5 papers
Cut-off Jastrow Factors and Spectral Barron Regularity of Coulombic Electronic Wave Functions
Virginie Ehrlacher
We study the spectral Barron regularity of Coulombic electronic eigenfunctions after extraction of a cut-off Jastrow factor. Let \(H=-Δ+V\) be an \(N\)-electron Coulomb Hamiltonian…
Low-complexity approximations with least-squares formulation of the time-dependent Schr{ö}dinger equation
Mi-Song Dupuy, Virginie Ehrlacher, Clément Guillot
We propose new methods designed to numerically approximate the solution to the time dependent Schr{ö}dinger equation, based on two types of ansatz: tensors, and approximation by a…
Comparison between tensor methods and neural networks in electronic structure calculations
Mathias Dus, Geneviève Dusson, Virginie Ehrlacher +2
This article compares the tensor method density matrix renormalization group (DMRG) with two neural network based methods -namely FermiNet and PauliNet) for determining the ground…
A space-time variational formulation for the many-body electronic Schr{ö}dinger evolution equation
Mi-Song Dupuy, Virginie Ehrlacher, Clément Guillot
We prove in this paper that the solution of the time-dependent Schr{ö}dinger equation can be expressed as the solution of a global space-time quadratic minimization problem that is…
Numerical solution of Poisson partial differential equations in high dimension using two-layer neural networks
Mathias Dus, Virginie Ehrlacher
The aim of this article is to analyze numerical schemes using two-layer neural networks with infinite width for the resolution of the high-dimensional Poisson-Neumann partial diffe…