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pith:2026:KA3KABDAVKQEFFT2DLIZGHFGVL
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Watch your neighbors: Training statistically accurate chaotic systems with local phase space information

Andrus Giraldo, Deok-Sun Lee, Joon-Hyuk Ko

A surrogate model for chaotic dynamics is trained by matching pushforward distributions of local phase space coverings under maximum mean discrepancy to achieve both accurate Jacobians and long-term statistics.

arxiv:2605.14405 v1 · 2026-05-14 · cs.LG · math.DS

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Claims

C1strongest claim

Our method constructs a local covering of a chaotic attractor in phase space and analyzes the expansion and contraction of these coverings under the dynamics. The surrogate model is trained by minimizing the maximum mean discrepancy between the pushforward distributions of the coverings under the surrogate and ground-truth dynamics. Experiments show that our method significantly improves Jacobian accuracy while remaining competitive with state-of-the-art statistically accurate dynamics learning methods.

C2weakest assumption

That the chosen local coverings are sufficiently representative of the attractor and that minimizing MMD on their pushforwards will simultaneously enforce accurate Jacobians without introducing new biases in the learned dynamics.

C3one line summary

The framework trains chaotic surrogates by minimizing MMD between pushforward distributions of local phase-space coverings under the model and ground truth, yielding improved Jacobian accuracy while staying competitive on statistical fidelity.

References

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[1] H. D. I. Abarbanel, R. Brown, and M. B. Kennel. Variation of Lyapunov exponents on a strange attractor.J Nonlinear Sci, 1(2):175–199, 1991 1991
[2] H. D. I. Abarbanel, R. Brown, and M. B. Kennel. Local Lyapunov exponents computed from observed data.J Nonlinear Sci, 2(3):343–365, 1992 1992
[3] K. T. Alligood, T. Sauer, and J. A. Yorke.Chaos: An Introduction to Dynamical Systems, chapter 2.1 Mathematical Models. Textbooks in Mathematical Sciences. Springer, New York, 1996 1996
[4] M. Ataei, A. Khaki-Sedigh, B. Lohmann, and C. Lucas. Estimating the Lyapunov exponents of chaotic time series: A model based method. In2003 European Control Conference (ECC), pages 3106–3111, 2003 2003
[5] D. Ayers, J. Lau, J. Amezcua, A. Carrassi, and V . Ojha. Supervised machine learning to estimate instabilities in chaotic systems: Estimation of local Lyapunov exponents.Quarterly Journal of the Royal 2023

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First computed 2026-05-17T23:39:07.435703Z
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5036a00460aaa042967a1ad1931ca6aaf1caccebd4e6c117cb64cf05f90fd599

Aliases

arxiv: 2605.14405 · arxiv_version: 2605.14405v1 · doi: 10.48550/arxiv.2605.14405 · pith_short_12: KA3KABDAVKQE · pith_short_16: KA3KABDAVKQEFFT2 · pith_short_8: KA3KABDA
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Canonical record JSON
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