ArticleEntropy (Basel, Switzerland)2025
Geometric Neural Ordinary Differential Equations: From Manifolds to Lie Groups.
Article in Entropy (Basel, Switzerland), 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.
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Abstract
Neural ordinary differential equations (neural ODEs) are a well-established tool for optimizing the parameters of dynamical systems, with applications in image classification, optimal control, and physics learning. Although dynamical systems of interest often evolve on Lie groups and more general differentiable manifolds, theoretical results for neural ODEs are frequently phrased on Rn. We collect recent results for neural ODEs on manifolds and present a unifying derivation of various results that serves as a tutorial to extend existing methods to differentiable manifolds. We also extend the results to the recent class of neural ODEs on Lie groups, highlighting a non-trivial extension of manifold neural ODEs that exploits the Lie group structure.
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