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remove PEtab cross references
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docs/src/inverse_problems/behaviour_optimisation.md

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# [Optimization for Non-data Fitting Purposes](@id behaviour_optimisation)
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In previous tutorials we have described how to use [PEtab.jl](@ref petab_parameter_fitting) and [Optimization.jl](@ref optimization_parameter_fitting) for parameter fitting. This involves solving an optimisation problem (to find the parameter set yielding the best model-to-data fit). There are, however, other situations that require solving optimisation problems. Typically, these involve the creation of a custom objective function, which minimizer can then be found using Optimization.jl. In this tutorial we will describe this process, demonstrating how parameter space can be searched to find values that achieve a desired system behaviour. Many options used here are described in more detail in [the tutorial on using Optimization.jl for parameter fitting](@ref optimization_parameter_fitting). A more throughout description of how to solve these problems is provided by [Optimization.jl's documentation](https://docs.sciml.ai/Optimization/stable/) and the literature[^1].
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In previous tutorials we have described how to use [PEtab.jl](https://github.com/sebapersson/PEtab.jl) and [Optimization.jl](@ref optimization_parameter_fitting) for parameter fitting. This involves solving an optimisation problem (to find the parameter set yielding the best model-to-data fit). There are, however, other situations that require solving optimisation problems. Typically, these involve the creation of a custom objective function, which minimizer can then be found using Optimization.jl. In this tutorial we will describe this process, demonstrating how parameter space can be searched to find values that achieve a desired system behaviour. Many options used here are described in more detail in [the tutorial on using Optimization.jl for parameter fitting](@ref optimization_parameter_fitting). A more throughout description of how to solve these problems is provided by [Optimization.jl's documentation](https://docs.sciml.ai/Optimization/stable/) and the literature[^1].
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## [Maximising the pulse amplitude of an incoherent feed forward loop](@id behaviour_optimisation_IFFL_example)
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Incoherent feedforward loops (network motifs where a single component both activates and deactivates a downstream component) are able to generate pulses in response to step inputs[^2]. In this tutorial we will consider such an incoherent feedforward loop, attempting to generate a system with as prominent a response pulse as possible.

docs/src/inverse_problems/optimization_ode_param_fitting.md

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1. Create a custom objective function which minimiser corresponds to the parameter set optimally fitting the data.
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2. Use Optimization.jl to minimize this objective function and find the parameter set providing the optimal fit.
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For simple parameter fitting problems (such as the one outlined below), [PEtab.jl often provides a more straightforward parameter fitting interface](@ref petab_parameter_fitting). However, Optimization.jl provides additional flexibility in defining your objective function. Indeed, it can also be used in other contexts, such as [finding parameter sets that maximise the magnitude of some system behaviour](@ref behaviour_optimisation). More details on how to use Optimization.jl can be found in its [documentation](https://docs.sciml.ai/DiffEqOptimizationParamEstim/stable/).
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For simple parameter fitting problems (such as the one outlined below), [PEtab.jl often provides a more straightforward parameter fitting interface](https://github.com/sebapersson/PEtab.jl). However, Optimization.jl provides additional flexibility in defining your objective function. Indeed, it can also be used in other contexts, such as [finding parameter sets that maximise the magnitude of some system behaviour](@ref behaviour_optimisation). More details on how to use Optimization.jl can be found in its [documentation](https://docs.sciml.ai/DiffEqOptimizationParamEstim/stable/).
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## [Basic example](@id optimization_parameter_fitting_basics)
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