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Seminar by Virginie Ehrlacher
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    :bdg-primary-line:`Speaker`

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        Virginie Ehrlacher (Ecole des Ponts ParisTech)

    :bdg-primary-line:`Title`

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        Nonlinear reduced basis methods using optimal transport in electronic structure calculations

    :bdg-primary-line:`Date`

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        * 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)

    :bdg-primary-line:`Abstract`

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        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.

    :bdg-primary-line:`Recording`

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        Watch the recording on `our YouTube channel <https://www.youtube.com/watch?v=gYGw8ggIIMw>`_.