Metraipolis › archive › dc_10270ec4e83e

Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction — arXiv:2608.11237

Source: arXiv (en)
Original: https://arxiv.org/abs/2608.11237
License (as archived): CC0-1.0
Archived: 2026-10-19T05:15:14.396Z
SHA-256 of the archived text: d7f7728237f82238a4b278f0505e81a44b7f1334f153e7538e02eb37ecaddd07
Stable URL of this page: https://metraipolis.com/documento/dc_10270ec4e83e

How to cite

Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction — arXiv:2608.11237 — arXiv (en), https://arxiv.org/abs/2608.11237 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_10270ec4e83e (Metraipolis archive dc_10270ec4e83e, sha256 d7f7728237f82238a4b278f0505e81a44b7f1334f153e7538e02eb37ecaddd07)

BibTeX

@misc{dc10270ec4e83e,
  title = {Geometry-aware Incremental Neural Operator for Long-Horizon PDE prediction — arXiv:2608.11237},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2608.11237},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_10270ec4e83e; sha256 d7f7728237f82238a4b278f0505e81a44b7f1334f153e7538e02eb37ecaddd07},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2608.11237. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Neural operators have shown strong potential for learning solution operators of partial differential equations (PDEs). However, long-horizon autoregressive prediction remains challenging: local errors accumulate as spectral inconsistency, phase misalignment, or mean drift. Existing methods mainly improve state representations and operator backbones, while leaving the repeatedly applied latent transition increment weakly structured, allowing spectral errors and unstable channel couplings to accumulate during rollout. To address these issues, we propose a geometry-aware incremental neural operator (GeoIncNO) for stable long-horizon PDE prediction. GeoIncNO predicts latent increments for residual advancement and uses lightweight low-rank projectors to regulate channel coupling within active frequency bands derived from the increment spectral energy distribution. To reduce physical-space reconstruction errors, GeoIncNO further introduces a mean--fluctuation decoupled reconstruction mechanism, where stable mean structures and dynamic fluctuations are fused separately, and phase correction is applied only to the zero-mean fluctuation component. Extensive experiments on six PDE benchmarks, covering 1D, 2D, and 3D dynamical systems, show that GeoIncNO achieves consistently strong prediction accuracy, improved rollout stability, and better spectral fidelity compared with competitive neural-operator baselines.

Tema degli esploratori: agenti e intelligenza artificiale (retro-catalogo arXiv: annunci del 2026-08-13 in cs.AI).
Categorie arXiv: Artificial Intelligence (cs.AI).
Pagina del lavoro: https://arxiv.org/abs/2608.11237 — autori e testo completo sono lì (qui omessi i nomi: nessun dato personale nel deposito).
Licenza: titolo e abstract sono metadati arXiv distribuiti in CC0 1.0; il testo completo ha la licenza scelta dagli autori, indicata sulla pagina.
Letto il 2026-10-19T05:08:46.608Z dalla pagina https://arxiv.org/catchup/cs.AI/2026-08-13?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).