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This paper presents a tensor-recovery method to solve probabilistic power flow problems. Our approach generates a high-dimensional and sparse generalized polynomial-chaos expansion that provides useful statistical information. The result…

We study the discretization of a linear evolution partial differential equation when its Green function is known. We provide error estimates both for the spatial approximation and for the time stepping approximation. We show that, in fact,…

This paper presents a multilevel tensor compression algorithm called tensor butterfly algorithm for efficiently representing large-scale and high-dimensional oscillatory integral operators, including Green's functions for wave equations and…

Calculations of excited states in Green's function formalism often invoke the diagonal approximation, in which the quasiparticle states are taken from a mean-field calculation. Here, we extend the stochastic approaches applied in the…

In this work, we propose an efficient computational scheme for first-principle quantum transport simulations to evaluate the open-boundary conditions. Its partitioning differentiates from conventional methods in that the contact self-energy…

Optimizing problems in a distributed manner is critical for systems involving multiple agents with private data. Despite substantial interest, a unified method for analyzing the convergence rates of distributed optimization algorithms is…

Starting with the Green's functions found for normal diffusion, we construct exact time-dependent Green's functions for subdiffusive equation (with fractional time derivatives), with the boundary conditions involving a linear combination of…

Computation of the Green's function is crucial to study the properties of quantum many-body systems such as strongly correlated systems. Although the high-precision calculation of the Green's function is a notoriously challenging task on…

The Green's function method which has been originally proposed for linear systems has several extensions to the case of nonlinear equations. A recent extension has been proposed to deal with certain applications in quantum field theory. The…

Nonequilibrium Green's functions represent a promising tool for describing central nuclear reactions. Even at the single-particle level, though, the Green's functions contain more information that computers may handle in the foreseeable…

Constrained counting is a fundamental problem in artificial intelligence. A promising new algebraic approach to constrained counting makes use of tensor networks, following a reduction from constrained counting to the problem of…

We introduce diagrammatic technique for Hubbard nonequilibrium Green functions (NEGF). The formulation is an extension of equilibrium considerations for strongly correlated lattice models to description of current carrying molecular…

Transport properties of strongly correlated quantum systems are of central interest in condensed matter, ultracold atoms and in dense plasmas. There, the proper treatment of strong correlations poses a great challenge to theory. Here, we…

Representations of multivariate functions with low-dimensional functions that depend on subsets of original coordinates (corresponding of different orders of coupling) are useful in quantum dynamics and other applications, especially where…

Many-body quantum systems in nonequilibrium remain one of the frontiers of many-body physics. While there has been significant advances in describing the short-time evolution of these systems using a variety of different numerical…

Radiative corrections to an atom are calculated near a half-space that has arbitrarily-shaped small depositions upon its surface. The method is based on calculation of the classical Green's function of the macroscopic Maxwell equations near…

Within the non-equilibrium Green's function (NEGF) formalism, the Generalized Kadanoff-Baym Ansatz (GKBA) has stood out as a computationally cheap method to investigate the dynamics of interacting quantum systems driven out of equilibrium.…

We develop a causal optimization method that ensures causality in numerical calculations of Green's functions in interacting electron systems. Our method removes noncausality of numerical data by finding causal functions closest to the…

Electronic structure calculations are routinely carried out within the framework of density-functional theory, often with great success. For electrons in reduced dimensions, however, there is still a need for better approximations to the…

Inverse design enables automating the discovery and optimization of devices achieving performance significantly exceeding that of traditional human-engineered designs. However, existing methodologies to inverse-design electromagnetic…