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Trying to fix the YouTube link in the new JOSS paper
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akaptano committed Jan 19, 2022
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Expand Up @@ -92,7 +92,7 @@ Given spatiotemporal data $\mathbf{Q}(\mathbf{x}, t) \in \mathbb{R}^{m\times n}$
\end{equation}
ODEs, implicit ODEs, PDEs, and other dynamical systems are subsets of Eq. \eqref{eq:pysindy_eq}. We can accommodate control terms and partial derivatives in the SINDy library by adding them as columns in $\mathbf{\Theta}(\mathbf{Q})$, which becomes $\mathbf{\Theta}(\mathbf{Q}, \mathbf Q_t, \mathbf Q_x, ..., \mathbf{u})$.

In addition, we have extended `PySINDy` to handle more complex modeling scenarios, including trapping SINDy for provably stable ODE models for fluids [@kaptanoglu2021promoting], models trained using multiple dynamic trajectories, and the generation of many models with sub-sampling and ensembling methods [@fasel2021ensemble] for cross-validation and probabilistic system identification. In order to solve Eq. \eqref{eq:pysindy_eq}, `PySINDy` implements several different sparse regression algorithms. Greedy sparse regression algorithms, including step-wise sparse regression (SSR) [@boninsegna2018sparse] and forward regression orthogonal least squares (FROLS) [@Billings2013book], are now available. For maximally versatile candidate libraries, the new `GeneralizedLibrary` class allows for tensoring, concatenating, and otherwise combining many different candidate libraries, along with optionally specifying a subset of the inputs to use for generating each of the libraries. \autoref{fig:package-structure} illustrates the `PySINDy` code structure, changes, and high-level goals for future work, and [YouTube tutorials][https://www.youtube.com/playlist?list=PLN90bHJU-JLoOfEk0KyBs2qLTV7OkMZ25] for this new functionality are available online.
In addition, we have extended `PySINDy` to handle more complex modeling scenarios, including trapping SINDy for provably stable ODE models for fluids [@kaptanoglu2021promoting], models trained using multiple dynamic trajectories, and the generation of many models with sub-sampling and ensembling methods [@fasel2021ensemble] for cross-validation and probabilistic system identification. In order to solve Eq. \eqref{eq:pysindy_eq}, `PySINDy` implements several different sparse regression algorithms. Greedy sparse regression algorithms, including step-wise sparse regression (SSR) [@boninsegna2018sparse] and forward regression orthogonal least squares (FROLS) [@Billings2013book], are now available. For maximally versatile candidate libraries, the new `GeneralizedLibrary` class allows for tensoring, concatenating, and otherwise combining many different candidate libraries, along with optionally specifying a subset of the inputs to use for generating each of the libraries. \autoref{fig:package-structure} illustrates the `PySINDy` code structure, changes, and high-level goals for future work, and [`YouTube` tutorials](https://www.youtube.com/playlist?list=PLN90bHJU-JLoOfEk0KyBs2qLTV7OkMZ25) for this new functionality are available online.

`PySINDy` includes extensive Jupyter notebook tutorials that demonstrate the usage of various features of the package and reproduce nearly the entirety of the examples from the original SINDy paper [@brunton2016pnas], trapping SINDy paper [@kaptanoglu2021promoting], and the PDE-FIND paper [@Rudy2017sciadv].
We include an extended example for the quasiperiodic shear-driven cavity flow [@callaham2021role].
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