Learn one size to infer all: Exploiting translational symmetries in delay-dynamical and spatiotemporal systems using scalable neural networks

Mirko Goldmann, Claudio R. Mirasso, Ingo Fischer, and Miguel C. Soriano
Phys. Rev. E 106, 044211 – Published 21 October 2022
PDFHTMLExport Citation

Abstract

We design scalable neural networks adapted to translational symmetries in dynamical systems, capable of inferring untrained high-dimensional dynamics for different system sizes. We train these networks to predict the dynamics of delay-dynamical and spatiotemporal systems for a single size. Then, we drive the networks by their own predictions. We demonstrate that by scaling the size of the trained network, we can predict the complex dynamics for larger or smaller system sizes. Thus, the network learns from a single example and by exploiting symmetry properties infers entire bifurcation diagrams.

  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
  • Figure
2 More
  • Received 5 November 2021
  • Revised 20 June 2022
  • Accepted 27 September 2022

DOI:https://doi.org/10.1103/PhysRevE.106.044211

©2022 American Physical Society

Physics Subject Headings (PhySH)

Nonlinear DynamicsInterdisciplinary Physics

Authors & Affiliations

Mirko Goldmann*, Claudio R. Mirasso, Ingo Fischer, and Miguel C. Soriano

  • Instituto de Física Interdisciplinar y Sistemas Complejos (IFISC, UIB-CSIC), Campus Universitat de les Illes Balears E-07122, Palma de Mallorca, Spain

  • *mirko@ifisc.uib-csic.es
  • ingo@ifisc.uib-csic.es
  • miguel@ifisc.uib-csic.es

Article Text (Subscription Required)

Click to Expand

Supplemental Material (Subscription Required)

Click to Expand

References (Subscription Required)

Click to Expand
Issue

Vol. 106, Iss. 4 — October 2022

Reuse & Permissions
Access Options
Author publication services for translation and copyediting assistance advertisement

Authorization Required


×
×

Images

×

Sign up to receive regular email alerts from Physical Review E

Log In

Cancel
×

Search


Article Lookup

Paste a citation or DOI

Enter a citation
×