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Séminaire Equations aux dérivées partielles

organisé par l'équipe Modélisation et contrôle

  • Mathias Dus

    Numerical solution of regular Schrödinger problems in high dimension using two-layer neural networks

    29 avril 2025 - 14:00Salle de conférences IRMA

    The objective of this presentation is to analyse fundamental neural numerical schemes utilising two-layer neural networks for the resolution of some Schrödinger problems, specifically the inversion of the Poisson operator and the eigenproblem for the Schrödinger operator, in the high-dimensional regime. By employing Barron's representation of the solution with a probability measure defined on the set of parameter values, the energy is minimised through a gradient curve dynamic on the 2-Wasserstein space of the set of parameter values defining the neural network. This approach is inspired by the work of Bach and Chizat. It is demonstrated that if the gradient curve converges, then the represented function is the solution of the elliptic equation under consideration. The method is then adapted to solve Schrödinger eigenvalue problems with smooth potentials, introducing a constrained gradient flow. The efficiency of the method is demonstrated through the presentation of numerical experiments in both cases. If time allows it, I will present the conceptual framework underlying the development of FermiNet and PauliNet. These are neural network-based methods whose objective is to solve the Schrödinger eigenvalue problem with Coulombic interaction and an antisymmetry constraint imposed on the wavefunction. Links : • https://hal.science/hal-04089961 • https://arxiv.org/abs/2409.01640 • https://sciencespo.hal.science/CHL/hal-04817039v1 These works are co-written with V. Ehrlacher, Geneviève Dusson, C. Guillot and J. Soffo Wambo.

  • Florian Salin

    TBA

    6 mai 2025 - 14:00Salle 301

  • Felix Kölher

    TBA

    13 mai 2025 - 14:00Salle 301

  • Marius Zeinhofer

    TBA

    20 mai 2025 - 14:00Salle 301

  • Nilo Schwencke

    TBA

    27 mai 2025 - 14:00A confirmer

  • Céline Van Landeghem

    TBA

    3 juin 2025 - 14:00Salle 301

    TBA

  • Ferdinand Thein

    TBA

    25 juin 2025 - 14:00Salle de conférences IRMA

  • Florian De Vuyst

    TBA

    30 septembre 2025 - 14:00Salle de conférences IRMA