---
_id: '55159'
abstract:
- lang: eng
  text: "We introduce a method based on Gaussian process regression to identify discrete
    variational principles from observed solutions of a field theory. The method is
    based on the data-based identification of a discrete Lagrangian density. It is
    a geometric machine learning technique in the sense that the variational structure
    of the true field theory is reflected in the data-driven model by design. We provide
    a rigorous convergence statement of the method. The proof circumvents challenges
    posed by the ambiguity of discrete Lagrangian densities in the inverse problem
    of variational calculus.\r\nMoreover, our method can be used to quantify model
    uncertainty in the equations of motions and any linear observable of the discrete
    field theory. This is illustrated on the example of the discrete wave equation
    and Schrödinger equation.\r\nThe article constitutes an extension of our previous
    article  arXiv:2404.19626 for the data-driven identification of (discrete) Lagrangians
    for variational dynamics from an ode setting to the setting of discrete pdes."
author:
- first_name: Christian
  full_name: Offen, Christian
  id: '85279'
  last_name: Offen
  orcid: 0000-0002-5940-8057
citation:
  ama: Offen C. Machine learning of discrete field theories with guaranteed convergence
    and uncertainty quantification.
  apa: Offen, C. (n.d.). <i>Machine learning of discrete field theories with guaranteed
    convergence and uncertainty quantification</i>.
  bibtex: '@article{Offen, title={Machine learning of discrete field theories with
    guaranteed convergence and uncertainty quantification}, author={Offen, Christian}
    }'
  chicago: Offen, Christian. “Machine Learning of Discrete Field Theories with Guaranteed
    Convergence and Uncertainty Quantification,” n.d.
  ieee: C. Offen, “Machine learning of discrete field theories with guaranteed convergence
    and uncertainty quantification.” .
  mla: Offen, Christian. <i>Machine Learning of Discrete Field Theories with Guaranteed
    Convergence and Uncertainty Quantification</i>.
  short: C. Offen, (n.d.).
date_created: 2024-07-10T13:43:50Z
date_updated: 2024-08-12T13:43:32Z
ddc:
- '510'
department:
- _id: '636'
external_id:
  arxiv:
  - '2407.07642'
file:
- access_level: open_access
  content_type: application/pdf
  creator: coffen
  date_created: 2024-07-10T13:39:32Z
  date_updated: 2024-07-10T13:39:32Z
  description: |-
    We introduce a method based on Gaussian process regression to identify discrete
    variational principles from observed solutions of a field theory. The method is based on the data-based identification of a discrete Lagrangian density. It is a geometric machine learning technique in the sense that the variational structure of the true field theory is reflected in the data-driven model by design.
    We provide a rigorous convergence statement of the method.
    The proof circumvents challenges posed by the ambiguity of discrete Lagrangian densities in the inverse problem of variational calculus.
    Moreover, our method can be used to quantify model uncertainty in the equations of motions and any linear observable of the discrete field theory.
    This is illustrated on the example of the discrete wave equation and Schrödinger equation.
    The article constitutes an extension of our previous article for the data-driven identification of (discrete) Lagrangians for variational dynamics from an ode setting to the setting of discrete pdes.
  file_id: '55160'
  file_name: L_Collocation.pdf
  file_size: 4569314
  relation: main_file
  title: Machine learning of discrete field theories with guaranteed convergence and
    uncertainty quantification
file_date_updated: 2024-07-10T13:39:32Z
has_accepted_license: '1'
keyword:
- System identification
- inverse problem of variational calculus
- Gaussian process
- Lagrangian learning
- physics informed machine learning
- geometry aware learning
language:
- iso: eng
oa: '1'
page: '28'
project:
- _id: '52'
  name: 'PC2: Computing Resources Provided by the Paderborn Center for Parallel Computing'
publication_status: submitted
related_material:
  link:
  - description: GitHub
    relation: software
    url: https://github.com/Christian-Offen/Lagrangian_GP_PDE
status: public
title: Machine learning of discrete field theories with guaranteed convergence and
  uncertainty quantification
type: preprint
user_id: '85279'
year: '2024'
...