Related papers: Data-driven Low-rank Approximation for Electron-ho…
The complexity of molecular dynamics simulations necessitates dimension reduction and coarse-graining techniques to enable tractable computation. The generalized Langevin equation (GLE) describes coarse-grained dynamics in reduced…
We formulate a rigorous method for calculating a nonadiabatic (frequency-dependent) exchange-correlation (XC) kernel required for correct description of both equilibrium and nonequilibrium properties of strongly correlated systems within…
This paper introduces an efficient multi-linear nonparametric (kernel-based) approximation framework for data regression and imputation, and its application to dynamic magnetic-resonance imaging (dMRI). Data features are assumed to reside…
Various representation learning methods for molecular structures have been devised to accelerate data-driven chemistry. However, the representation capabilities of existing methods are essentially limited to atom-level information, which is…
It is challenging to perform system identification on soft robots due to their underactuated, high-dimensional dynamics. In this work, we present a data-driven modeling framework, based on geometric mechanics (also known as gauge theory)…
In this paper, we analyze several experiments that address the effects of electron-electron interactions in 2D electron (hole) systems in the regime of low carrier density. The interaction effects result in renormalization of the effective…
We present a novel kernel-based machine learning algorithm for identifying the low-dimensional geometry of the effective dynamics of high-dimensional multiscale stochastic systems. Recently, the authors developed a mathematical framework…
An efficient technique based on low-rank separated approximations is proposed for computation of three-dimensional integrals arising in the energy deposition model that describes ion-atomic collisions. Direct tensor-product quadrature…
We consider an analytically solvable model of two interacting electrons that allows for the calculation of the exact exchange-correlation kernel of time-dependent density functional theory. This kernel, as well as the corresponding density…
Time-dependent orbital-free DFT is an efficient method for calculating the dynamic properties of large scale quantum systems due to the low computational cost compared to standard time-dependent DFT. We formalize this method by mapping the…
Accurate ab-initio prediction of electronic energies is very expensive for macromolecules by explicitly solving post-Hartree-Fock equations. We here exploit the physically justified local correlation feature in compact basis of small…
Low-lying electronically excited states in metallic and semiconductor nanoparticles continue to be actively investigated because of their relevance in a wide variety of technological applications. However, first-principles electronic…
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 continuous scaling of metal-oxide-semiconductor field-effect transistors (MOSFETs) has led to device geometries where charged carriers are increasingly confined to ever smaller channel cross sections. This development is associated with…
Various methods in statistical learning build on kernels considered in reproducing kernel Hilbert spaces. In applications, the kernel is often selected based on characteristics of the problem and the data. This kernel is then employed to…
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…
First-principles calculations of electron interactions in materials have seen rapid progress in recent years, with electron-phonon (e-ph) interactions being a prime example. However, these techniques use large matrices encoding the…
The recent success of neural networks for solving difficult decision tasks has incentivized incorporating smart decision making "at the edge." However, this work has traditionally focused on neural network inference, rather than training,…
We present a unified theoretical framework for parametric low-rank approximation, a research area devoted to the development of efficient algorithms that act as adaptive alternatives of traditional methods such as Singular Value…
Kernel-based methods enjoy powerful generalization capabilities in handling a variety of learning tasks. When such methods are provided with sufficient training data, broadly-applicable classes of nonlinear functions can be approximated…