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Spatio-temporal Latent Denoising Diffusion Probabilistic Models for Reduced-order Modeling of Parametrized Dynamical Systems — arXiv:2609.17768

Source: arXiv (en)
Original: https://arxiv.org/abs/2609.17768
License (as archived): CC0-1.0
Archived: 2026-10-15T15:48:49.876Z
SHA-256 of the archived text: a2bcc5ddd0e76bf07e814da5d80a33ab4b3655c538a104384deec40e44b8e40b
Stable URL of this page: https://metraipolis.com/documento/dc_79110a89c65a

How to cite

Spatio-temporal Latent Denoising Diffusion Probabilistic Models for Reduced-order Modeling of Parametrized Dynamical Systems — arXiv:2609.17768 — arXiv (en), https://arxiv.org/abs/2609.17768 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_79110a89c65a (Metraipolis archive dc_79110a89c65a, sha256 a2bcc5ddd0e76bf07e814da5d80a33ab4b3655c538a104384deec40e44b8e40b)

BibTeX

@misc{dc79110a89c65a,
  title = {Spatio-temporal Latent Denoising Diffusion Probabilistic Models for Reduced-order Modeling of Parametrized Dynamical Systems — arXiv:2609.17768},
  howpublished = {arXiv (en)},
  url = {https://arxiv.org/abs/2609.17768},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_79110a89c65a; sha256 a2bcc5ddd0e76bf07e814da5d80a33ab4b3655c538a104384deec40e44b8e40b},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv (en), https://arxiv.org/abs/2609.17768. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Many scientific problems require accurate modeling of complex physical phenomena, such as fluid dynamics or climate modeling. These phenomena often result in high-dimensional and thus computationally expensive computational models that can limit their application to real-time and multi-query problems. Model-order reduction (MOR) is an approach that seeks to approximate full-order models (FOMs) using reduced-order models (ROMs), trading a minor reduction in accuracy for a major reduction in computational cost. In this work, we propose a non-intrusive MOR method using generative machine learning by means of denoising diffusion probabilistic models (DDPMs) for generating solutions of the dynamical systems under different instances of their parameters. Unlike conventional DDPMs, which often operate purely in the spatial domain, we aim to generate spatio-temporal solutions to improve quality and temporal coherence. In addition, we embed the DDPM in a latent space obtained by sequentially applying proper orthogonal decomposition and an autoencoder to reduce the data dimensionality and the computational cost of the DDPM. We test our approach on a parametrized 2D fluid flow around an obstacle. The numerical experiments demonstrate that our latent DDPM can (i) produce accurate and temporally coherent solutions, (ii) achieve strong generalization capabilities to scenarios involving unseen parameter values, and (iii) extrapolate in time beyond the training horizon.

Tema degli esploratori: matematica e informatica teorica (retro-catalogo arXiv: annunci del 2026-09-17 in math.NA).
Categorie arXiv: Numerical Analysis (math.NA).
Pagina del lavoro: https://arxiv.org/abs/2609.17768 — 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 2026-10-15T15:09:07.950Z dalla pagina https://arxiv.org/catchup/math.NA/2026-09-17?abs=True (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).