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## CNMc predictions {#sec-sec_3_5_Pred} | |
In this section, some representative outputs for the \gls{cnmc} predicted trajectories shall be discussed. | |
For that, first, the quality measurement abilities implemented in \gls{cnmc} are elaborated. | |
Next, the model *SLS* is analyzed and explained in detail in the subsection [-@sec-subsec_3_5_1_SLS]. | |
Finally, the outcome for other models shall be presented briefly in subsection [-@sec-subsec_3_5_2_Models].\newline | |
There are several methods implemented in \gls{cnmc} to assess the quality of the predicted trajectories. | |
The first one is the autocorrelation, which will be calculated for all $\vec{\beta}_{unseen}$ and all provided $\vec{L}$, for the true, \gls{cnm} and \gls{cnmc} predicted trajectories. | |
As usual, the output is plotted and saved as HTML files for a feature-rich visual inspection. | |
For qualitative assessment, the MAE errors are calculated for all $\vec{\beta}_{unseen}$ and $\vec{L}$ for two sets. | |
The first set consists of the MAE errors between the true and the \gls{cnm} predicted trajectories. | |
The second set contains the MAE errors between the true and the \gls{cnmc} predicted trajectories. | |
Both sets are plotted as MAE errors over $L$ and stored as HTML files. | |
Furthermore, the one $L$ value which exhibits the least MAE error is printed in the terminal and can be found in the log file as well. \newline | |
The second technique is the \gls{cpd}, which will also be computed for all the 3 trajectories, i.e., true, \gls{cnm} and \gls{cnmc} predicted trajectories. | |
The \gls{cpd} depicts the probability of being at one centroid $c_i$. | |
For each $\vec{\beta}_{unseen}$ and all $L$ the \gls{cpd} is plotted and saved. | |
The third method displays all the 3 trajectories in the state space. | |
Moreover, the trajectories are plotted as 2-dimensional graphs, i.e., each axis as a subplot over the time $t$. | |
The final method calculates the MAE errors of the $\boldsymbol Q / \boldsymbol T$ tensors for all $L$.\newline | |
The reason why more than one quality measurement method is integrated into \gls{cnmc} is that \gls{cnmc} should be able to be applied to, among other dynamical systems, chaotic systems. | |
The motion of the Lorenz system @eq-eq_6_Lorenz is not as complex as of the, e.g., the *Four Wing* @eq-eq_10_4_Wing . | |
Nevertheless, the Lorenz system already contains quasi-random elements, i.e., the switching from one ear to the other cannot be captured exactly with a surrogate mode. However, the characteristic of the Lorenz system and other chaotic dynamical systems as well can be replicated. | |
In order to prove the latter, more than one method to measure the prediction quality is required. | |
{{<include 6_SLS.qmd>}} | |
{{<include 7_Models.qmd>}} |