ArticleProceedings of the National Academy of Sciences of the United States of America2017
Reconstruction of normal forms by learning informed observation geometries from data.
Article in Proceedings of the National Academy of Sciences of the United States of America, 2017. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 13 papers.
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Who cites it
13 citing papers in PubMed.
- From disorganized data to emergent dynamic models: Questionnaires to partial differential equations.PNAS nexus · 2025Article
- Discovering conservation laws using optimal transport and manifold learning.Nature communications · 2023Article
- Ensemble-SINDy: Robust sparse model discovery in the low-data, high-noise limit, with active learning and control.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- Insights into population behavior during the COVID-19 pandemic from cell phone mobility data and manifold learning.Nature computational science · 2021Article
- Percolation on feature-enriched interconnected systems.Nature communications · 2021Article
- SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Provable Convex Co-clustering of Tensors.Journal of machine learning research : JMLR · 2020Article
- Data-driven discovery of coordinates and governing equations.Proceedings of the National Academy of Sciences of the United States of America · 2019Article
- Model selection for hybrid dynamical systems via sparse regression.Proceedings. Mathematical, physical, and engineering sciences · 2019Article
- Network inference in stochastic systems from neurons to currencies: Improved performance at small sample size.Physical review. E · 2019Article
- Data-driven Evolution Equation Reconstruction for Parameter-Dependent Nonlinear Dynamical Systems.Israel journal of chemistry · 2018Article
- From understanding of color perception to dynamical systems by manifold learning.Proceedings of the National Academy of Sciences of the United States of America · 2017Article
- Synthesizing developmental trajectories.PLoS computational biology · 2017Article
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4 authors.
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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.
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Read under generation 80e0d062 · epoch 390. Bibliography from PubMed, PubMed Central and OpenAlex; grants from NIH RePORTER; trial links from ClinicalTrials.gov; estimates, votes and beliefs from the OpenQuestion graph.