Marginalization on Bifurcation Diagrams: A New Perspective on Infinite-Horizon Prediction

Helmuth Naumer, Yizhen Lu, Farzad Kamalabadi

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract

This work addresses the problem of accurate infinite-horizon forecasting of dynamical systems with uncertain parameters. We introduce an intermediate representation of the probability distribution though the marginalization onto the sparse bifurcation structure of an ordinary differential equation (ODE) through integration over regions of attraction. With operations on this representation naturally completed in the space of parameter and state, metrics for the space of limiting behavior can be directly applied. Both limit points and limit cycles are investigated using the Hausdorff distance to treat them in a unified manner. The technique is further applied to stability detection, resulting in a likelihood ratio test.

Original languageEnglish (US)
Title of host publication2021 IEEE Statistical Signal Processing Workshop, SSP 2021
PublisherIEEE Computer Society
Pages431-435
Number of pages5
ISBN (Electronic)9781728157672
DOIs
StatePublished - Jul 11 2021
Event21st IEEE Statistical Signal Processing Workshop, SSP 2021 - Virtual, Rio de Janeiro, Brazil
Duration: Jul 11 2021Jul 14 2021

Publication series

NameIEEE Workshop on Statistical Signal Processing Proceedings
Volume2021-July

Conference

Conference21st IEEE Statistical Signal Processing Workshop, SSP 2021
Country/TerritoryBrazil
CityVirtual, Rio de Janeiro
Period7/11/217/14/21

Keywords

  • Forecasting
  • Infinite-Horizon
  • Nonlinear Dynamics
  • System Identification

ASJC Scopus subject areas

  • Electrical and Electronic Engineering
  • Applied Mathematics
  • Signal Processing
  • Computer Science Applications

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