Manifold learning for parameter reduction
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 dimension...
| Veröffentlicht in: | Journal of computational physics. - 1986. - 392(2019) vom: 01. Sept., Seite 419-431 |
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| 1. Verfasser: | |
| Weitere Verfasser: | , , , , |
| Format: | Online-Aufsatz |
| Sprache: | English |
| Veröffentlicht: |
2019
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| Zugriff auf das übergeordnete Werk: | Journal of computational physics |
| Schlagworte: | Journal Article data driven perturbation theory data mining diffusion maps model reduction parameter sloppiness |
| Zusammenfassung: | 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 |
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| Beschreibung: | Date Revised 11.10.2023 published: Print-Electronic Citation Status PubMed-not-MEDLINE |
| ISSN: | 0021-9991 |
| DOI: | 10.1016/j.jcp.2019.04.015 |