Related papers: Low-rank matrix decompositions for ab initio nucle…
Nonnegative Matrix Factorization consists in (approximately) factorizing a nonnegative data matrix by the product of two low-rank nonnegative matrices. It has been successfully applied as a data analysis technique in numerous domains, e.g.,…
Quantum computers offer the potential to efficiently simulate the dynamics of quantum systems, a task whose difficulty scales exponentially with system size on classical devices. To assess the potential for near-term quantum computers to…
We compare the theoretical frameworks and the phenomenological applications of the factorization approaches to exclusive $B$ meson decays, which include QCD-improved factorization, perturbative QCD, and soft-collinear effective theory.…
Many applications in scientific computing and data science require the computation of a rank-revealing factorization of a large matrix. In many of these instances the classical algorithms for computing the singular value decomposition are…
An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…
We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…
Nuclear structure and reaction theory are undergoing a major renaissance with advances in many-body methods, realistic interactions with greatly improved links to Quantum Chromodynamics, the advent of high performance computing, and…
Low-rank representation learning has emerged as a powerful tool for recovering missing values in power load data due to its ability to exploit the inherent low-dimensional structures of spatiotemporal measurements. Among various techniques,…
Effective field theories have established themselves as key pillars of modern nuclear physics. They enable a quantitative understanding of the strong nuclear force, provided low-energy constants that parametrize short-distance physics can…
In this paper, we propose a domain decomposition dynamical low-rank method to solve high-dimensional radiative transfer problems and similar kinetic equations. The algorithm uses a separate low-rank approximation on each spatial subdomain,…
Given a limited number of entries from the superposition of a low-rank matrix plus the product of a known fat compression matrix times a sparse matrix, recovery of the low-rank and sparse components is a fundamental task subsuming…
With the recent success of representation learning methods, which includes deep learning as a special case, there has been considerable interest in developing techniques that incorporate known physical constraints into the learned…
We study the decomposition of the Coulomb integrals of periodic systems into a tensor contraction of six matrices of which only two are distinct. We find that the Coulomb integrals can be well approximated in this form already with small…
Through the development of many-body methodology and algorithms, it has become possible to describe quantum systems composed of a large number of particles with great accuracy. Essential to all these methods is the application of auxiliary…
We present new algorithms to detect and correct errors in the lower-upper factorization of a matrix, or the triangular linear system solution, over an arbitrary field. Our main algorithms do not require any additional information or…
We investigate two distinct sources of uncertainty in low-energy nuclear physics calculations and develop ways to account for them. Harmonic oscillator basis expansions are widely used in ab-initio nuclear structure calculations. Finite…
We show how the renormalization group is used to construct a low-momentum nucleon-nucleon interaction V_{low k}, which unifies all potential models used in nuclear structure calculations. V_{low k} can be directly applied to the nuclear…
We describe an algorithm to reduce the cost of auxiliary-field quantum Monte Carlo (AFQMC) calculations for the electronic structure problem. The technique uses a nested low-rank factorization of the electron repulsion integral (ERI). While…
Matrix factorization exploits the idea that, in complex high-dimensional data, the actual signal typically lies in lower-dimensional structures. These lower dimensional objects provide useful insight, with interpretability favored by sparse…
We study self-adjoint operators defined by factorizing second order differential operators in first order ones. We discuss examples where such factorizations introduce singular interactions into simple quantum mechanical models like the…