Related papers: Analytic continuation of Green's functions with a …
Searching for accurate Machine and Deep Learning models is a computationally expensive and awfully energivorous process. A strategy which has been gaining recently importance to drastically reduce computational time and energy consumed is…
We present a detailed study of the real-time dynamics and spectral properties of the one-dimensional fermionic Hubbard model at infinite temperature. Using tensor network simulations in Liouville space, we compute the single-particle…
The imaginary-time Green's function is a building block of various numerical methods for correlated electron systems. Recently, it was shown that a model-independent compact orthogonal representation of the Green's function can be…
Graph neural networks, trained on experimental or calculated data are becoming an increasingly important tool in computational materials science. Networks, once trained, are able to make highly accurate predictions at a fraction of the cost…
We derive an estimator of the spectral density of a functional time series that is the output of a multilayer perceptron neural network. The estimator is motivated by difficulties with the computation of existing spectral density estimators…
Monte Carlo methods are widely used importance sampling techniques for studying complex physical systems. Integrating these methods with deep learning has significantly improved efficiency and accuracy in high-dimensional problems and…
Let $L$ be a second-order, homogeneous, constant (complex) coefficient elliptic system in ${\mathbb{R}}^n$. The goal of this article is provide a qualitative and quantitative study of the nature of the Green function associated with the…
In this paper, we consider a model of impulsive recurrent neural networks with piecewise constant delay. The dynamics are presented by differential equations with discontinuities such as impulses at fixed moments and piecewise constant…
The problem of spin-charge separation is analyzed numerically in the metallic phase of the one-band Hubbard model in one dimension by studying the behavior of the single-particle Green's function and of the spin and charge susceptibilities.…
This article studies the dynamics of the mean-field approximation of continuous random networks. These networks are stochastic integrodifferential equations driven by Gaussian noise. The kernels in the integral operators are realizations of…
We consider a model for 2D electrons in a very strong magnetic field (i.e. projected onto a single Landau level) and a random potential $V$. The computation of the averaged Green function for this system reduces to calculating the averaged…
Solving inverse problems with neural networks benefits from very few theoretical guarantees when it comes to the recovery guarantees. We provide in this work convergence and recovery guarantees for self-supervised neural networks applied to…
Machine learning is a powerful tool to design accurate, highly non-local, exchange-correlation functionals for density functional theory. So far, most of those machine learned functionals are trained for systems with an integer number of…
Deep generative models are rapidly gaining traction in medical imaging. Nonetheless, most generative architectures struggle to capture the underlying probability distributions of volumetric data, exhibit convergence problems, and offer no…
A common theoretical approach to understanding neural networks is to take an infinite-width limit, at which point the outputs become Gaussian process (GP) distributed. This is known as a neural network Gaussian process (NNGP). However, the…
Two of the most widely used electronic structure theory methods, namely Hartree-Fock and Kohn-Sham density functional theory, both requires the iterative solution of a set of Schr\"odinger-like equations. The speed of convergence of such…
We study Green's function and the large time behavior of the one-dimensional Euler-Maxwell System with relaxation. Firstly, we construct the Green's function of linearized system and obtain the optimal time decay rates of its solutions. And…
Neural networks are emerging as a powerful tool for determining the quantum states of interacting many-body fermionic systems. The standard approach trains a neural-network ansatz by minimizing the mean local energy estimated from Monte…
Deep neural networks can represent very different sorts of functions, including complex quantum many-body states. Tensor networks can also represent these states, have more structure and are easier to optimize. However, they can be…
Discovering hidden partial differential equations (PDEs) and operators from data is an important topic at the frontier between machine learning and numerical analysis. This doctoral thesis introduces theoretical results and deep learning…