arXiv:2606.01596v1 Announce Type: cross Abstract: Learning chaotic dynamical systems from data requires more than short-term predictive accuracy: the learned model must preserve the attractor geometry and its invariant statistics. Trajectory (zero-order) and Jacobian (first-order) matching supervise the values and tangent structure of the vector field, but neither constrains how the field bends away from its tangent plane. A model can thus match values and tangents at the supervised states yet curve differently from the truth, remaining locally accurate while drifting toward spurious attractor
This paper represents continued progress in AI's ability to model complex, non-linear systems, which is a foundational challenge for advanced AI applications.
Improved learning of chaotic dynamics could lead to better predictive models in fields ranging from climate to financial markets, and enhance the robustness of AI agents interacting with complex environments.
The proposed method offers a more robust way for AI models to capture the underlying geometric and statistical properties of chaotic systems, moving beyond short-term predictive accuracy discrepancies.
- · AI researchers
- · Quantitative finance
- · Climate modeling
- · Robotics
- · Traditional statistical modeling approaches
AI models become more adept at understanding and predicting complex, non-linear systems.
This improved understanding could lead to more stable and reliable AI control systems for various dynamic processes.
Enhanced AI capability in chaotic dynamics could open new avenues for scientific discovery and advanced engineering, particularly in fields with high complexity and uncertainty.
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Read at arXiv cs.LG