Manifold learning for parameter reduction.

Autor: Holiday A; Chemical and Biological Engineering, Princeton University, USA., Kooshkbaghi M; The Program in Applied and Computational Mathematics (PACM), Princeton University, USA., Bello-Rivas JM; The Program in Applied and Computational Mathematics (PACM), Princeton University, USA., Gear CW; Chemical and Biological Engineering, Princeton University, USA., Zagaris A; Wageningen Bioveterinary Research, Wageningen UR, The Netherlands., Kevrekidis IG; Chemical and Biological Engineering, Princeton University, USA.; The Program in Applied and Computational Mathematics (PACM), Princeton University, USA.; Department of Chemical and Biomolecular Engineering, John Hopkins University, USA.
Jazyk: angličtina
Zdroj: Journal of computational physics [J Comput Phys] 2019 Sep 01; Vol. 392, pp. 419-431. Date of Electronic Publication: 2019 Apr 24.
DOI: 10.1016/j.jcp.2019.04.015
Abstrakt: 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 manifoldlearning 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.
Databáze: MEDLINE
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