Geometric Principles for Machine Learning of Dynamical Systems

• URL: http://arxiv.org/abs/2502.13895v1
• Date: Wed, 19 Feb 2025 17:28:40 GMT
• Title: Geometric Principles for Machine Learning of Dynamical Systems
• Authors: Zack Xuereb Conti, David J Wagg, Nick Pepper,
• Abstract summary: This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural generalization. We illustrate this view through the machine learning of linear time-invariant dynamical systems.
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• Abstract: Mathematical descriptions of dynamical systems are deeply rooted in topological spaces defined by non-Euclidean geometry. This paper proposes leveraging structure-rich geometric spaces for machine learning to achieve structural generalization when modeling physical systems from data, in contrast to embedding physics bias within model-free architectures. We consider model generalization to be a function of symmetry, invariance and uniqueness, defined as a topological mapping from state space dynamics to the parameter space. We illustrate this view through the machine learning of linear time-invariant dynamical systems, whose dynamics reside on the symmetric positive definite manifold.

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