Manifold learning for parameter reduction

Alexander Holiday

doi:10.1016/j.jcp.2019.04.015

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Manifold learning for parameter reduction

2019-09-01

Ioannis G. Kevrekidis *

DOI：10.1016/j.jcp.2019.04.015

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Abstract

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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. (C) 2019 Elsevier Inc. All rights reserved.

Keywords:

Model reduction

Data mining

Diffusion maps

Data driven perturbation theory

Parameter sloppiness

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