Related papers: Non-parametric learning critical behavior in Ising…
Estimating intrinsic dimensionality of data is a classic problem in pattern recognition and statistics. Principal Component Analysis (PCA) is a powerful tool in discovering dimensionality of data sets with a linear structure; it, however,…
We apply unsupervised machine learning techniques, mainly principal component analysis (PCA), to compare and contrast the phase behavior and phase transitions in several classical spin models - the square and triangular-lattice Ising…
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the…
Interacting quantum systems illustrate complex phenomena including phase transitions to novel ordered phases. The universal nature of critical phenomena reduces their description to determining only the transition temperature and the…
Unsupervised learning makes manifest the underlying structure of data without curated training and specific problem definitions. However, the inference of relationships between data points is frustrated by the `curse of dimensionality' in…
In statistical physics, if we successively divide an equilibrium system into two parts, we will face a situation that, within a certain length $\xi$, the physics of a subsystem is no longer the same as the original system. Then the…
It is shown that the von Neumann entropy, a measure of quantum entanglement, does have its classical counterpart in thermodynamic systems, which we call partial entropy. Close to the critical temperature the partial entropy shows perfect…
We study the critical behavior of the entropy production of the Ising model subject to a magnetic field that oscillates in time. The mean-field model displays a phase transition that can be either first or second-order, depending on the…
Principal component analysis (PCA) is a widely used dimension reduction tool in the analysis of many kind of high-dimensional data. It is used in signal processing, mechanical engineering, psychometrics, and other fields under different…
We develop a one-class, deep-learning framework to detect the phase transition and recover critical behavior of the 3D Ising model. A 3D convolutional neural network autoencoder (CAE) is trained on ground-state configurations only, without…
The data-driven characterization of the ``complexity'' present in dynamical systems remains an open problem with broad applications across the physical sciences. We investigate the ``structural complexity'' of the 2D ferromagnetic Ising…
Principal Component Analysis (PCA) is a classical method for reducing the dimensionality of data by projecting them onto a subspace that captures most of their variation. Effective use of PCA in modern applications requires understanding…
Active Infrared thermography (AIRT) is a widely adopted non-destructive testing (NDT) technique for detecting subsurface anomalies in industrial components. Due to the high dimensionality of AIRT data, current approaches employ non-linear…
Principal component analysis (PCA) plays an important role in the analysis of cryo-EM images for various tasks such as classification, denoising, compression, and ab-initio modeling. We introduce a fast method for estimating a compressed…
Principal Component Analysis (PCA) is a method for estimating a subspace given noisy samples. It is useful in a variety of problems ranging from dimensionality reduction to anomaly detection and the visualization of high dimensional data.…
Principal component analysis (PCA) is a fundamental technique for dimensionality reduction and denoising; however, its application to three-dimensional data with arbitrary orientations -- common in structural biology -- presents significant…
Principal component analysis (PCA) aims at estimating the direction of maximal variability of a high-dimensional dataset. A natural question is: does this task become easier, and estimation more accurate, when we exploit additional…
In this study, we computed three critical exponents ($\alpha, \beta, \gamma$) for the 3D Ising model with Metropolis Algorithm using Finite-Size Scaling Analysis on six cube length scales (L=20,30,40,60,80,90), and performed a supervised…
We extend the Prometheus framework for unsupervised phase transition discovery from two-dimensional classical systems to three-dimensional classical systems and quantum many-body systems. Building upon preliminary observations from a 2D…
In many reacting flow systems, the thermo-chemical state-space is known or assumed to evolve close to a low-dimensional manifold (LDM). Various approaches are available to obtain those manifolds and subsequently express the original…