Manifold learning for parameter reduction

Alexander Holiday, Mahdi Kooshkbaghi, Juan M. Bello-Rivas, C. William Gear, Antonios Zagaris, Ioannis G. Kevrekidis

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

Abstract

Large scale dynamical systems (e.g. many nonlinear coupled differential equations)can often be summarized in terms of only a few state variables (a few equations), a trait that reduces complexity and facilitates exploration of behavioral aspects of otherwise intractable models. High model dimensionality and complexity makes symbolic, pen–and–paper model reduction tedious and impractical, a difficulty addressed by recently developed frameworks that computerize reduction. Symbolic work has the benefit, however, of identifying both reduced state variables and parameter combinations that matter most (effective parameters, “inputs”); whereas current computational reduction schemes leave the parameter reduction aspect mostly unaddressed. As the interest in mapping out and optimizing complex input–output relations keeps growing, it becomes clear that combating the curse of dimensionality also requires efficient schemes for input space exploration and reduction. Here, we explore systematic, data-driven parameter reduction by means of effective parameter identification, starting from current nonlinear manifold-learning techniques enabling state space reduction. Our approach aspires to extend the data-driven determination of effective state variables with the data-driven discovery of effective model parameters, and thus to accelerate the exploration of high-dimensional parameter spaces associated with complex models.

Original languageEnglish (US)
Pages (from-to)419-431
Number of pages13
JournalJournal of Computational Physics
Volume392
DOIs
StatePublished - Sep 1 2019

All Science Journal Classification (ASJC) codes

  • Numerical Analysis
  • Modeling and Simulation
  • Physics and Astronomy (miscellaneous)
  • Physics and Astronomy(all)
  • Computer Science Applications
  • Computational Mathematics
  • Applied Mathematics

Keywords

  • Data driven perturbation theory
  • Data mining
  • Diffusion maps
  • Model reduction
  • Parameter sloppiness

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