ArticleProceedings. Mathematical, physical, and engineering sciences2020
SINDy-PI: a robust algorithm for parallel implicit sparse identification of nonlinear dynamics.
Article in Proceedings. Mathematical, physical, and engineering sciences, 2020. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 35 papers.
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35 citing papers in PubMed.
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- Implicit Runge-Kutta based sparse identification of governing equations in biologically motivated systems.Scientific reports · 2025Article
- Dynamical systems theory as an organizing principle for single-cell biology.NPJ systems biology and applications · 2025Review
- A control theory framework and in situ experimental platform for informing restoration of coral reefs.Nature ecology & evolution · 2025Review
- Learning stochastic reaction-diffusion models from limited data using spatiotemporal features.bioRxiv : the preprint server for biology · 2025Article
- Learning Physics Informed Neural ODEs with Partial Measurements.Proceedings of the ... AAAI Conference on Artificial Intelligence. AAAI Conference on Artificial Intelligence · 2025Article
- Training stiff neural ordinary differential equations with implicit single-step methods.Chaos (Woodbury, N.Y.) · 2024Article
- Physics-informed genetic programming for discovery of partial differential equations from scarce and noisy data.Journal of computational physics · 2024Article
- Bayesian polynomial neural networks and polynomial neural ordinary differential equations.PLoS computational biology · 2024Article
- Integrating dynamic models and neural networks to discover the mechanism of meteorological factors on Aedes population.PLoS computational biology · 2024Article
- Development of data-driven modeling method for nonlinear coupling components.Scientific reports · 2024Article
- From biological data to oscillator models using SINDy.iScience · 2024Article
- The rise of scientific machine learning: a perspective on combining mechanistic modelling with machine learning for systems biology.Frontiers in systems biology · 2024Review
- OKRidge: Scalable Optimal k-Sparse Ridge Regression.Advances in neural information processing systems · 2023Article
- Distilling identifiable and interpretable dynamic models from biological data.PLoS computational biology · 2023Article
- The experimental multi-arm pendulum on a cart: A benchmark system for chaos, learning, and control.HardwareX · 2023Article
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3 authors.
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Abstract
Accurately modelling the nonlinear dynamics of a system from measurement data is a challenging yet vital topic. The sparse identification of nonlinear dynamics (SINDy) algorithm is one approach to discover dynamical systems models from data. Although extensions have been developed to identify implicit dynamics, or dynamics described by rational functions, these extensions are extremely sensitive to noise. In this work, we develop SINDy-PI (parallel, implicit), a robust variant of the SINDy algorithm to identify implicit dynamics and rational nonlinearities. The SINDy-PI framework includes multiple optimization algorithms and a principled approach to model selection. We demonstrate the ability of this algorithm to learn implicit ordinary and partial differential equations and conservation laws from limited and noisy data. In particular, we show that the proposed approach is several orders of magnitude more noise robust than previous approaches, and may be used to identify a class of ODE and PDE dynamics that were previously unattainable with SINDy, including for the double pendulum dynamics and simplified model for the Belousov-Zhabotinsky (BZ) reaction.
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