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Seminar by Angelo Iollo
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    :bdg-primary-line:`Speaker`

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        Angelo Iollo (University of Bordeaux and Inria Bordeaux Sud-Ouest)

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        Convex Displacement Interpolation for Parametric Fields

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        * March 12, 2024 16:00 CET+0100 (Europe/Rome)
        * March 12, 2024 11:00 EDT-0400 (US/Eastern)
        * March 12, 2024 10:00 CDT-0500 (US/Central)
        * March 12, 2024 08:00 PDT-0700 (US/Pacific)

    :bdg-primary-line:`Abstract`

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        We will present a nonlinear interpolation technique for parametric
        fields that exploits optimal transportation of coherent structures of
        the solution to improve interpolation accuracy and contour the so-called
        Kolmogorov barrier problem. The approach generalizes the nonlinear
        interpolation procedure introduced in (Iollo and Taddei 2022) to
        multi-dimensional parameter domains and to datasets of several
        snapshots. Given a library of high-fidelity simulations, we rely on a
        scalar testing function and on a point set registration method to
        identify coherent structures of the solution field in the form of sorted
        point clouds. Given a new parameter value, we exploit a regression
        method to predict the new point cloud; then, we resort to a
        boundary-aware registration technique to define bijective mappings that
        deform the new point cloud into the point clouds of the neighboring
        elements of the dataset, while preserving the boundary of the domain;
        finally, we define the estimate as a weighted combination of modes
        obtained by composing the neighboring snapshots with the
        previously-built mappings. In our presentation, we will explain in some
        details this approach named Convex Displacement Interpolation and delve
        into its recent expansion into multi-dimensional parameter domains and
        datasets with multiple snapshots, as discussed in (Cucchiara et al.
        2023). Exemples pertaining to compressible flows in high speed regimes
        or viscous incompressible flows with recirculations will be presented.
        
        This work is done in collaboration with Simona Cucchiara, Tommaso
        Taddei, and Haysam Telib.
        
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              :name: ref-Iollo2023
        
              Cucchiara, Simona, Angelo Iollo, Tommaso Taddei, and Haysam Telib.
              2023. “Model Order Reduction by Convex Displacement
              Interpolation.”
        
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              :name: ref-Iollo2022
        
              Iollo, Angelo, and Tommaso Taddei. 2022. “Mapping of Coherent
              Structures in Parameterized Flows by Learning Optimal
              Transportation with Gaussian Models.” *Journal of Computational
              Physics* 471: 111671.

    :bdg-primary-line:`Recording`

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        Watch the recording on `our YouTube channel <https://www.youtube.com/watch?v=2gtws5cx4dg>`_.