Manifold-valued function approximation from multiple tangent spaces
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arXiv
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912333020790784 |
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| author | Wang, Hang Vandebril, Raf Van der Veken, Joeri Vannieuwenhoven, Nick |
| author_facet | Wang, Hang Vandebril, Raf Van der Veken, Joeri Vannieuwenhoven, Nick |
| contents | Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that leverages and unifies two prior techniques: (i) approximating a pullback to the tangent space, and (ii) the Riemannian moving least squares method. The core idea of the new scheme is to combine pullbacks to multiple tangent spaces with a weighted Fréchet mean. The effectiveness of this approach is illustrated with numerical experiments on model problems from parametric model order reduction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_12892 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Manifold-valued function approximation from multiple tangent spaces Wang, Hang Vandebril, Raf Van der Veken, Joeri Vannieuwenhoven, Nick Numerical Analysis 65D15, 65D40, 65J99, 46T20, 53B20, 58C25 Approximating a manifold-valued function from samples of input-output pairs consists of modeling the relationship between an input from a vector space and an output on a Riemannian manifold. We propose a function approximation method that leverages and unifies two prior techniques: (i) approximating a pullback to the tangent space, and (ii) the Riemannian moving least squares method. The core idea of the new scheme is to combine pullbacks to multiple tangent spaces with a weighted Fréchet mean. The effectiveness of this approach is illustrated with numerical experiments on model problems from parametric model order reduction. |
| title | Manifold-valued function approximation from multiple tangent spaces |
| topic | Numerical Analysis 65D15, 65D40, 65J99, 46T20, 53B20, 58C25 |
| url | https://arxiv.org/abs/2504.12892 |