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

We explore the principles of many-body Hamiltonian complexity reduction via downfolding on an effective low-dimensional representation. We present a unique measure of fidelity between the effective (reduced-rank) description and the full…

Principal Component Analysis (PCA) is a widely utilized technique for dimensionality reduction; however, its inherent lack of interpretability-stemming from dense linear combinations of all feature-limits its applicability in many domains.…

Principal Component Analysis is a novel way of of dimensionality reduction. This problem essentially boils down to finding the top k eigen vectors of the data covariance matrix. A considerable amount of literature is found on algorithms…

Principal component analysis (PCA) is an unsupervised method for learning low-dimensional features with orthogonal projections. Multilinear PCA methods extend PCA to deal with multidimensional data (tensors) directly via tensor-to-tensor…

Vertex functions are a crucial ingredient of several forefront many-body algorithms in condensed matter physics. However, the full treatment of their frequency and momentum dependence severely restricts numerical calculations. A significant…

We present a theory for the dynamical evolution of a quantum system coupled to a complex many-body intrinsic system/environment. By modelling the intrinsic many-body system with parametric random matrices, we study the types of effective…

Principal component analysis (PCA) is a widely used unsupervised dimensionality reduction technique in machine learning, applied across various fields such as bioinformatics, computer vision and finance. However, when the response variables…

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…

A low-dimensional representation of thermochemical scalars based on cokurtosis principal component analysis (CoK-PCA) has been shown to effectively capture stiff chemical dynamics in reacting flows relative to the widely used principal…

Quantum phases of naturally-occurring systems exhibit distinctive collective phenomena as manifestation of their many-body correlations, in contrast to our persistent technological challenge to engineer at will such strong correlations…

We perform a principal component analysis (PCA) of two one-dimensional lattice models belonging to distinct nonequilibrium universality classes - directed bond percolation and branching and annihilating random walks with even number of…

The following paper presents two simulation strategies for compressible two-phase or multicomponent flows. One is a full non-equilibrium model in which the pressure and velocity are driven towards the equilibrium at interfaces by numerical…

Deep learning models hold state of the art performance in many fields, yet their design is still based on heuristics or grid search methods that often result in overparametrized networks. This work proposes a method to analyze a trained…

Protein folding -- the problem of predicting the spatial structure of a protein given its sequence of amino-acids -- has attracted considerable research effort in biochemistry in recent decades. In this work, we explore the potential of…

We propose a multiple imputation method based on principal component analysis (PCA) to deal with incomplete continuous data. To reflect the uncertainty of the parameters from one imputation to the next, we use a Bayesian treatment of the…

Principal component analysis (PCA) is arguably the most widely used dimension-reduction method for vector-type data. When applied to a sample of images, PCA requires vectorization of the image data, which in turn entails solving an…

The relative energies of different phases or polymorphs of molecular solids can be small, less than a kiloJoule/mol. Reliable description of such energy differences requires high quality treatment of electron correlations, typically beyond…

This study presents a scalable data-driven algorithm designed to efficiently address the challenging problem of reachability analysis. Analysis of cyber-physical systems (CPS) relies typically on parametric physical models of dynamical…

Principal Component Analysis (PCA) is a cornerstone of dimensionality reduction, yet its classical formulation relies critically on second-order moments and is therefore fragile in the presence of heavy-tailed data and impulsive noise.…

Multivariate binary data is becoming abundant in current biological research. Logistic principal component analysis (PCA) is one of the commonly used tools to explore the relationships inside a multivariate binary data set by exploiting the…