Parameter Space Compression Underlies Emergent Theories and Predictive Models
Parameter Space Compression Underlies Emergent Theories and Predictive Models
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DOI：
10.1126/science.1238723
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发表时间：
2013-11-01
期刊：
影响因子：
56.9
通讯作者：
Sethna, James P.
中科院分区：
文献类型：
--
作者：
Machta, Benjamin B.;Chachra, Ricky;Sethna, James P.
微观上复杂的真实的世界所表现出的行为，往往可以用简单而又定量准确的描述来描述。尽管在物理学和其他科学领域的多参数模型中，微观参数存在很大的不确定性，但预测是可能的。我们通过分析原型连续介质理论（扩散）和自相似临界点（伊辛模型）中的参数敏感性将两者连接起来。我们跟踪出现了一个有效的理论，为长尺度的可观的压缩量化的参数空间的特征值的Fisher信息矩阵。类似的压缩在不同科学领域的模型中普遍存在，这表明物理学中有效连续统和普适理论的参数空间结构也允许更普遍的预测建模。
The microscopically complicated real world exhibits behavior that often yields to simple yet quantitatively accurate descriptions. Predictions are possible despite large uncertainties in microscopic parameters, both in physics and in multiparameter models in other areas of science. We connect the two by analyzing parameter sensitivities in a prototypical continuum theory (diffusion) and at a self-similar critical point (the Ising model). We trace the emergence of an effective theory for long-scale observables to a compression of the parameter space quantified by the eigenvalues of the Fisher Information Matrix. A similar compression appears ubiquitously in models taken from diverse areas of science, suggesting that the parameter space structure underlying effective continuum and universal theories in physics also permits predictive modeling more generally.