Résumé |
Models of systems biology, climate change, ecology, complex instruments, and
macroeconomics have parameters that are hard or impossible to measure directly. If
we fit these unknown parameters, fiddling with them until they agree with past
experiments, how much can we trust their predictions? We have found that
predictions can be made despite huge uncertainties in the parameters many
parameter combinations are mostly unimportant to the collective behavior. We will
use ideas and methods from differential geometry and approximation theory to
explain sloppiness as a hyperribbon structure of the manifold of possible model
predictions. We show that physics theories are also sloppy that sloppiness may
be the underlying reason why the world is comprehensible. We will present new
methods for visualizing this model manifold for probabilistic systems such as
the Ising model and the space of possible universes (as measured by the cosmic
microwave background radiation). Based on collaboration with Katherine Quinn, Mark
Transtrum, Han Kheng Teoh, Ben Machta,
Colin Clement, Archishman Raju, Heather Wilber, Ricky Chachra, Ryan Gutenkunst,
Joshua J. Waterfall, Fergal P. Casey, Kevin S. Brown, Christopher R. Myers. |