Related papers: Machine learning-based compression of quantum many…

Embeddings provide low-dimensional representations that organize complex function spaces and support generalization. They provide a geometric representation that supports efficient retrieval, comparison, and generalization. In this work we…

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…

This paper examines several applications of principal component analysis (PCA) to physical systems. The first of these demonstrates that the principal components in a basis of appropriate system variables can be employed to identify…

An accurate prediction of the translational and rotational motion of particles suspended in a fluid is only possible if a complete set of correlations for the force coefficients of fluid-particle interaction is known. The present study is…

We outline how principal component analysis (PCA) can be applied to particle configuration data to detect a variety of phase transitions in off-lattice systems, both in and out of equilibrium. Specifically, we discuss its application to…

The Min-Max Fair PCA problem seeks a low-rank representation of multi-group data such that the the approximation error is as balanced as possible across groups. Existing approaches to this problem return a rank-$d$ fair subspace, but lack…

Network data are commonly collected in a variety of applications, representing either directly measured or statistically inferred connections between features of interest. In an increasing number of domains, these networks are collected…

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…

We analyze the computational aspects of detecting topological order in a quantum many-body system. We contrast the widely used topological entanglement entropy with a recently introduced operational definition for topological order based on…

A basic challenge in experimental physics is the extraction of information related to variables that are not directly measured. The challenge is particularly severe in quantum systems where one may be interested in correlations of operators…

While the equilibrium properties, states, and phase transitions of interacting systems are well described by statistical mechanics, the lack of suitable state parameters has hindered the understanding of non-equilibrium phenomena in diverse…

Efficient characterization of highly entangled multi-particle systems is an outstanding challenge in quantum science. Recent developments have shown that a modest number of randomized measurements suffices to learn many properties of a…

Disorder in condensed matter and atomic physics is responsible for a great variety of fascinating quantum phenomena, which are still challenging for understanding, not to mention the relevant dynamical control. Here we introduce proof of…

A computational approach by an implementation of the Principle Component Analysis (PCA) with K-means and Gaussian Mixture (GM) clustering methods from Machine Learning (ML) algorithms to identify structural and dynamical heterogeneities of…

Principal component analysis (PCA) is a widely used dimension reduction technique in machine learning and multivariate statistics. To improve the interpretability of PCA, various approaches to obtain sparse principal direction loadings have…

A physics-based data-driven computational framework for the quantitative analysis of vortex kinematics and vortex-induced loads in vortex-dominated problems is presented. Such flows are characterized by the dominant influence of a small…

We present an approach called guaranteed block autoencoder that leverages Tensor Correlations (GBATC) for reducing the spatiotemporal data generated by computational fluid dynamics (CFD) and other scientific applications. It uses a…

Studying general quantum many-body systems is one of the major challenges in modern physics because it requires an amount of computational resources that scales exponentially with the size of the system.Simulating the evolution of a state,…

Given the notably increasing complexity of mathematical models to study realistic systems and their coupling to their environment that constrains their dynamics, both analytical approaches and numerical methods that build on these models,…

As we continue to find applications where the currently available noisy devices exhibit an advantage over their classical counterparts, the efficient use of quantum resources is highly desirable. The notion of quantum autoencoders was…