Manifold learning for parameter reduction

TL;DR

This paper proposes a data-driven approach using manifold learning to identify effective parameters in large dynamical systems, aiming to reduce both state and parameter space complexity for better exploration.

Contribution

It extends nonlinear manifold learning techniques to discover effective model parameters, enhancing parameter reduction alongside state space reduction.

Findings

Successful identification of effective parameters in complex models

Improved efficiency in exploring high-dimensional parameter spaces

Framework integrates state and parameter reduction methods

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.