Related papers: Dimensionality reduction of many-body problem usin…

Accurately resolving many-body satellite features in molecular core-level spectra requires theoretical approaches that capture electron correlation both efficiently and systematically. The recently developed time-dependent double…

We review the basics of the coupled-cluster expansion formalism for numerical solutions of the many-body problem, and we outline the principles of an approach directed towards an adequate inclusion of continuum effects in the associated…

In fractured natural formations, the equations governing fluid flow and geomechanics are strongly coupled. Hydrodynamical properties depend on the mechanical configuration, and they are therefore difficult to accurately resolve using…

Subspace clustering refers to the problem of clustering unlabeled high-dimensional data points into a union of low-dimensional linear subspaces, assumed unknown. In practice one may have access to dimensionality-reduced observations of the…

We present an embedding scheme for periodic systems that facilitates the treatment of the physically important part (here the unit cell) with advanced electronic-structure methods, that are computationally too expensive for periodic…

Quantum computing has demonstrated potential for solving complex optimization problems; however, its application to spatial regionalization remains underexplored. Spatial contiguity, a fundamental constraint requiring spatial entities to…

The central problem in electronic structure theory is the computation of the eigenvalues of the electronic Hamiltonian -- an unbounded, self-adjoint operator acting on a Hilbert space of antisymmetric functions. Coupled cluster (CC)…

We propose a reinterpretation and reformulation of the single-particle Green's function in nonrelativistic quantum many-body theory with an emphasis on normalization. By downfolding a correlation function covering all of Fock space into the…

In this paper we propose a unified framework to simultaneously discover the number of clusters and group the data points into them using subspace clustering. Real data distributed in a high-dimensional space can be disentangled into a union…

Many-body perturbation theory provides a powerful framework to study the ground state and thermodynamic properties of nuclear matter as well as associated single-particle potentials and response functions within a systematic order-by-order…

A method for dimension reduction with clustering, classification, or discriminant analysis is introduced. This mixture model-based approach is based on fitting generalized hyperbolic mixtures on a reduced subspace within the paradigm of…

Clustering methods with dimension reduction have been receiving considerable wide interest in statistics lately and a lot of methods to simultaneously perform clustering and dimension reduction have been proposed. This work presents a novel…

We extend coupled-cluster theory performed on top of a Slater determinant breaking rotational symmetry to allow for the exact restoration of the angular momentum at any truncation order. The main objective relates to the description of…

We introduce a dimension reduction method for visualizing the clustering structure obtained from a finite mixture of Gaussian densities. Information on the dimension reduction subspace is obtained from the variation on group means and,…

The Coupled Cluster (CC) method is used to compute the electronic correlation energy in atoms and molecules and often leads to highly accurate results. However, due to its single-reference nature, standard CC in its projected form fails to…

The study of many-body quantum dynamics in strongly-correlated systems is extremely challenging. To date few numerical methods exist which are capable of simulating the non-equilibrium dynamics of two-dimensional quantum systems, in part…

Most dimensionality reduction methods employ frequency domain representations obtained from matrix diagonalization and may not be efficient for large datasets with relatively high intrinsic dimensions. To address this challenge, Correlated…

Decoupling approach presents a novel solution/alternative to the highly time-consuming fluid-thermal-structural simulation procedures when thermal effects and resultant displacements on machine tools are analyzed. Using high dimensional…

We propose a novel probabilistic dimensionality reduction framework that can naturally integrate the generative model and the locality information of data. Based on this framework, we present a new model, which is able to learn a smooth…

Computer vision and machine learning tools offer an exciting new way for automatically analyzing and categorizing information from complex computer simulations. Here we design an ensemble machine learning framework that can independently…