Parametric vector flows for registration fields in bounded domains with applications to nonlinear interpolation of shock-dominated flows
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arXiv
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| Format: | Preprint |
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2026
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| author | Labatut, Jon Chapelier, Jean-Baptiste Iollo, Angelo Taddei, Tommaso |
| author_facet | Labatut, Jon Chapelier, Jean-Baptiste Iollo, Angelo Taddei, Tommaso |
| contents | We present a registration procedure for parametric model order reduction (MOR) in two- and three-dimensional bounded domains. In the MOR framework, registration methods exploit solution snapshots to identify a parametric coordinate transformation that improves the approximation of the solution set through linear subspaces. For each training parameter, optimization-based (or variational) registration methods minimize a target function that measures the alignment of the coherent structures of interest (e.g., shocks, shear layers, cracks) for different parameter values, over a family of bijections of the computational domain $Ω$. We consider diffeomorphisms $Φ$ that are vector flows of given velocity fields $v$ with vanishing normal component on $\partial Ω$; we rely on a sensor to extract appropriate point clouds from the solution snapshots and we develop an expectation-maximization procedure to simultaneously solve the point cloud matching problem and to determine the velocity $v$ (and thus the bijection $Φ$); finally, we combine our registration method with the nonlinear interpolation technique of [Iollo, Taddei, J. Comput. Phys., 2022] to perform accurate interpolations of fluid dynamic fields in the presence of shocks. Numerical results for a two-dimensional inviscid transonic flow past a NACA airfoil and a three-dimensional viscous transonic flow past an ONERA M6 wing illustrate the many elements of the methodology and demonstrate the effectiveness of nonlinear interpolation for shock-dominated fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_22712 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Parametric vector flows for registration fields in bounded domains with applications to nonlinear interpolation of shock-dominated flows Labatut, Jon Chapelier, Jean-Baptiste Iollo, Angelo Taddei, Tommaso Fluid Dynamics Numerical Analysis 76J20, 90C26, 65M60 We present a registration procedure for parametric model order reduction (MOR) in two- and three-dimensional bounded domains. In the MOR framework, registration methods exploit solution snapshots to identify a parametric coordinate transformation that improves the approximation of the solution set through linear subspaces. For each training parameter, optimization-based (or variational) registration methods minimize a target function that measures the alignment of the coherent structures of interest (e.g., shocks, shear layers, cracks) for different parameter values, over a family of bijections of the computational domain $Ω$. We consider diffeomorphisms $Φ$ that are vector flows of given velocity fields $v$ with vanishing normal component on $\partial Ω$; we rely on a sensor to extract appropriate point clouds from the solution snapshots and we develop an expectation-maximization procedure to simultaneously solve the point cloud matching problem and to determine the velocity $v$ (and thus the bijection $Φ$); finally, we combine our registration method with the nonlinear interpolation technique of [Iollo, Taddei, J. Comput. Phys., 2022] to perform accurate interpolations of fluid dynamic fields in the presence of shocks. Numerical results for a two-dimensional inviscid transonic flow past a NACA airfoil and a three-dimensional viscous transonic flow past an ONERA M6 wing illustrate the many elements of the methodology and demonstrate the effectiveness of nonlinear interpolation for shock-dominated fields. |
| title | Parametric vector flows for registration fields in bounded domains with applications to nonlinear interpolation of shock-dominated flows |
| topic | Fluid Dynamics Numerical Analysis 76J20, 90C26, 65M60 |
| url | https://arxiv.org/abs/2601.22712 |