Metraipolis › archive › dc_9607cfe64710

Neural differential equation — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Neural_differential_equation
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-15T14:37:07.692Z
SHA-256 of the archived text: b4b338a94d25b1d34d83e00a90a9897653cc6c3e38e86fab292af026816e61d1
Stable URL of this page: https://metraipolis.com/documento/dc_9607cfe64710

How to cite

Neural differential equation — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Neural_differential_equation (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_9607cfe64710 (Metraipolis archive dc_9607cfe64710, sha256 b4b338a94d25b1d34d83e00a90a9897653cc6c3e38e86fab292af026816e61d1)

BibTeX

@misc{dc9607cfe64710,
  title = {Neural differential equation — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Neural_differential_equation},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_9607cfe64710; sha256 b4b338a94d25b1d34d83e00a90a9897653cc6c3e38e86fab292af026816e61d1},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Neural_differential_equation. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

Neural differential equations are a class of models in machine learning that combine neural networks with the mathematical framework of differential equations. These models provide an alternative approach to neural network design, particularly for systems that evolve over time or through continuous transformations. The most common type, a neural ordinary differential equation (neural ODE), defines the evolution of a system's state using an ordinary differential equation whose dynamics are governed by a neural network: d h ( t ) d t = f θ ( h ( t ) , t ) . {\displaystyle {\frac {\mathrm {d} \mathbf {h} (t)}{\mathrm {d} t}}=f_{\theta }(\mathbf {h} (t),t).} In this formulation, the neural network parameters θ determine how the state changes at each point in time. This approach contrasts with conventional neural networks, where information flows through discrete layers indexed by natural numbers. Neural ODEs instead use continuous layers indexed by positive real numbers, where the function h : R ≥ 0 → R {\displaystyle h:\mathbb {R} _{\geq 0}\to \mathbb {R} } represents the network's state at any given layer depth t. Neural ODEs can be understood as continuous-time control systems, where their ability to interpolate data can be interpreted in terms of controllability. They have found applications in time series analysis, generative modeling, and the study of complex dynamical systems.

Tema degli esploratori: matematica e informatica teorica (deposito sistematico; ricerca «differential equation»).
Fonte: Wikipedia in inglese, voce «Neural differential equation» — https://en.wikipedia.org/wiki/Neural_differential_equation
Wikidata Q130213955 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q130213955
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Neural_differential_equation?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1360712677, consultata il 2026-10-15T13:58:38.645Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: b5160e653821335c730407d940b4c510d81b3227b1228e9be9d89dc5263fb6b5