{
  "abstract": "Deep learning surrogates have become powerful tools for simulating and forecasting complex dynamical systems, yet their utility remains limited by catastrophic error accumulation during long-term autoregressive rollouts. This behavior is partly tied to the nature of the underlying systems: chaotic spatiotemporal systems visit phase space unevenly, with dynamics dominated by recurrent, low-dimensional quiescent states and characterized by rare and dynamically complex regime transitions. Trained under a sample-wise uniform objective, standard neural surrogates allocate their finite capacity to the statistically more numerous low-dimensional quiescent states, systematically under-representing the transient regimes that trigger disproportionate, localized errors. Existing imbalanced-regression methods tackle this issue by reweighting samples according to target-space density. However, statistical target-space rarity does not coincide with the intrinsic dynamical rarity encoded in the recurrence geometry of the attractor. To address this, we introduce Dynamics-Aware Weighting (DAW), a data-centric objective reweighting framework. Using the local dimension $d$ from dynamical systems theory as an a priori measure of a state's dynamical complexity, DAW reshapes the loss landscape to allocate representational capacity toward the sparse, high-$d$ regimes where forecast errors are systematically large. On the chaotic KS equation, DAW consistently outperforms uniform training as well as weighting based on target-space rarity, and its randomly permuted ablation, reducing long-term autoregressive error relative to all baselines. Event-level analysis shows that DAW achieves this by suppressing the localized error amplifications incurred during sharp jumps in the local dimension $d$, which typically accompany complex physical processes such as wave-merging in the KS system.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2608.22277",
  "author_total": 2,
  "authors": [
    {
      "name": "Zhou Fang"
    },
    {
      "name": "Gianmarco Mengaldo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7qndqvgww0rn9.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2608.22277",
  "fulltext_url": null,
  "id": "7qndqvgww0rn9",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2608.22277",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.LG"
    ],
    [
      "arxiv",
      "physics.comp-ph"
    ],
    [
      "openalex",
      "3109|Model Reduction and Neural Networks"
    ]
  ],
  "openalex": "W7204162538",
  "pdf_url": "https://arxiv.org/pdf/2608.22277",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-29",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7qndqvgww0rn9.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:25:31Z",
      "native_id": "2608.22277",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2608.22277"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "arxiv:physics.comp-ph",
      "subfield": "computational"
    }
  ],
  "title": "Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems",
  "title_text": "Dynamics-Aware Weighting for Deep Learning Forecasts of Chaotic Systems",
  "type": "preprint",
  "updated_at": "2026-10-30T12:25:31Z",
  "url": "https://research.draconitic.com/paper/7qndqvgww0rn9",
  "venue": "arXiv",
  "versions": []
}