### Abstract

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.

Original language | English (US) |
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Pages (from-to) | E7865-E7874 |

Journal | Proceedings of the National Academy of Sciences of the United States of America |

Volume | 114 |

Issue number | 38 |

DOIs | |

State | Published - Sep 19 2017 |

### All Science Journal Classification (ASJC) codes

- General

### Keywords

- Data analysis
- Dynamical systems
- Empirical models
- Geometry
- Graph theory

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## Cite this

*Proceedings of the National Academy of Sciences of the United States of America*,

*114*(38), E7865-E7874. https://doi.org/10.1073/pnas.1620045114