---
_id: '42163'
abstract:
- lang: eng
  text: 'The article shows how to learn models of dynamical systems from data which
    are governed by an unknown variational PDE. Rather than employing reduction techniques,
    we learn a discrete field theory governed by a discrete Lagrangian density $L_d$
    that is modelled as a neural network. Careful regularisation of the loss function
    for training $L_d$ is necessary to obtain a field theory that is suitable for
    numerical computations: we derive a regularisation term which optimises the solvability
    of the discrete Euler--Lagrange equations. Secondly, we develop a method to find
    solutions to machine learned discrete field theories which constitute travelling
    waves of the underlying continuous PDE.'
author:
- first_name: Christian
  full_name: Offen, Christian
  id: '85279'
  last_name: Offen
  orcid: 0000-0002-5940-8057
- first_name: Sina
  full_name: Ober-Blöbaum, Sina
  id: '16494'
  last_name: Ober-Blöbaum
citation:
  ama: 'Offen C, Ober-Blöbaum S. Learning discrete Lagrangians for variational PDEs
    from data and detection of travelling waves. In: Nielsen F, Barbaresco F, eds.
    <i>Geometric Science of Information</i>. Vol 14071. Lecture Notes in Computer
    Science (LNCS). Springer, Cham.; 2023:569-579. doi:<a href="https://doi.org/10.1007/978-3-031-38271-0_57">10.1007/978-3-031-38271-0_57</a>'
  apa: Offen, C., &#38; Ober-Blöbaum, S. (2023). Learning discrete Lagrangians for
    variational PDEs from data and detection of travelling waves. In F. Nielsen &#38;
    F. Barbaresco (Eds.), <i>Geometric Science of Information</i> (Vol. 14071, pp.
    569–579). Springer, Cham. <a href="https://doi.org/10.1007/978-3-031-38271-0_57">https://doi.org/10.1007/978-3-031-38271-0_57</a>
  bibtex: '@inproceedings{Offen_Ober-Blöbaum_2023, series={Lecture Notes in Computer
    Science (LNCS)}, title={Learning discrete Lagrangians for variational PDEs from
    data and detection of travelling waves}, volume={14071}, DOI={<a href="https://doi.org/10.1007/978-3-031-38271-0_57">10.1007/978-3-031-38271-0_57</a>},
    booktitle={Geometric Science of Information}, publisher={Springer, Cham.}, author={Offen,
    Christian and Ober-Blöbaum, Sina}, editor={Nielsen, F and Barbaresco, F}, year={2023},
    pages={569–579}, collection={Lecture Notes in Computer Science (LNCS)} }'
  chicago: Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians
    for Variational PDEs from Data and Detection of Travelling Waves.” In <i>Geometric
    Science of Information</i>, edited by F Nielsen and F Barbaresco, 14071:569–79.
    Lecture Notes in Computer Science (LNCS). Springer, Cham., 2023. <a href="https://doi.org/10.1007/978-3-031-38271-0_57">https://doi.org/10.1007/978-3-031-38271-0_57</a>.
  ieee: 'C. Offen and S. Ober-Blöbaum, “Learning discrete Lagrangians for variational
    PDEs from data and detection of travelling waves,” in <i>Geometric Science of
    Information</i>, Saint-Malo, Palais du Grand Large, France, 2023, vol. 14071,
    pp. 569–579, doi: <a href="https://doi.org/10.1007/978-3-031-38271-0_57">10.1007/978-3-031-38271-0_57</a>.'
  mla: Offen, Christian, and Sina Ober-Blöbaum. “Learning Discrete Lagrangians for
    Variational PDEs from Data and Detection of Travelling Waves.” <i>Geometric Science
    of Information</i>, edited by F Nielsen and F Barbaresco, vol. 14071, Springer,
    Cham., 2023, pp. 569–79, doi:<a href="https://doi.org/10.1007/978-3-031-38271-0_57">10.1007/978-3-031-38271-0_57</a>.
  short: 'C. Offen, S. Ober-Blöbaum, in: F. Nielsen, F. Barbaresco (Eds.), Geometric
    Science of Information, Springer, Cham., 2023, pp. 569–579.'
conference:
  end_date: 2023-09-01
  location: Saint-Malo, Palais du Grand Large, France
  name: '  GSI''23 6th International Conference on Geometric Science of Information'
  start_date: 2023-08-30
date_created: 2023-02-16T11:32:48Z
date_updated: 2024-08-12T13:46:29Z
ddc:
- '510'
department:
- _id: '636'
doi: 10.1007/978-3-031-38271-0_57
editor:
- first_name: F
  full_name: Nielsen, F
  last_name: Nielsen
- first_name: F
  full_name: Barbaresco, F
  last_name: Barbaresco
external_id:
  arxiv:
  - '2302.08232 '
file:
- access_level: open_access
  content_type: application/pdf
  creator: coffen
  date_created: 2023-08-02T12:04:17Z
  date_updated: 2023-08-02T12:04:17Z
  description: |-
    The article shows how to learn models of dynamical systems
    from data which are governed by an unknown variational PDE. Rather
    than employing reduction techniques, we learn a discrete field theory
    governed by a discrete Lagrangian density Ld that is modelled as a neural network. Careful regularisation of the loss function for training Ld is
    necessary to obtain a field theory that is suitable for numerical computations: we derive a regularisation term which optimises the solvability of
    the discrete Euler–Lagrange equations. Secondly, we develop a method to
    find solutions to machine learned discrete field theories which constitute
    travelling waves of the underlying continuous PDE.
  file_id: '46273'
  file_name: LDensityLearning.pdf
  file_size: 1938962
  relation: main_file
  title: Learning discrete Lagrangians for variational PDEs from data and detection
    of travelling waves
file_date_updated: 2023-08-02T12:04:17Z
has_accepted_license: '1'
intvolume: '     14071'
keyword:
- System identification
- discrete Lagrangians
- travelling waves
language:
- iso: eng
oa: '1'
page: 569-579
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication: Geometric Science of Information
publication_identifier:
  eisbn:
  - 978-3-031-38271-0
publication_status: published
publisher: Springer, Cham.
quality_controlled: '1'
related_material:
  link:
  - description: GitHub
    relation: software
    url: https://github.com/Christian-Offen/LagrangianDensityML
series_title: Lecture Notes in Computer Science (LNCS)
status: public
title: Learning discrete Lagrangians for variational PDEs from data and detection
  of travelling waves
type: conference
user_id: '85279'
volume: 14071
year: '2023'
...