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A method for calculating the Kohn--Sham exchange-correlation potential, $v_\text{XC}(\mathbf{r})$, from a given electronic wavefunction is devised and implemented. It requires on input one- and two-electron density matrices and involves…
We apply the adaptive time-dependent Density Matrix Renormalization Group method (tDMRG) to the study of transport properties of quantum-dot systems connected to metallic leads. Finite-size effects make the usual tDMRG description of the…
We solve the time-dependent Schr\"odinger equation by learning the score function, the gradient of the log-probability density, on Bohmian trajectories. In Bohm's formulation of quantum mechanics, particles follow deterministic paths under…
A myriad of phenomena in materials science and chemistry rely on quantum-level simulations of the electronic structure in matter. While moving to larger length and time scales has been a pressing issue for decades, such large-scale…
The incorporation of appropriate inductive bias plays a critical role in learning dynamics from data. A growing body of work has been exploring ways to enforce energy conservation in the learned dynamics by encoding Lagrangian or…
Complex systems in science and engineering sometimes exhibit behavior that changes across different regimes. Traditional global models struggle to capture the full range of this complex behavior, limiting their ability to accurately…
In this paper we show how an infinite system of coupled Toda-type nonlinear differential equations derived by one of us can be used efficiently to calculate the time-dependent pair-correlations in the Ising chain in a transverse field. The…
We establish a time-stepping learning algorithm and apply it to predict the solution of the partial differential equation of motion in micromagnetism as a dynamical system depending on the external field as parameter. The data-driven…
The dissipative dynamics of many-electron systems interacting with a thermal environment has remained a long-standing challenge within time-dependent density functional theory (TDDFT). Recently, the formal foundations of open quantum…
We analytically construct the wave function that, for a given initial state, produces a prescribed density for a quantum ring with two non-interacting particles in a singlet state. In this case the initial state is completely determined by…
A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground state density of a given system. Then, the…
All-atom dynamics simulations are an indispensable quantitative tool in physics, chemistry, and materials science, but large systems and long simulation times remain challenging due to the trade-off between computational efficiency and…
We simulate the dynamics of a single-electron source, modeled as a quantum dot with on-site Coulomb interaction and tunnel coupling to an adjacent lead, in time-dependent density functional theory. Based on this system, we develop a…
Time-series representation learning is a fundamental task for time-series analysis. While significant progress has been made to achieve accurate representations for downstream applications, the learned representations often lack…
In this paper, we investigate the energy minimization model of the ensemble Kohn-Sham density functional theory for metallic systems, in which a pseudo-eigenvalue matrix and a general smearing approach are involved. We study the invariance…
Spatio-temporal forecasting is of great importance in a wide range of dynamical systems applications from atmospheric science, to recent COVID-19 spread modeling. These applications rely on accurate predictions of spatio-temporal structured…
The real-time electronic dynamics on material surfaces is critically important to a variety of applications. However, their simulations have remained challenging for conventional methods such as the time-dependent density-functional theory…
Machine-learned interatomic potentials (MLPs) provide near density functional theory (DFT) accuracy at reduced computational cost, but their reliability depends on representative training data and often deteriorates in transition-state…
Based on recent advancements in using machine learning for classical density functional theory for systems with one-dimensional, planar inhomogeneities, we propose a machine learning model for application in two dimensions (2D) akin to…
By introducing a set of auxiliary equations representing a many-body system, we have derived an extension of the Kohn-Sham scheme for the density functional theory. These equations consist of a Kohn-Sham-type equation determining…