Skip to content
  • Publications
  • Jobs
  • enzuazua
  • Seminars
  • Events Calendar
  • Home
  • About us
    • About the Chair
    • Head of the Chair
    • Team
    • Past Members
  • Research
    • Projects
    • ERC – DyCon
    • DyCon Blog
    • DyCon Toolbox
    • Industrial & Social TransferenceContents related to the industrial and social transference aspects of the work in the Chair of Computational Mathematics.
  • Publications
    • Publications (All)
    • Publications Relased
      • Publications 2022
      • Publications 2021
      • Publications 2020
      • Publications 2019
      • Publications 2018
      • Publications 2017
      • Publications 2016
    • AcceptedAccepted to be released
    • SubmittedSubmitted publications
  • Activities
    • Events calendar
    • Past Events
    • News
    • Seminars
    • Courses
    • enzuazua
    • Gallery
  • Jobs
  • Contact

Optimal control for neural ODE in a long time horizon and applications to the classification and simultaneous controllability problems

Jon Asier Bárcena-Petisco. Optimal control for neural ODE in a long time horizon and applications to the classification (2021)

Abstract. We study the optimal control in a long time horizon of neural ordinary differential equations which are affine or whose activation function is homogeneous. When considering the classical regularized empirical risk minimization problem we show that, in long time and under suitable assumptions, the final state of the optimal trajectories has zero training error. We assume that the data can be interpolated and that the error can be taken to zero with a cost proportional to the error. These hypotheses are fulfilled in the classification and simultaneous controllability problems for some relevant activation and loss functions. Our proofs are mainly constructive combined with reductio ad absurdum: We find that in long time horizon if the final error is not zero, we can construct a less expensive control which takes the error to zero. Moreover, we prove that the norm of the optimal control is constant. Finally, we show the sharpness of our hypotheses by giving an example for which the error of the optimal state, even if it decays to 0, is strictly positive for any time.

Read Full Paper

Last updated on March 17, 2022

Post navigation

Previous Post
33rd. CBM – Brazilian Colloquium of Mathematics 33rd. CBM – Brazilian Colloquium of Mathematics
Next Post
Summer course (China): Control, Machine Learning and Numerics by E. Zuazua Summer course (China): Control, Machine Learning and Numerics by E. Zuazua

Last Publications

Optimal actuator design via Brunovsky’s normal form

Stability and Convergence of a Randomized Model Predictive Control Strategy

Slow decay and Turnpike for Infinite-horizon Hyperbolic LQ problems

Control of certain parabolic models from biology and social sciences

Relaxation approximation and asymptotic stability of stratified solutions to the IPM equation

  • Postdoc at DASEL project -Open position
  • FAU MoD Lecture: Applications of AAA Rational Approximation
  • DASEL
  • Optimal actuator design via Brunovsky’s normal form
  • ERC DyCon Impact Dimension (2016-2022)
  • Postdoc at DASEL project -Open position
  • FAU MoD Lecture: Applications of AAA Rational Approximation
  • DASEL
  • Optimal actuator design via Brunovsky’s normal form
  • ERC DyCon Impact Dimension (2016-2022)
Copyright 2016 - 2023 — . All rights reserved. Chair of Computational Mathematics, Deusto Foundation - University of Deusto
Scroll to Top
  • Aviso Legal
  • Política de Privacidad
  • Política de Cookies
  • Configuración de Cookies
WE USE COOKIES ON THIS SITE TO ENHANCE USER EXPERIENCE. We also use analytics. By navigating any page you are giving your consent for us to set cookies.    more information
Privacidad