Related papers: Data-driven Low-rank Approximation for Electron-ho…
Learning kernels in operators from data lies at the intersection of inverse problems and statistical learning, providing a powerful framework for capturing non-local dependencies in function spaces and high-dimensional settings. In contrast…
A method for the calculation of the damping rate due to electron-hole pair excitation for atomic and molecular motion at metal surfaces is presented. The theoretical basis is provided by Time Dependent Density Functional Theory (TDDFT) in…
Traditional linear methods for forecasting multivariate time series are not able to satisfactorily model the non-linear dependencies that may exist in non-Gaussian series. We build on the theory of learning vector-valued functions in the…
Hamiltonian dynamics describe a wide range of physical systems. As such, data-driven simulations of Hamiltonian systems are important for many scientific and engineering problems. In this work, we propose kernel-based methods for…
Functional data analysis almost always involves smoothing discrete observations into curves, because they are never observed in continuous time and rarely without error. Although smoothing parameters affect the subsequent inference,…
We review a recent proposal of a first principles approach to the electronic structure of materials with strong electronic correlations. The scheme combines the GW method with dynamical mean field theory, which enables one to treat strong…
Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…
Signal processing tasks as fundamental as sampling, reconstruction, minimum mean-square error interpolation and prediction can be viewed under the prism of reproducing kernel Hilbert spaces. Endowing this vantage point with contemporary…
Systems of interacting particles or agents have wide applications in many disciplines such as Physics, Chemistry, Biology and Economics. These systems are governed by interaction laws, which are often unknown: estimating them from…
For dynamical systems with a non hyperbolic equilibrium, it is possible to significantly simplify the study of stability by means of the center manifold theory. This theory allows to isolate the complicated asymptotic behavior of the system…
Learning from data has led to a paradigm shift in computational materials science. In particular, it has been shown that neural networks can learn the potential energy surface and interatomic forces through examples, thus bypassing the…
We introduce a new low-dimensional model of high-dimensional numerical simulation data based on low-rank tensor decompositions. Our new model aims to minimize differences between the model data and simulation data as well as functions of…
In this contribution, we extend our framework for analyzing and visualizing correlated many-electron dynamics to non-variational, highly scalable electronic structure method. Specifically, an explicitly time-dependent electronic wave packet…
Exploratory variational pseudopotential density functional calculations are performed for the electronic properties of many-electron systems in the 3D cartesian coordinate grid (CCG). The atom-centered localized gaussian basis set,…
A first-principles approach to describe electron dynamics in open quantum systems driven far from equilibrium via external time-dependent stimuli is introduced. Within this approach, the driven Liouville von Neumann methodology is used to…
The Keldysh formalism for nonequilibrium Green's functions is a powerful theoretical framework for the description of the electronic structure, spectroscopy, and dynamics of strongly correlated systems. However, the underlying Kadanoff-Baym…
We use hyperbolic wavelet regression for the fast reconstruction of high-dimensional functions having only low dimensional variable interactions. Compactly supported periodic Chui-Wang wavelets are used for the tensorized hyperbolic wavelet…
We consider a class of statistical inverse problems involving the estimation of a regression operator from a Polish space to a separable Hilbert space, where the target lies in a vector-valued reproducing kernel Hilbert space induced by an…
To address the impact of electron correlations in the linear and non-linear response regimes of interacting many-electron systems exposed to time-dependent external fields, we study one-dimensional (1D) systems where the interacting problem…
We study one-loop covariant effective action of \say{non-minimally coupled} $\mathcal{N}=1$, $d=4$ Einstein-Maxwell supergravity theory by heat kernel tool. By fluctuating the fields around the classical background, we study the functional…