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The Deep Fourier Residual (DFR) method is a specific type of variational physics-informed neural networks (VPINNs). It provides a robust neural network-based solution to partial differential equations (PDEs). The DFR strategy is based on…
In this paper, we investigate decentralized non-convex optimization with orthogonal constraints. Conventional algorithms for this setting require either manifold retractions or other types of projection to ensure feasibility, both of which…
We study transport properties of quantum impurity systems using the functional renormalization group. The latter is an RG-based diagrammatic tool to treat Coulomb interactions in a fast and flexible way. Prior applications, which employed a…
The analysis of quasielastic neutrino and antineutrino-nucleus scattering cross sections requires relativistic theoretical descriptions also accounting for the role of final-state interactions (FSI). In the relativistic Green's function…
The damped Gauss-Newton (dGN) algorithm for CANDECOMP/PARAFAC (CP) decomposition can handle the challenges of collinearity of factors and different magnitudes of factors; nevertheless, for factorization of an $N$-D tensor of size $I_1\times…
Determining the properties of molecules and materials is one of the premier applications of quantum computing. A major question in the field is: how might we use imperfect near-term quantum computers to solve problems of practical value? We…
Extended Huckel theory (EHT) along with NEGF (Non-equilibrium Green's function formalism) has been used for modeling coherent transport through molecules. Incorporating dephasing has been proposed to theoretically reproduce experimental…
This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition. We show that, although solution trajectories of gradient-based algorithms may vary depending on the learning task, they behave…
Modern graphics processing units (GPUs) provide an unprecedented level of computing power. In this study, we present a high-performance, multi-GPU implementation of the analytical nuclear gradient for Kohn-Sham time-dependent density…
Using the non-equilibrium Keldysh Green's function formalism, we show that the non-equilibrium charge transport in nanoscopic quantum networks takes place via {\it current eigenmodes} that possess characteristic spatial patterns. We…
The functional renormalization group (FRG) approach is a powerful tool for studies of a large variety of systems, ranging from statistical physics over the theory of the strong interaction to gravity. The practical application of this…
One-particle Green's functions obtained from the self-consistent solution of the Dyson equation can be employed in evaluation of spectroscopic and thermodynamic properties for both molecules and solids. However, typical acceleration…
The theory of Nonequilibrium Green functions (NEGF) has seen a rapid development over the recent three decades. Applications include diverse correlated many-body systems in and out of equilibrium. Very good agreement with experiments and…
A practical algorithm for many-electron systems based on the path-integral renormalization group (PIRG) method is proposed in the real-space finite-difference (RSFD) approach. The PIRG method, developed for investigating strongly correlated…
We consider a distributed non-convex optimization where a network of agents aims at minimizing a global function over the Stiefel manifold. The global function is represented as a finite sum of smooth local functions, where each local…
In this paper, we provide the first convergence guarantee for the factorization approach. Specifically, to avoid the scaling ambiguity and to facilitate theoretical analysis, we optimize over the so-called left-orthogonal TT format which…
A fully quantum mechanical description of the precessional damping of Pt/Co bilayer is presented in the framework of the Keldysh Green function approach using {\it ab initio} electronic structure calculations. In contrast to previous…
Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is…
Two-terminal spintronic devices remain challenging to model under realistic operating conditions, where the interplay of complex electronic structures, correlation effects and bias-driven non-equilibrium dynamics may significantly impact…
A nonlocal quantum-field model is constructed for the system of hydrodynamic equations for incompressible viscous fluid (the stochastic Navier--Stokes (NS) equation and the continuity equation). This model is studied by the following two…