pith:KA3KABDA
Watch your neighbors: Training statistically accurate chaotic systems with local phase space information
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
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.
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.
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.
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| First computed | 2026-05-17T23:39:07.435703Z |
|---|---|
| Builder | pith-number-builder-2026-05-17-v1 |
| Signature | Pith Ed25519
(pith-v1-2026-05) · public key |
| Schema | pith-number/v1.0 |
Canonical hash
5036a00460aaa042967a1ad1931ca6aaf1caccebd4e6c117cb64cf05f90fd599
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curl -sH 'Accept: application/ld+json' https://pith.science/pith/KA3KABDAVKQEFFT2DLIZGHFGVL \
| jq -c '.canonical_record' \
| python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
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Canonical record JSON
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