Seminar by Angelo Iollo

Speaker

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

Title

Convex Displacement Interpolation for Parametric Fields

Date

  • 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)

Abstract

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.

Cucchiara, Simona, Angelo Iollo, Tommaso Taddei, and Haysam Telib. 2023. “Model Order Reduction by Convex Displacement Interpolation.”

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.

Recording

Watch the recording on our YouTube channel.