Sloppy-model universality class and the vandermonde matrix

Joshua J. Waterfall, Fergal P. Casey, Ryan N. Gutenkunst, Kevin S. Brown, Christopher R. Myers, Piet W. Brouwer, Veit Elser, James P. Sethna

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Abstract

In a variety of contexts, physicists study complex, nonlinear models with many unknown or tunable parameters to explain experimental data. We explain why such systems so often are sloppy: the system behavior depends only on a few "stiff" combinations of the parameters and is unchanged as other "sloppy" parameter combinations vary by orders of magnitude. We observe that the eigenvalue spectra for the sensitivity of sloppy models have a striking, characteristic form with a density of logarithms of eigenvalues which is roughly constant over a large range. We suggest that the common features of sloppy models indicate that they may belong to a common universality class. In particular, we motivate focusing on a Vandermonde ensemble of multiparameter nonlinear models and show in one limit that they exhibit the universal features of sloppy models.

Original languageEnglish (US)
Article number150601
JournalPhysical review letters
Volume97
Issue number15
DOIs
StatePublished - Oct 20 2006
Externally publishedYes

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ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Waterfall, J. J., Casey, F. P., Gutenkunst, R. N., Brown, K. S., Myers, C. R., Brouwer, P. W., Elser, V., & Sethna, J. P. (2006). Sloppy-model universality class and the vandermonde matrix. Physical review letters, 97(15), [150601]. https://doi.org/10.1103/PhysRevLett.97.150601