ArticleProceedings. Mathematical, physical, and engineering sciences2019
Model selection for hybrid dynamical systems via sparse regression.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2019. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 15 papers.
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15 citing papers in PubMed.
- Predicting mosquito flight behavior using Bayesian dynamical systems learning.Science advances · 2026Article
- Data-driven discovery of digital twins in biomedical research.Briefings in bioinformatics · 2026Review
- Nonlinear memory in cell-division dynamics across species.Proceedings of the National Academy of Sciences of the United States of America · 2025Article
- Data-driven model discovery and model selection for noisy biological systems.PLoS computational biology · 2025Article
- Weak-form inference for hybrid dynamical systems in ecology.Journal of the Royal Society, Interface · 2024Article
- Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data.Journal of computational physics · 2024Article
- Quantifying changes in individual-specific template-based representations of center-of-mass dynamics during walking with ankle exoskeletons using Hybrid-SINDy.Scientific reports · 2024Article
- Stability selection enables robust learning of differential equations from limited noisy data.Proceedings. Mathematical, physical, and engineering sciences · 2022Article
- Quantifying nanoscale forces using machine learning in dynamic atomic force microscopy.Nanoscale advances · 2022Article
- Multiscale modeling meets machine learning: What can we learn?Archives of computational methods in engineering : state of the art reviews · 2021Article
- Modeling of dynamical systems through deep learning.Biophysical reviews · 2020Review
- SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics.Proceedings. Mathematical, physical, and engineering sciences · 2020Article
- Algorithmic discovery of dynamic models from infectious disease data.Scientific reports · 2020Article
- Time-dependent antagonist-agonist switching in receptor tyrosine kinase-mediated signaling.BMC bioinformatics · 2019Article
- Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences.NPJ digital medicine · 2019Review
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5 authors.
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Abstract
Hybrid systems are traditionally difficult to identify and analyse using classical dynamical systems theory. Moreover, recently developed model identification methodologies largely focus on identifying a single set of governing equations solely from measurement data. In this article, we develop a new methodology, Hybrid-Sparse Identification of Nonlinear Dynamics, which identifies separate nonlinear dynamical regimes, employs information theory to manage uncertainty and characterizes switching behaviour. Specifically, we use the nonlinear geometry of data collected from a complex system to construct a set of coordinates based on measurement data and augmented variables. Clustering the data in these measurement-based coordinates enables the identification of nonlinear hybrid systems. This methodology broadly empowers nonlinear system identification without constraining the data locally in time and has direct connections to hybrid systems theory. We demonstrate the success of this method on numerical examples including a mass-spring hopping model and an infectious disease model. Characterizing complex systems that switch between dynamic behaviours is integral to overcoming modern challenges such as eradication of infectious diseases, the design of efficient legged robots and the protection of cyber infrastructures.
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