From 60c42916496f63b11d1e425f5a69ab01d4ffd11a Mon Sep 17 00:00:00 2001 From: JuliusMartensen Date: Tue, 18 Jun 2024 12:26:45 +0200 Subject: [PATCH] Update paper.md (#32) Add space --- paper/paper.md | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/paper/paper.md b/paper/paper.md index 6fa0132..752c482 100644 --- a/paper/paper.md +++ b/paper/paper.md @@ -67,7 +67,7 @@ where $\mathcal{T} = [t_0, t_f]$ is the fixed time horizon and $x : \mathcal{T} For more information on optimal experimental design for DAEs and their sensitivity analysis, we refer to [@Koerkel2002; @Li2000SensitivityAnalysisDifferential]. -The functionality in this package integrates into Julia's [`SciML`](https://sciml.ai/) ecosystem. The model is provided in symbolic form as an `ODESystem` using `ModelingToolkit.jl`[@ma2021modelingtoolkit] with additional frequency information for the observed and control variables. Both ODE or DAE systems can be provided. `DynamicOED.jl` augments the given system symbolically with its sensitivity equations and the dynamics of the FIM. The resulting system together with a sufficient information criterion defines an `OEDProblem`, solveable using `DifferentialEquations.jl` [@rackauckas2017]. Here, all sampling and control decisions are discretized in time and can be used to model additional constraints. At last, the `OEDProblem` can be transformed into an `OptimizationProblem` as a sufficient input to `Optimization.jl` [@vaibhav_kumar_dixit_2023_7738525]. Here, a variety of optimization solvers for nonlinear programming and mixed-integer nonlinear programming available as additional backends, e.g. `Juniper` [@juniper] or `Ipopt` [@Waechter2006]. A simple example demonstrates the usage of `DynamicOED.jl` for the Lotka-Volterra system [@Sager2013]. +The functionality in this package integrates into Julia's [`SciML`](https://sciml.ai/) ecosystem. The model is provided in symbolic form as an `ODESystem` using `ModelingToolkit.jl` [@ma2021modelingtoolkit] with additional frequency information for the observed and control variables. Both ODE or DAE systems can be provided. `DynamicOED.jl` augments the given system symbolically with its sensitivity equations and the dynamics of the FIM. The resulting system together with a sufficient information criterion defines an `OEDProblem`, solveable using `DifferentialEquations.jl` [@rackauckas2017]. Here, all sampling and control decisions are discretized in time and can be used to model additional constraints. At last, the `OEDProblem` can be transformed into an `OptimizationProblem` as a sufficient input to `Optimization.jl` [@vaibhav_kumar_dixit_2023_7738525]. Here, a variety of optimization solvers for nonlinear programming and mixed-integer nonlinear programming available as additional backends, e.g. `Juniper` [@juniper] or `Ipopt` [@Waechter2006]. A simple example demonstrates the usage of `DynamicOED.jl` for the Lotka-Volterra system [@Sager2013]. \autoref{fig:lotka} shows the solution of the example above including the differential states, sensitivities $G$ and the sampling decisions $w$. More examples can be found in the [documentation](https://mathopt.github.io/DynamicOED.jl/dev/). @@ -133,4 +133,4 @@ The work was funded by the German Research Foundation DFG within the priority program 2331 'Machine Learning in Chemical Engineering' under grants KI 417/9-1, SA 2016/3-1, SE 586/25-1 -# References \ No newline at end of file +# References