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Added Zach as an author in the new JOSS paper.md file
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akaptano authored Jan 6, 2022
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Expand Up @@ -20,6 +20,8 @@ authors:
affiliation: 3
- name: Charles B. Delahunt
affiliation: 2
- name: Zachary G. Nicolaou
affiliation: 2
- name: Kathleen Champion
affiliation: 2
- name: Jean-Christophe Loiseau
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In order to incorporate these new developments and accommodate the wide variety of possible dynamical systems, we have extended `PySINDy` to a more general setting and added significant new functionality. Our code\footnote{\url{https://github.com/dynamicslab/pysindy}} is thoroughly documented, contains extensive examples, and integrates a wide range of functionality, some of which may be found in a number of other local SINDy implementations\footnote{\url{https://github.com/snagcliffs/PDE-FIND}, \url{https://github.com/eurika-kaiser/SINDY-MPC},\\ \url{https://github.com/dynamicslab/SINDy-PI}, \url{https://github.com/SchatzLabGT/SymbolicRegression},\\ \url{https://github.com/dynamicslab/databook_python}, \url{https://github.com/sheadan/SINDy-BVP},\\ \url{https://github.com/sethhirsh/BayesianSindy}, \url{https://github.com/racdale/sindyr},\\ \url{https://github.com/SciML/DataDrivenDiffEq.jl}, \url{https://github.com/MathBioCU/WSINDy_PDE},\\ \url{https://github.com/pakreinbold/PDE_Discovery_Weak_Formulation}, \url{https://github.com/ZIB-IOL/CINDy}}. In contrast to some of these existing implementations, `PySINDy` is completely open-source, professionally-maintained (for instance, providing unit tests and adhering to PEP8 stylistic standards), and minimally dependent on non-standard Python packages.

# New features
Given spatiotemporal data $\mathbf{Q}(\mathbf{x}, t) \in \mathbb{R}^{m\times n}$, and optional control inputs $\mathbf{u} \in \mathbb{R}^{m \times r}$ (note $m$ has been redefined here to be the product of the number of spatial measurements and the number of time samples), `PySINDy` can now approximate algebraic systems of PDEs (and corresponding weak forms) in up to 3 spatial dimensions. Assuming the system is described by a function $\mathbf{g}$, we have
Given spatiotemporal data $\mathbf{Q}(\mathbf{x}, t) \in \mathbb{R}^{m\times n}$, and optional control inputs $\mathbf{u} \in \mathbb{R}^{m \times r}$ (note $m$ has been redefined here to be the product of the number of spatial measurements and the number of time samples), `PySINDy` can now approximate algebraic systems of PDEs (and corresponding weak forms) in an arbitrary number of spatial dimensions. Assuming the system is described by a function $\mathbf{g}$, we have
\begin{equation}\label{eq:pysindy_eq}
\mathbf{g}(\mathbf{q},\mathbf q_t, \mathbf q_x, \mathbf q_y, \mathbf q_{xx}, ..., \mathbf{u}) = 0.
\end{equation}
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