---
_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. Predicting PDEs Fast and Efficiently with Equivariant Extreme
    Learning Machines.
  apa: Harder, H., &#38; Peitz, S. (n.d.). <i>Predicting PDEs Fast and Efficiently
    with Equivariant Extreme Learning Machines</i>.
  bibtex: '@article{Harder_Peitz, title={Predicting PDEs Fast and Efficiently with
    Equivariant Extreme Learning Machines}, author={Harder, Hans and Peitz, Sebastian}
    }'
  chicago: Harder, Hans, and Sebastian Peitz. “Predicting PDEs Fast and Efficiently
    with Equivariant Extreme Learning Machines,” n.d.
  ieee: H. Harder and S. Peitz, “Predicting PDEs Fast and Efficiently with Equivariant
    Extreme Learning Machines.” .
  mla: Harder, Hans, and Sebastian Peitz. <i>Predicting PDEs Fast and Efficiently
    with Equivariant Extreme Learning Machines</i>.
  short: H. Harder, S. Peitz, (n.d.).
date_created: 2024-04-30T08:43:14Z
date_updated: 2024-04-30T08:45:24Z
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'
publication_status: unpublished
status: public
title: Predicting PDEs Fast and Efficiently with Equivariant Extreme Learning Machines
type: preprint
user_id: '98879'
year: '2024'
...