optim:start
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optim:start [2019/06/18 11:44] helene [Objective] |
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| ====== OPTIM: Parameter optimization tool for Lagamine ====== | ====== OPTIM: Parameter optimization tool for Lagamine ====== | ||
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| ===== Objective ===== | ===== Objective ===== | ||
| - | This optimization program allows the identification of the values of parameters likely to minimize an objective function representing the difference between two curves. The program will take a reference curve as an input (an experimental curve for instance) and will attempt to approach this curve with the finite element code Lagamine using different parameters obtained through the **Levenberg-Marquardt** algorithm. A schematic representation of th algorithm is shown in <imgref image1>. \\ \\ | + | This optimization program allows the identification of the values of parameters likely to minimize an objective function representing the difference between two curves. The program will take a reference curve as an input (an experimental curve for instance) and will attempt to approach this curve with the finite element code Lagamine using different parameters obtained through the **Levenberg-Marquardt** algorithm. A schematic representation of the algorithm is shown in <imgref image1>. \\ \\ |
| <imgcaption image1|Optim algorithm>{{ :optim:optim_gen1.png?600 |}}</imgcaption> \\ | <imgcaption image1|Optim algorithm>{{ :optim:optim_gen1.png?600 |}}</imgcaption> \\ | ||
| The optimization process is iterative and stops once a stop criterion is met, such as the stabilization of the objective function for instance. \\ | The optimization process is iterative and stops once a stop criterion is met, such as the stabilization of the objective function for instance. \\ | ||
| The code gives the possibility to optimize a set of parameters using several curves for one simulation, or several simulations at a time. All the curves are then concatenated in one global curve for the computation of the objective function. | The code gives the possibility to optimize a set of parameters using several curves for one simulation, or several simulations at a time. All the curves are then concatenated in one global curve for the computation of the objective function. | ||
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| + | ---- | ||
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| ===== Description ===== | ===== Description ===== | ||
| The objective function to be minimized by the algorithm is the following: \\ | The objective function to be minimized by the algorithm is the following: \\ | ||
| - | \[S=\sqrt{\displaystyle\sum_{i=1}^{n_{total}} (u_i^{FE}-u_i^{REF})^2}\] \\ | + | \[S=\sqrt{\displaystyle\sum_{i=1}^{n_{total}} (u_i^{FE}-u_i^{REF})^2}\] |
| Where: | Where: | ||
| * $i$ represents one of the $n_{total}$ points of the global reference curve. If the global curve is constituted of several curves, $n_{total}$ is the sum of the $n$ points of each curve (each curve can have a different number of points). In Optim, the number of points $n$ to be used for each curve is defined by the user (NPOI) in the *.info file. Giving a larger NPOI to a curve gives it more weight in the objective function. | * $i$ represents one of the $n_{total}$ points of the global reference curve. If the global curve is constituted of several curves, $n_{total}$ is the sum of the $n$ points of each curve (each curve can have a different number of points). In Optim, the number of points $n$ to be used for each curve is defined by the user (NPOI) in the *.info file. Giving a larger NPOI to a curve gives it more weight in the objective function. | ||
optim/start.1560851060.txt.gz ยท Last modified: 2020/08/25 15:36 (external edit)
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