Regression Methods for Discoverying Nonlinear Dynamical Systems
Lecture 1
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Model Discovery (ODEs): This lecture provides an introduction to model discovery through sparse regression for dynamical systems.
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Lecture 2
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Model Discovery (PDEs): This lecture generalizes model discovery to spatio-temporal PDEs through a sparse regression framework.
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Lecture 3
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Model Discovery (Time-Delays): This lecture generalizes the model discovery process for latent variables by time-delay embeddings.
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KEY REFERENCES AND SUPPLEMENTARY VIDEOS
Data-driven Discovery of Governing Equations
This video highlights recent innovations for discovering nonlinear dynamical systems from time series data.
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Discovering governing equations from data by sparse identification of nonlinear dynamical systems
This video highlights the recent innovation of using overcomplete libraries and sparse regression to discover nonlinear dynamical systems from time series data.
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- S. Brunton, J. Proctor and J. N. Kutz, Discovering governing equations from data by sparse identification of nonlinear dynamical systems, Proceedings of the National Academy of Sciences (2016).
Hankel Alternative View of Koopman (HAVOK) Analysis
This video highlights a new algorithm to decompose chaos into a linear system with intermitting forcing.
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- S. Brunton, B. Brunton, J. L. Proctor, E. Kaiser and J. N. Kutz Chaos as an intermittently forced linear system, Nature Communications 8:19 (2017)
Data-driven discovery of partial differential equations
This video highlights extensions of our sparse identification for nonlinear dynamical systems (SINDy) to partial differential equations.
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- S. Rudy, J. L. Proctor, S. L. Brunton, and J. N. Kutz Data-driven discovery of partial differential equations, Science Advances 3, e1602614 (2017)