Geometric Principles for Machine Learning of Dynamical Systems
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866917929385197568 |
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| author | Conti, Zack Xuereb Wagg, David J Pepper, Nick |
| author_facet | Conti, Zack Xuereb Wagg, David J Pepper, Nick |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_13895 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometric Principles for Machine Learning of Dynamical Systems Conti, Zack Xuereb Wagg, David J Pepper, Nick Machine Learning 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. |
| title | Geometric Principles for Machine Learning of Dynamical Systems |
| topic | Machine Learning |
| url | https://arxiv.org/abs/2502.13895 |