Related papers: Data-driven Low-rank Approximation for Electron-ho…

Reduced modeling of a computationally demanding dynamical system aims at approximating its trajectories, while optimizing the trade-off between accuracy and computational complexity. In this work, we propose to achieve such an approximation…

A complete understanding of a material requires both knowledge of the excited states as well as of the ground state. In particular, the low energy excitations are of utmost importance while studying the electronic, magnetic, dynamical, and…

We introduce a data-driven order reduction method for nonlinear control systems, drawing on recent progress in machine learning and statistical dimensionality reduction. The method rests on the assumption that the nonlinear system behaves…

Modeling a high-dimensional Hamiltonian system in reduced dimensions with respect to coarse-grained (CG) variables can greatly reduce computational cost and enable efficient bottom-up prediction of main features of the system for many…

We demonstrate that a machine learning framework based on kernel ridge regression can encode and predict the self-energy of one-dimensional Hubbard models using only mean-field features such as static and dynamic Hartree-Fock quantities and…

Machine learning (ML) entered the field of computational micromagnetics only recently. The main objective of these new approaches is the automatization of solutions of parameter-dependent problems in micromagnetism such as fast response…

We propose a method to improve the computational and memory efficiency of numerical solvers for the nonequilibrium Dyson equation in the Keldysh formalism. It is based on the empirical observation that the nonequilibrium Green's functions…

Reduced modeling in high-dimensional reproducing kernel Hilbert spaces offers the opportunity to approximate efficiently non-linear dynamics. In this work, we devise an algorithm based on low rank constraint optimization and kernel-based…

Data-driven control algorithms use observations of system dynamics to construct an implicit model for the purpose of control. However, in practice, data-driven techniques often require excessive sample sizes, which may be infeasible in…

Microscopic models of electronic subsystems with orbital degeneracy of energy states and non-diagonal matrix elements of electron interactions (correlated hopping) are considered within the configuration-operator approach. Equations for…

We propose a nonadiabatic time-dependent spin-density functional theory (TDSDFT) approach for studying the single-electron excited states and the ultrafast response of systems with strong electron correlations. The correlations are…

The particle-hole interaction problem is longstanding within time-dependent density functional theory (TDDFT) and leads to extreme errors in the prediction of K-edge X-ray absorption spectra (XAS). We derive a linear-response formalism that…

The adiabatic approximation has formed the basis for much of our understandings of the interaction of light and electrons. The classical non-recoil approximation or quantum mechanical Wolkow states of free electron waves have been routinely…

We consider learning in decentralized heterogeneous networks: agents seek to minimize a convex functional that aggregates data across the network, while only having access to their local data streams. We focus on the case where agents seek…

Many scientific problems involve data exhibiting both temporal and cross-sectional dependencies. While linear dependencies have been extensively studied, the theoretical analysis of regression estimators under nonlinear dependencies remains…

The low-rank approximation is a complexity reduction technique to approximate a tensor or a matrix with a reduced rank, which has been applied to the simulation of high dimensional problems to reduce the memory required and computational…

The electronic exchange-correlation (XC) kernel constitutes a fundamental input for the estimation of a gamut of material properties such as the dielectric characteristics, the thermal and electrical conductivity, or the response to an…

In this work we include electron-electron interaction beyond Hartree-Fock level in our non-equilibrium Green's function approach by a crude form of GW through the Single Plasmon Pole Approximation. This is achieved by treating all…

We study non-linear data-dimension reduction. We are motivated by the classical linear framework of Principal Component Analysis. In nonlinear case, we introduce instead a new kernel-Principal Component Analysis, manifold and feature space…

In this paper, we address the role of electron-electron interactions on the velocities of spin and charge transport in one-dimensional systems typified by conjugated polymers. We employ the Hubbard model to model electron-electron…