory

Collective behaviour is known to be the result of diverse dynamics and is sometimes likened to a living system. Although many studies have revealed the dynamics of various collective behaviours, their main focus was on the information process inside the collective, not on the whole system itself. For example, the qualitative difference between two elements and three elements as a system has rarely been investigated. Tononi et al. have proposed Integrated Information Theory (IIT) to measure the degree of consciousness $Φ$. IIT postulates that the amount of information loss caused by certain partitions is equivalent to the degree of information integration in the system. This measure is not only useful for estimating the degree of consciousness but can also be applied to more general network systems. Here we applied IIT (in particular, IIT 3.0 using PyPhi) to analyse real fish schools ({\it Plecoglossus altivelis}). Our hypothesis in this study is a very simple one: a living system evolves to raise its $Φ$ value. If we accept this hypothesis, IIT reveals the existence of continuous and discontinuous properties as group size varies. For example, leadership in the fish school emerged for a school size of four or above; but not below three. Furthermore, this transition was not observed by measuring mutual information or in a simple Boids model. This result suggests that integrated information $Φ$ can reveal some inherent properties which cannot be observed using other measures. We also discuss how the fish recognition of the figure-ground relation, that is, what determines the relevant ON and OFF states, may reveal various optimal paths for obtaining the functional evolution of collective behaviour.

physics.soc-ph↗