Seminar by Virginie Ehrlacher

Speaker

Virginie Ehrlacher (Ecole des Ponts ParisTech)

Title

Nonlinear reduced basis methods using optimal transport in electronic structure calculations

Date

  • February 13, 2024 16:00 CET+0100 (Europe/Rome)

  • February 13, 2024 10:00 EST-0500 (US/Eastern)

  • February 13, 2024 09:00 CST-0600 (US/Central)

  • February 13, 2024 07:00 PST-0800 (US/Pacific)

Abstract

Electronic structure calculations involving a large number of electrons are computationally very demanding. For example, in the design of machine-learned interatomic potentials for materials or molecules, generating ab initio data for a large number of atomic configurations is often the most time-consuming part. Therefore, there is still a strong need in reducing the computational cost of such methods.

In this talk, I will present recent work which aims at efficiently computing approximate solutions to electronic structire calculation problems. The latter read as eigenvalue problems parametrized by the nuclei positions within a molecule using a nonlinear reduced basis method based on optimal transport. Indeed, standard linear reduced-order modeling techniques do not work in the present context due to the localisation of the electronic density around the nuclei. However, by combining a sparse representation of the solution as a mixture of well-chosen functions with optimal transport methods, we obtain accurate nonlinear reduced-order models which enable to nicely approximate the solution of the problem. I will present theoretical results on the mathematical analysis of the approach on a 1D toy model, in particular on the decay rate of linear and nonlinear Kolmogorov widths. I will finally discuss possible extensions to larger systems.

This is joint work with Maxime Daléry, Geneviève Dusson and Alexei Lozinski.

Recording

Watch the recording on our YouTube channel.