Sloppiness and Emergent Theories in Physics, Biology, and Beyond
By M. Transtrum, B. Machta, Kevin S. Brown, Bryan C. Daniels, Christopher R. Myers, James P. Sethna. 2015
324 citations recorded by the source corpus.
Large scale models of physical phenomena demand the development of new statistical and computational tools in order to be effective. Many such models are `sloppy', i.e., exhibit behavior controlled by a relatively small number of parameter combinations. We review an information theoretic framework for analyzing sloppy models. This formalism is based on the Fisher Information Matrix, which we interpret as a Riemannian metric on a parameterized space of models. Distance in this space is a measure of how distinguishable two models are based on their predictions. Sloppy model manifolds are bounded with a hierarchy of widths and extrinsic curvatures. We show how the manifold boundary approximation can extract the simple, hidden theory from complicated sloppy models. We attribute the success of simple effective models in physics as likewise emerging from complicated processes exhibiting a low effective dimensionality. We discuss the ramifications and consequences of sloppy models for biochemistry and science more generally. We suggest that the reason our complex world is understandable is due to the same fundamental reason: simple theories of macroscopic behavior are hidden inside complicated microscopic processes.
Subfields: Condensed Matter Physics, Mathematical Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/6b266b88a246199ea0a3360ff06eeb76809a5a49
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In Statistical and Nonlinear Physics
Citations in the corpus
- General Relativity and Cosmology: Unsolved Questions and Future Directions (2016, background): “The patterns fall within some hyper-ribbon of stability in the theory [17].”