Related papers: Principled interpolation of Green's functions lear…
We present a numerically efficient technique to evaluate the Green's function for extended two dimensional systems without relying on periodic boundary conditions. Different regions of interest, or `patches', are connected using self energy…
We propose a simple interpolation-based method for the efficient approximation of gradients in neural ODE models. We compare it with the reverse dynamic method (known in the literature as "adjoint method") to train neural ODEs on…
We extend the concept of the multichannel Dyson equation that we have recently derived to model photoemission spectra by coupling the one- and the three-body Green's functions, to higher-order Green's functions and to other spectroscopies.…
A classical problem in acoustic (and electromagnetic) scattering concerns the evaluation of the Green's function for the Helmholtz equation subject to impedance boundary conditions on a half-space. The two principal approaches used for…
We investigate state feedback and observation for infinite-dimensional linear systems, including a variety of partial differential equations with boundary control and observation. We extend the modulating function approach to…
We use a diagrammatic hopping expansion to calculate finite-temperature Green functions of the Bose-Hubbard model which describes bosons in an optical lattice. This technique allows for a summation of subsets of diagrams, so the divergence…
Many machine/deep learning artificial neural networks are trained to simply be interpolation functions that map input variables to output values interpolated from the training data in a linear/nonlinear fashion. Even when the input/output…
Predicting the evolution of spatiotemporal physical systems from sparse and scattered observational data poses a significant challenge in various scientific domains. Traditional methods rely on dense grid-structured data, limiting their…
Including finite-temperature effects from the electronic degrees of freedom in electronic structure calculations of semiconductors and metals is desired; however, in practice it remains exceedingly difficult when using zero-temperature…
Green's function methods within many-body perturbation theory provide a general framework for treating electronic correlations in excited states. Here we investigate the cumulant form of the one-electron Green's function based on the…
We develop a causal optimization method that ensures causality in numerical calculations of Green's functions in interacting electron systems. Our method removes noncausality of numerical data by finding causal functions closest to the…
An ensemble Green's function formalism, based on the von Neumann density matrix approach, to calculate one-electron excitation spectra of a many-electron system with degenerate ground states is proposed. A set of iterative equations for the…
In this paper, we present a numerical algorithm for the accurate and efficient computation of the convolution of the frequency domain layered media Green's function with a given density function. Instead of compressing the convolution…
We develop a method to learn physical systems from data that employs feedforward neural networks and whose predictions comply with the first and second principles of thermodynamics. The method employs a minimum amount of data by enforcing…
Ordinary differential equations (ODEs), commonly used to characterize the dynamic systems, are difficult to propose in closed-form for many complicated scientific applications, even with the help of domain expert. We propose a fast and…
A rigorous non perturbative adiabatic approximation of the evolution operator in the many-body physics of degenerate systems is derived. This approximation is used to solve the long-standing problem of the choice of the initial states of H0…
In this work we present a numerical method to solve the set of Dyson-like equations arising the context of non-equilibrium Green's functions. The technique is based on the self-consistent solution of the Dyson equations for the interacting…
In this paper, we propose a method to learn a minimizing geodesic within a data manifold. Along the learned geodesic, our method can generate high-quality interpolations between two given data samples. Specifically, we use an autoencoder…
The data-driven discovery of interpretable models approximating the underlying dynamics of a physical system has gained attraction in the past decade. Current approaches employ pre-specified functional forms or basis functions and often…
We present a Green's function technique for studying the nonlinear conductance of a nanocontact system with two electrodes at different chemical potentials. The retarded Green's function for a single-impurity Anderson model with two…