Toward Nonlinear Reduced Basis Methods Using Optimal Transport for Electronic Structure Calculations

Geneviève Dusson, CNRS, Université Bourgogne Franche-Comté
April 24, 2023 3:00 pm LSK 306

Electronic structure calculations, which are needed to predict a large variety of physical properties of molecular and materials systems, are computationally very demanding, as they involve in general (possibly nonlinear) large-scale eigenvalue problems. Such calculations indeed represent a large part of the use of supercomputers. It would therefore be very valuable to reduce the computational cost of such methods.
     In this talk, I will present recent work that aims at efficiently computing approximate solutions to eigenvalue problems parameterized by the nuclei positions in a molecular system using a nonlinear reduced basis method based on optimal transport–so far for a toy model in 1D. Indeed, unlike in many applications where solutions for a given parameter can be efficiently approximated by linear combinations of solutions for other parameters, this approach does not work in electronic structure due to the localisation of the electronic density around the nuclei. However, by combining a sparse representation of the solution as a mixture of chosen functions with optimal transport methods, we manage to nicely approximate the solution of the problem. I will illustrate the method with a few numerical results.

Refreshments will be served preceding the talk, starting at 2:30.

This lecture will also be broadcast via Zoom.
Zoom meeting link.
Meeting ID: 616 0351 7027
Passcode: 390647