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, and James P. Sethna
Phys. Rev. Lett. 97, 150601 – Published 12 October 2006

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.

  • Figure
  • Received 15 May 2006

DOI:https://doi.org/10.1103/PhysRevLett.97.150601

©2006 American Physical Society

Authors & Affiliations

Joshua J. Waterfall1, Fergal P. Casey2, Ryan N. Gutenkunst1, Kevin S. Brown3, Christopher R. Myers4, Piet W. Brouwer1, Veit Elser1, and James P. Sethna1

  • 1Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA
  • 2Center for Applied Mathematics, Cornell University, Ithaca, New York 14853, USA
  • 3Department of Molecular and Cellular Biology, Harvard University, Cambridge, Massachusetts 02138, USA
  • 4Cornell Theory Center, Cornell University, Ithaca, New York 14853, USA

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Issue

Vol. 97, Iss. 15 — 13 October 2006

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