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Copy file name to clipboardExpand all lines: docs/src/libs/datadrivendmd/example_04.jl
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# # [Nonlinear Time Continuous System](@id nonlinear_continuos)
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# Similarly, we can use the [Extended Dynamic Mode Decomposition](https://link.springer.com/article/10.1007/s00332-015-9258-5) via a nonlinear [`Basis`](@ref) of observables. Here, we will look at a rather [famous example](https://arxiv.org/pdf/1510.03007.pdf) with a finite dimensional solution.
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# Similarly, we can use the [Extended Dynamic Mode Decomposition](https://link.springer.com/article/10.1007/s00332-015-9258-5) via a nonlinear [`Basis`](@ref) of observables. Here, we will look at a rather [famous example](https://arxiv.org/pdf/1510.03007) with a finite dimensional solution.
# What if you want to estimate an implicitly defined system of the form ``f(u_t, u, p, t) = 0``?
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# The solution : Implicit Sparse Identification. This method was originally described in [this paper](http://ieeexplore.ieee.org/document/7809160/), and currently there exist [robust algorithms](https://royalsocietypublishing.org/doi/10.1098/rspa.2020.0279) to identify these systems.
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# The solution : Implicit Sparse Identification. This method was originally described in [this paper](https://ieeexplore.ieee.org/document/7809160/), and currently there exist [robust algorithms](https://royalsocietypublishing.org/doi/10.1098/rspa.2020.0279) to identify these systems.
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# We will focus on [Michaelis-Menten Kinetics](https://en.wikipedia.org/wiki/Michaelis%E2%80%93Menten_kinetics). As before, we will define the [`DataDrivenProblem`](@ref) and the [`Basis`](@ref) containing possible candidate functions for our [sparse regression](@ref sparse_algorithms).
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# Let's generate some data! We will use two experiments starting from different initial conditions.
Copy file name to clipboardExpand all lines: docs/src/libs/datadrivensr/example_01.jl
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# Hence, the performance might differ and depends strongly on the hyperparameters of the optimization.
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# This example might not recover the groundtruth, but is showing off the use within `DataDrivenDiffEq.jl`.
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# DataDrivenDiffEq offers an interface to [`SymbolicRegression.jl`](https://docs.sciml.ai/SymbolicRegression/stable/) to infer more complex functions.
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# DataDrivenDiffEq offers an interface to [`SymbolicRegression.jl`](https://ai.damtp.cam.ac.uk/symbolicregression/dev/) to infer more complex functions.
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