New method learns dynamical systems from finite trajectory data

Researchers have developed a new method for learning ergodic dynamical systems from a single finite trajectory. This approach utilizes nonlinear least squares to estimate the optimal one-step prediction function, providing high-probability guarantees with respect to the invariant measure. The technique extends to higher-order systems and finite-state spaces, and can also be applied to learning Koopman operators. The methodology draws upon statistical learning theory and quantitative ergodic theory for Markov chains, incorporating a concentration inequality for uniformly geometrically ergodic Markov chains. AI

IMPACT This research could advance the ability to model and predict complex systems using limited data, potentially impacting fields that rely on time-series analysis.

RANK_REASON The item is an academic paper published on arXiv detailing a new methodology in statistical learning theory and ergodic theory. [lever_c_demoted from research: ic=1 ai=1.0]

Read on arXiv stat.ML →

• arXiv
• ergodic theory
• Hilbert space
• Invariant measure
• Koopman Operators
• Markov chain
• Markov Processes And Related Fields
• statistical learning theory

• paper
• other

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