# Geometric Principles for Machine Learning of Dynamical Systems

arXiv: https://arxiv.org/abs/2502.13895 · HTML: https://mlsanity.com/paper/2502.13895/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- First posted on arXiv 19 Feb 2025.

## Abstract (arXiv)

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.