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README.md

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[![SciML Code Style](https://img.shields.io/static/v1?label=code%20style&message=SciML&color=9558b2&labelColor=389826)](https://github.com/SciML/SciMLStyle)
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ModelingToolkit.jl is a modeling framework for high-performance symbolic-numeric computation
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in scientific computing and scientific machine learning.
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in scientific computing and scientific machine learning.
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It allows for users to give a high-level description of a model for
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symbolic preprocessing to analyze and enhance the model. ModelingToolkit can
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automatically generate fast functions for model components like Jacobians
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![Lorenz2](https://user-images.githubusercontent.com/1814174/79118645-744eb580-7d5c-11ea-9c37-13c4efd585ca.png)
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This automatically will have generated fast Jacobian functions, making
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This will have automatically generated fast Jacobian functions, making
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it more optimized than directly building a function. In addition, we can then
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use ModelingToolkit to compose multiple ODE subsystems. Now, let's define two
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interacting Lorenz equations and simulate the resulting Differential-Algebraic
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using ModelingToolkit
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using ModelingToolkit: t_nounits as t, D_nounits as D
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# Defines two lorenz system model.s
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# Defines two lorenz system models.
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eqs = [
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D(x) ~ σ * (y - x),
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D(y) ~ x *- z) - y,
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![](https://user-images.githubusercontent.com/17304743/187790221-528046c3-dbdb-4853-b977-799596c147f3.png)
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# Citation
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## Citation
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If you use ModelingToolkit.jl in your research, please cite [this paper](https://arxiv.org/abs/2103.05244):
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