Related papers: Low-rank matrix decompositions for ab initio nucle…
One of the main challenges for ab initio nuclear many-body theory is the growth of computational and storage costs as calculations are extended to heavy, exotic, and structurally complex nuclei. Here, we investigate the factorization of…
Low-rank approximation of a matrix by means of random sampling has been consistently efficient in its empirical studies by many scientists who applied it with various sparse and structured multipliers, but adequate formal support for this…
We present a many-body $GW$ formalism for quantum subsystems embedded in discrete polarizable environments containing up to several hundred thousand atoms described at a fully ab initio random phase approximation level. Our approach is…
The decoupling of multivariate functions is a powerful modeling paradigm for learning multivariate input-output relations from data. For the single-layer case, established CPD-based methods are available, but the multi-layer case remained…
A novel reduced-scaling, general-order coupled-cluster approach is formulated by exploiting hierarchical representations of many-body tensors, combined with the recently suggested formalism of scale-adaptive tensor algebra. Inspired by the…
An ab-initio description of atomic nuclei that solves the nuclear many-body problem for realistic nuclear forces is expected to possess a high degree of predictive power. In this contribution we treat the main obstacle, namely the…
For the problems of low-rank matrix completion, the efficiency of the widely-used nuclear norm technique may be challenged under many circumstances, especially when certain basis coefficients are fixed, for example, the low-rank correlation…
We begin with a brief overview of lattice calculations using chiral effective field theory and some recent applications. We then describe several methods for computing scattering on the lattice. After that we focus on the main goal,…
The purpose of this text is to provide an accessible introduction to a set of recently developed algorithms for factorizing matrices. These new algorithms attain high practical speed by reducing the dimensionality of intermediate…
Ab initio calculations play an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions to quantum chemistry and from atomic and molecular systems to nuclear…
This Review is devoted to the presentation of the exact factorization as a framework employed to study a variety of quantum-mechanical many-body problems. Since its original formulation in the 70s, the main applications of the exact…
Matrix factorization methods are important tools in data mining and analysis. They can be used for many tasks, ranging from dimensionality reduction to visualization. In this paper we concentrate on the use of matrix factorizations for…
In the last years, chiral effective field theory has been successfully developed for and applied to systems with few nucleons. Here, I present a new approach for ab initio calculations of nuclei that combines these precise and systematic…
This review gives a brief introduction to the chiral effective field theory of nuclear forces and atomic nuclei. We discuss the status of the nuclear Hamiltonian derived in this framework and some recent applications in few-nucleon systems.…
We study several variants of decomposing a symmetric matrix into a sum of a low-rank positive semidefinite matrix and a diagonal matrix. Such decompositions have applications in factor analysis and they have been studied for many decades.…
Low rank approximation of matrices has been well studied in literature. Singular value decomposition, QR decomposition with column pivoting, rank revealing QR factorization (RRQR), Interpolative decomposition etc are classical deterministic…
Simulating quantum algorithms on classical computers is challenging when the system size, i.e., the number of qubits used in the quantum algorithm, is moderately large. However, some quantum algorithms and the corresponding quantum circuits…
A comprehensive assessment of theoretical uncertainties defines an important frontier in nuclear structure research. Ideally, theory predictions include uncertainty estimates that take into account truncation effects from both the…
Low-rank plus diagonal (LRPD) decompositions provide a powerful structural model for large covariance matrices, simultaneously capturing global shared factors and localized corrections that arise in covariance estimation, factor analysis,…
Matrix Factorization has emerged as a widely adopted framework for modeling data exhibiting low-rank structures. To address challenges in manifold learning, this paper presents a subspace-constrained quadratic matrix factorization model.…