Pith Number

pith:A7UYUFT2

pith:2025:A7UYUFT2V7XILCJFG6ZGNBNFAM

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Artifacts of Numerical Integration in Learning Dynamical Systems

Bing-Ze Lu, Richard Tsai

The stability region of a numerical integrator can distort learned dynamical systems, turning a damped oscillator into an anti-damped one with reversed direction.

arxiv:2507.14491 v4 · 2025-07-19 · math.NA · cs.LG · cs.NA

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Claims

C1strongest claim

a damped oscillatory system may be incorrectly identified as having 'anti-damping' and exhibiting a reversed oscillation direction, even though it adequately fits the given data points. This paper shows that the stability region of the selected integrator will distort the nature of the learned dynamics.

C2weakest assumption

The learning procedure formulates an optimization problem that uses a numerical integrator to compute predicted trajectories and assess mismatch with observed data points; the analysis further assumes the underlying system is autonomous.

C3one line summary

Numerical integration schemes used in optimizing models of dynamical systems from sampled data can distort learned stability properties, inducing anti-damping artifacts in originally damped systems.

References

43 extracted · 43 resolved · 1 Pith anchors

[1] G. Ariel, B. Engquist, H.-O. Kreiss, and R. Tsai. Multiscale computations for highly oscillatory problems. In Multiscale modeling and simulation in science, pages 237–287. Springer Berlin Heidelberg B 2009

[2] T. Bertalan, F. Dietrich, I. Mezi´c, and I. G. Kevrekidis. On learning hamiltonian systems from data. Chaos: An Interdisciplinary Journal of Nonlinear Science, 29(12), 2019 2019

[3] S. L. Brunton, J. L. Proctor, and J. N. Kutz. Discovering governing equations from data by sparse identification of nonlinear dynamical systems.Proceedings of the national academy of sciences, 113(15) 2016

[4] M. Calvo, A. Murua, and J. Sanz-Serna. Modified equations for odes. Contem- porary Mathematics, 172:63–63, 1994 1994

[5] R. T. Chen, Y . Rubanova, J. Bettencourt, and D. K. Duvenaud. Neural ordinary differential equations. Advances in neural information processing systems, 31, 2018 2018

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Receipt and verification

First computed	2026-08-06T01:14:38.547389Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

07e98a167aafee85892537b26685a503239a6defc0def0e491f17aeb2d892772

Aliases

arxiv: 2507.14491 · arxiv_version: 2507.14491v4 · doi: 10.48550/arxiv.2507.14491 · pith_short_12: A7UYUFT2V7XI · pith_short_16: A7UYUFT2V7XILCJF · pith_short_8: A7UYUFT2

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Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/A7UYUFT2V7XILCJFG6ZGNBNFAM \
  | 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())"
# expect: 07e98a167aafee85892537b26685a503239a6defc0def0e491f17aeb2d892772

Canonical record JSON

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  "metadata": {
    "abstract_canon_sha256": "d53de8d20933acce96745e1f68b03ed9156dd73aad55d4eea557ee4bb952fb77",
    "cross_cats_sorted": [
      "cs.LG",
      "cs.NA"
    ],
    "license": "http://creativecommons.org/licenses/by/4.0/",
    "primary_cat": "math.NA",
    "submitted_at": "2025-07-19T05:23:39Z",
    "title_canon_sha256": "d3d2f7ce2876e6ccf260417f0360c3f791afe51c8c9ecddb2acfcf21a7cca438"
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  "source": {
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    "kind": "arxiv",
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