## 5 Conclusions  
Evaluating model suitability is a very challenging task, as there is no objective way of knowing what is a suitable model and what is not. This article has provided insight into the dynamics between simulation and validation and how these techniques can improve the overall quality and credibility of predictive models in various applications. Specifically, this study provides an in-depth examination of the processes and tools involved in the transition from simulation to validation in predictive modelling. Using MATLAB's Curve Fitting Toolbox as the primary environment, we demonstrated how advanced modelling and validation techniques can be applied to ensure the accuracy and reliability of predictive models. Our analysis focused on composite absorption data and highlighted the dynamics of balancing model complexity and performance. Among the various models tested (e.g., polynomial, Gaussian, Fourier), the Gaussian regression model emerged as the most suitable, achieving a high coefficient of determination (R\({}^{2}\) = 0.9429) for a six-parameter configuration. This reflects its superior ability to capture the underlying patterns of the data compared to other models. Incremental increases in model complexity, represented by the number of parameters, led to improvements in key metrics such as Sum of Squared Errors (SSE), Root Mean Square Error (RMSE), Mean Squared Error (MSE) and symmetric mean absolute percentage error (SMAPE). For example, the RMSE decreased from 0.021555 (four-parameter model) to 0.013537 (six-parameter model) and the SSE decreased from 0.675565 to 0.266441 over the same range. The SMAPE showed improvements, decreasing from 0.000442 to 0.000343, indicating greater agreement between predicted and actual values. We can also see that while increasing the number of parameters to 7 further reduced errors and improved R\({}^{2}\) to 0.94663, the Akaike Information Criterion (AIC) showed diminishing returns in model performance relative to complexity. The AIC for the six-parameter model (\(-\)2806.93) was significantly better than that for the seven-parameter model (\(-\)2847.17), highlighting the importance of parsimony in model selection. In addition, metrics such as MAPE and MAE also supported the selection of the six-parameter model as optimal for balancing accuracy with practical applicability. These results demonstrate the importance of systematically evaluating model performance across multiple dimensions. While a higher R\({}^{2}\) can be appealing, relying solely on \begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{4}{c}{**Number of Coefficients**} \\ \hline  & **4** & **5** & **6** & **7** \\ \hline R\({}^{2}\) & 0.855315 & 0.929122 & 0.942937 & 0.94663 \\ adjR\({}^{2}\) & 0.854916 & 0.928877 & 0.942700 & 0.946371 \\ AIC & \(-\)2223.45 & \(-\)2672.05 & \(-\)2806.93 & \(-\)2847.17 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Results of AIC. this metric can lead to overly complex models that may lack interpretability and robustness. Instead, integrating a range of metrics, including SSE, RMSE, AIC and BIC, ensures a balanced approach to model validation. Future work could explore larger datasets, different application domains, or alternative modelling frameworks to generalise these findings. In addition, the incorporation of real-time data streams or ensemble modelling techniques could further improve the accuracy and reliability of predictions. We will also focus on evaluating the residuals and statistical significance of individual parameters affecting the balance between model quality and complexity. This study provides a basis for improving model evaluation procedures and highlights the need for robust validation protocols to ensure that predictive models provide practical and reliable solutions in various scientific and engineering fields. Conceptualisation, S.H. and K.A. ; methodology, S.H. and K.A. ; software, J.H. and A.V. ; validation, S.H., K.A. and J.H. ; formal analysis, A.V. ; investigation, S.H. and K.A. ; resources, S.H. and J.H.