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Research questionHow can learned chaotic systems preserve long-term statistics and stability beyond short-term trajectory matching?A learned vector field can match short trajectories and local derivatives while developing incorrect attractors or long-term distributions. Constraining higher-order variation may help, but directly representing that information can be expensive in high-dimensional systems.
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Statistical Machine Learning
Latest papersRecent research connected to this question, newest first.Second-order consistency for learning chaotic dynamics via randomized Jacobian matchingThe source studies randomized perturbation-based Jacobian supervision as a computational alternative to explicit Hessian supervision and tests it in Lorenz systems under limited temporal supervision. Its evidence is restricted to those simulated systems and training conditions and does not establish performance for general chaotic dynamics.research paper · Sep 4, 2026
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