Journal
JOURNAL OF COMPUTATIONAL PHYSICS
Volume 392, Issue -, Pages 419-431Publisher
ACADEMIC PRESS INC ELSEVIER SCIENCE
DOI: 10.1016/j.jcp.2019.04.015
Keywords
Model reduction; Data mining; Diffusion maps; Data driven perturbation theory; Parameter sloppiness
Funding
- SNSF grant [P2EZP2_168833]
- US National Science Foundation grant [1510149]
- DARPA grant [HR00-11-18-C-0100]
- National Institutes of Health (NIBIB) [1U01EB021956-01]
- Swiss National Science Foundation (SNF) [P2EZP2_168833] Funding Source: Swiss National Science Foundation (SNF)
- Div Of Chem, Bioeng, Env, & Transp Sys
- Directorate For Engineering [1510149] Funding Source: National Science Foundation
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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.
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