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arXiv · 2601.03010

Mathematical aspects of registration methods in bounded domains

Angelo Iollo·Jon Labatut·Pierre Mounoud·Tommaso Taddei
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Abstract

Registration methods in bounded domains have received significant attention in the model reduction literature, as a valuable tool for nonlinear approximation. The aim of this work is to provide a concise yet complete overview of relevant results for registration methods in $n$-dimensional domains, from the perspective of parametric model reduction. We present a thorough analysis of two classes of methods, vector flows and compositional maps: we discuss the enforcement of the bijectivity constraint and we comment on the approximation properties of the two methods, for Lipschitz $n$-dimensional domains.

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Angelo Iollo, Jon Labatut, Pierre Mounoud, Tommaso Taddei. 2026-01-06. Mathematical aspects of registration methods in bounded domains. https://arxiv.org/abs/2601.03010

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