Perspective: Sloppiness and emergent theories in physics, biology, and beyond

被引:200
作者
Transtrum, Mark K. [1 ]
Machta, Benjamin B. [2 ]
Brown, Kevin S. [3 ,4 ,5 ,6 ]
Daniels, Bryan C. [7 ]
Myers, Christopher R. [8 ,9 ]
Sethna, James P. [8 ]
机构
[1] Brigham Young Univ, Dept Phys & Astron, Provo, UT 84602 USA
[2] Princeton Univ, Lewis Sigler Inst Integrat Genom, Princeton, NJ 08544 USA
[3] Univ Connecticut, Dept Biomed Engn, Storrs, CT 06269 USA
[4] Univ Connecticut, Dept Phys, Storrs, CT 06269 USA
[5] Univ Connecticut, Dept Biomol Engn & Marine Sci, Storrs, CT 06269 USA
[6] Univ Connecticut, Inst Syst Genom, Storrs, CT 06030 USA
[7] Univ Wisconsin, Wisconsin Inst Discovery, Ctr Complex & Collect Computat, Madison, WI 53715 USA
[8] Cornell Univ, Lab Atom & Solid State Phys, Ithaca, NY 14853 USA
[9] Cornell Univ, Inst Biotechnol, Ithaca, NY 14853 USA
基金
美国国家科学基金会;
关键词
MODEL-REDUCTION; SINGULAR PERTURBATIONS; PARAMETER UNCERTAINTY; BALANCED TRUNCATION; CONFIDENCE-REGIONS; REACTION SYSTEMS; LUMPING ANALYSIS; SLOPPY MODELS;
D O I
10.1063/1.4923066
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
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 is interpreted 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. 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. (C) 2015 Author(s). All article content, except where otherwise noted, is licensed under a Creative Commons Attribution 3.0 Unported License.
引用
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页数:13
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