Manifold-valued function approximation from multiple tangent spaces

2025/04/17 by Wang, Hang, Vandebril, Raf, Van der Veken, Joeri +1
#46T20 #53B20 #58C25 #65D15 #65D40 #65J99 #FOS: Mathematics #Numerical Analysis (math.NA)

paper · doi:10.48550/arxiv.2504.12892

Abstract

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.

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