期刊
PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA
卷 114, 期 38, 页码 E7865-E7874出版社
NATL ACAD SCIENCES
DOI: 10.1073/pnas.1620045114
关键词
dynamical systems; geometry; graph theory; data analysis; empirical models
资金
- European Union's Seventh Framework Program (FP7) under Marie Curie Grant [630657]
- Israel Science Foundation Grant [1490/16]
- National Science Foundation Grant [1309858]
- Institute for Advanced Study-Technical University of Munich
- National Science Foundation
- Air Force Office of Scientific Research
- Defense Advanced Research Projects Agency [HR0011-16-C-0016]
- Div Of Civil, Mechanical, & Manufact Inn
- Directorate For Engineering [1309858] Funding Source: National Science Foundation
The discovery of physical laws consistent with empirical observations is at the heart of (applied) science and engineering. These laws typically take the form of nonlinear differential equations depending on parameters; dynamical systems theory provides, through the appropriate normal forms, an intrinsic prototypical characterization of the types of dynamical regimes accessible to a given model. Using an implementation of data-informed geometry learning, we directly reconstruct the relevant normal forms: a quantitative mapping from empirical observations to prototypical realizations of the underlying dynamics. Interestingly, the state variables and the parameters of these realizations are inferred from the empirical observations; without prior knowledge or understanding, they parametrize the dynamics intrinsically without explicit reference to fundamental physical quantities.
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