Sloppy-model universality class and the Vandermonde matrix.
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.
Waterfall
Joshua J
JJ
Laboratory of Atomic and Solid State Physics, Cornell University, Ithaca, New York 14853, USA.
Casey
Fergal P
FP
Gutenkunst
Ryan N
RN
Brown
Kevin S
KS
Myers
Christopher R
CR
Brouwer
Piet W
PW
Elser
Veit
V
Sethna
James P
JP
D000465:Algorithms; D006207:Half-Life; D008962:Models, Theoretical; D017711:Nonlinear Dynamics; D011868:Radioisotopes
D011868:Radioisotopes