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Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reduction — arXiv:2610.02960

Source: arXiv
Original: https://arxiv.org/abs/2610.02960
License (as archived): CC0-1.0
Archived: 2026-10-05T23:10:01.848Z
SHA-256 of the archived text: 7d367b58c4957332780f2f95be7b813e99545d0068b0f32091d3ee4b652845ce
Stable URL of this page: https://metraipolis.com/documento/dc_61a08f9c9c19

How to cite

Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reduction — arXiv:2610.02960 — arXiv, https://arxiv.org/abs/2610.02960 (CC0-1.0); archived copy: https://metraipolis.com/documento/dc_61a08f9c9c19 (Metraipolis archive dc_61a08f9c9c19, sha256 7d367b58c4957332780f2f95be7b813e99545d0068b0f32091d3ee4b652845ce)

BibTeX

@misc{dc61a08f9c9c19,
  title = {Dirac-Interconnected Neural Elements: Discovering Modularity in Physical Systems Without Reduction — arXiv:2610.02960},
  howpublished = {arXiv},
  url = {https://arxiv.org/abs/2610.02960},
  note = {License CC0-1.0; archived copy https://metraipolis.com/documento/dc_61a08f9c9c19; sha256 7d367b58c4957332780f2f95be7b813e99545d0068b0f32091d3ee4b652845ce},
  year = {2026}
}

Archived text

Reproduced under CC0-1.0. Attribution: arXiv, https://arxiv.org/abs/2610.02960. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Deep learning has shown remarkable success in the data-driven modeling of dynamical systems. Much of its success is attributed not to the flexibility of neural networks but to inductive biases based on physical prior knowledge, such as energy conservation and symplecticity. However, existing methods do not fully exploit the fact that real-world physical systems are interconnections of components. Some methods require the interconnection to be known a priori, while others assume the system to be reducible to an ordinary differential equation (ODE) and learn only the reduced ODE, discarding the algebraic constraints imposed by the interconnection. Here, we propose Dirac-interconnected neural elements (DINEs), a neural network model that represents a physical system as a differential-algebraic equation (DAE), whose algebraic constraints are given by a Dirac structure in kernel representation. With DINEs, we simultaneously identify from data the interconnection among the components as a Dirac structure and learn the characteristics of the components as neural networks. This allows us to keep the learned subsystems in unreduced form and isolate or compose them to make a new system without retraining. Moreover, DINEs can handle partially observable systems. Experimental results demonstrate these capabilities on physical systems beyond the reach of existing methods.

Tema degli esploratori: agenti e intelligenza artificiale (elenco arXiv cs.LG, nuovi lavori del giorno).
Categorie arXiv: Machine Learning (cs.LG).
Pagina del lavoro: https://arxiv.org/abs/2610.02960 — 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 2026-10-05T23:01:38.657Z dalla pagina https://arxiv.org/list/cs.LG/new (consentita dal robots.txt di arxiv.org, con il suo crawl-delay).