---
_id: '53793'
abstract:
- lang: eng
  text: We utilize extreme learning machines for the prediction of partial differential
    equations (PDEs). Our method splits the state space into multiple windows that
    are predicted individually using a single model. Despite requiring only few data
    points (in some cases, our method can learn from a single full-state snapshot),
    it still achieves high accuracy and can predict the flow of PDEs over long time
    horizons. Moreover, we show how additional symmetries can be exploited to increase
    sample efficiency and to enforce equivariance.
author:
- first_name: Hans
  full_name: Harder, Hans
  id: '98879'
  last_name: Harder
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
citation:
  ama: 'Harder H, Peitz S. Solving partial differential equations with equivariant
    extreme learning machines. In: Berberich J, Ianelli A, Allgöwer F, eds. <i>Systems
    Theory in Data and Optimization</i>. Springer; 2025:153-168. doi:<a href="https://doi.org/10.1007/978-3-031-83191-1_10">10.1007/978-3-031-83191-1_10</a>'
  apa: Harder, H., &#38; Peitz, S. (2025). Solving partial differential equations
    with equivariant extreme learning machines. In J. Berberich, A. Ianelli, &#38;
    F. Allgöwer (Eds.), <i>Systems theory in data and optimization</i> (pp. 153–168).
    Springer. <a href="https://doi.org/10.1007/978-3-031-83191-1_10">https://doi.org/10.1007/978-3-031-83191-1_10</a>
  bibtex: '@inproceedings{Harder_Peitz_2025, place={Cham}, title={Solving partial
    differential equations with equivariant extreme learning machines}, DOI={<a href="https://doi.org/10.1007/978-3-031-83191-1_10">10.1007/978-3-031-83191-1_10</a>},
    booktitle={Systems theory in data and optimization}, publisher={Springer}, author={Harder,
    Hans and Peitz, Sebastian}, editor={Berberich, J. and Ianelli, A. and Allgöwer,
    F.}, year={2025}, pages={153–168} }'
  chicago: 'Harder, Hans, and Sebastian Peitz. “Solving Partial Differential Equations
    with Equivariant Extreme Learning Machines.” In <i>Systems Theory in Data and
    Optimization</i>, edited by J. Berberich, A. Ianelli, and F. Allgöwer, 153–68.
    Cham: Springer, 2025. <a href="https://doi.org/10.1007/978-3-031-83191-1_10">https://doi.org/10.1007/978-3-031-83191-1_10</a>.'
  ieee: 'H. Harder and S. Peitz, “Solving partial differential equations with equivariant
    extreme learning machines,” in <i>Systems theory in data and optimization</i>,
    2025, pp. 153–168, doi: <a href="https://doi.org/10.1007/978-3-031-83191-1_10">10.1007/978-3-031-83191-1_10</a>.'
  mla: Harder, Hans, and Sebastian Peitz. “Solving Partial Differential Equations
    with Equivariant Extreme Learning Machines.” <i>Systems Theory in Data and Optimization</i>,
    edited by J. Berberich et al., Springer, 2025, pp. 153–68, doi:<a href="https://doi.org/10.1007/978-3-031-83191-1_10">10.1007/978-3-031-83191-1_10</a>.
  short: 'H. Harder, S. Peitz, in: J. Berberich, A. Ianelli, F. Allgöwer (Eds.), Systems
    Theory in Data and Optimization, Springer, Cham, 2025, pp. 153–168.'
date_created: 2024-04-30T08:43:14Z
date_updated: 2026-10-01T11:39:19Z
doi: 10.1007/978-3-031-83191-1_10
editor:
- first_name: J.
  full_name: Berberich, J.
  last_name: Berberich
- first_name: A.
  full_name: Ianelli, A.
  last_name: Ianelli
- first_name: F.
  full_name: Allgöwer, F.
  last_name: Allgöwer
keyword:
- extreme learning machines
- partial differential equations
- data-driven prediction
- high-dimensional systems
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/abs/2404.18530
oa: '1'
page: 153-168
place: Cham
publication: Systems theory in data and optimization
publication_identifier:
  isbn:
  - 978-3-031-83191-1
publication_status: published
publisher: Springer
status: public
title: Solving partial differential equations with equivariant extreme learning machines
type: conference
user_id: '47427'
year: '2025'
...