---
_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publication_status: unpublished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'
...
---
_id: '52758'
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. On the continuity and smoothness of the value function in
    reinforcement learning and optimal control. Published online 2024.
  apa: Harder, H., &#38; Peitz, S. (2024). <i>On the continuity and smoothness of
    the value function in reinforcement learning and optimal control</i>.
  bibtex: '@article{Harder_Peitz_2024, title={On the continuity and smoothness of
    the value function in reinforcement learning and optimal control}, author={Harder,
    Hans and Peitz, Sebastian}, year={2024} }'
  chicago: Harder, Hans, and Sebastian Peitz. “On the Continuity and Smoothness of
    the Value Function in Reinforcement Learning and Optimal Control,” 2024.
  ieee: H. Harder and S. Peitz, “On the continuity and smoothness of the value function
    in reinforcement learning and optimal control.” 2024.
  mla: Harder, Hans, and Sebastian Peitz. <i>On the Continuity and Smoothness of the
    Value Function in Reinforcement Learning and Optimal Control</i>. 2024.
  short: H. Harder, S. Peitz, (2024).
date_created: 2024-03-25T08:20:37Z
date_updated: 2024-04-30T08:45:54Z
language:
- iso: eng
status: public
title: On the continuity and smoothness of the value function in reinforcement learning
  and optimal control
type: preprint
user_id: '98879'
year: '2024'
...
---
_id: '46579'
abstract:
- lang: eng
  text: "The Koopman operator has become an essential tool for data-driven analysis,
    prediction and control of complex systems, the main reason being the enormous
    potential of identifying linear function space representations of nonlinear\r\ndynamics
    from measurements. Until now, the situation where for large-scale systems, we
    (i) only have access to partial observations (i.e., measurements, as is very common
    for experimental data) or (ii) deliberately perform coarse\r\ngraining (for efficiency
    reasons) has not been treated to its full extent. In this paper, we address the
    pitfall associated with this situation, that the classical EDMD algorithm does
    not automatically provide a Koopman operator approximation for the underlying
    system if we do not carefully select the number of observables. Moreover, we show
    that symmetries in the system dynamics can be carried over to the Koopman operator,
    which allows us to massively increase the model efficiency. We also briefly draw
    a connection to domain decomposition techniques for partial differential equations
    and present numerical evidence using the Kuramoto--Sivashinsky equation."
author:
- first_name: Sebastian
  full_name: Peitz, Sebastian
  id: '47427'
  last_name: Peitz
  orcid: 0000-0002-3389-793X
- first_name: Hans
  full_name: Harder, Hans
  id: '98879'
  last_name: Harder
- first_name: Feliks
  full_name: Nüske, Feliks
  last_name: Nüske
- first_name: Friedrich
  full_name: Philipp, Friedrich
  last_name: Philipp
- first_name: Manuel
  full_name: Schaller, Manuel
  last_name: Schaller
- first_name: Karl
  full_name: Worthmann, Karl
  last_name: Worthmann
citation:
  ama: Peitz S, Harder H, Nüske F, Philipp F, Schaller M, Worthmann K. Partial observations,
    coarse graining and equivariance in Koopman  operator theory for large-scale dynamical
    systems. <i>arXiv:230715325</i>. Published online 2023.
  apa: Peitz, S., Harder, H., Nüske, F., Philipp, F., Schaller, M., &#38; Worthmann,
    K. (2023). Partial observations, coarse graining and equivariance in Koopman 
    operator theory for large-scale dynamical systems. In <i>arXiv:2307.15325</i>.
  bibtex: '@article{Peitz_Harder_Nüske_Philipp_Schaller_Worthmann_2023, title={Partial
    observations, coarse graining and equivariance in Koopman  operator theory for
    large-scale dynamical systems}, journal={arXiv:2307.15325}, author={Peitz, Sebastian
    and Harder, Hans and Nüske, Feliks and Philipp, Friedrich and Schaller, Manuel
    and Worthmann, Karl}, year={2023} }'
  chicago: Peitz, Sebastian, Hans Harder, Feliks Nüske, Friedrich Philipp, Manuel
    Schaller, and Karl Worthmann. “Partial Observations, Coarse Graining and Equivariance
    in Koopman  Operator Theory for Large-Scale Dynamical Systems.” <i>ArXiv:2307.15325</i>,
    2023.
  ieee: S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, and K. Worthmann,
    “Partial observations, coarse graining and equivariance in Koopman  operator theory
    for large-scale dynamical systems,” <i>arXiv:2307.15325</i>. 2023.
  mla: Peitz, Sebastian, et al. “Partial Observations, Coarse Graining and Equivariance
    in Koopman  Operator Theory for Large-Scale Dynamical Systems.” <i>ArXiv:2307.15325</i>,
    2023.
  short: S. Peitz, H. Harder, F. Nüske, F. Philipp, M. Schaller, K. Worthmann, ArXiv:2307.15325
    (2023).
date_created: 2023-08-21T05:52:24Z
date_updated: 2023-08-21T05:53:35Z
department:
- _id: '655'
external_id:
  arxiv:
  - '2307.15325'
language:
- iso: eng
main_file_link:
- open_access: '1'
  url: https://arxiv.org/pdf/2307.15325
oa: '1'
publication: arXiv:2307.15325
status: public
title: Partial observations, coarse graining and equivariance in Koopman  operator
  theory for large-scale dynamical systems
type: preprint
user_id: '47427'
year: '2023'
...