## 3 Results
### Rules for Explaining the Results
Apart from this modification, ChatGPT's explanations are all presented exactly as they were generated during user interaction with the application. For Figure 3, the following explanation was created, along with a general overview of the graphs required for comprehension in the first interaction with user:  
_Thick isoline provides the predicted values for elongation as a function of casting speed and Si content. Thin isolate reflects the data density, which indicates the concentration of data points used to create the model in that area of the graph; higher values suggest more confidence in the predictions. Dashed thick line shows the standard deviation, which measures the uncertainty or variability in the predictions; lower standard deviation values indicate more precise predictions. The background shading, which is absent from these graphs, would normally indicate data density, with darker areas suggesting a higher number of data points. This influences the confidence in the predictions made by the model: more data typically yields more reliable predictions._  
_The provided graphs allow interpretation of the results. For instance, at a certain point on the graph, we can identify the predicted elongation value, assess how dense the data is around that prediction, and understand the variability of the prediction by examining the standard deviation. This information together gives us a comprehensive understanding of the model's output for any given set of parameters (casting speed and Si content)._  
Occasionally, we are more interested in a smaller (limited) area of the phenomenon. For instance, we would like a more thorough explanation of the outcomes for the predicted mean value close to the point of casting speed of 7.4 mm/s and Si content of 0.90 wt.%:  
_At the point where the casting speed is 7.4 mm/s and the Si content is 0.90 wt.%, the results from the matrices are as follows:_  
* _Elongation: The predicted elongation at this point is approximately 11.95. This is the expected outcome of the elongation test given these specific conditions of casting speed and Si content._
* _Standard Deviation: The standard deviation associated with this prediction is not directly quoted, but it can be inferred from the provided text files that it would likely be a value close to the nearby standard deviation values. A lower standard deviation would indicate that the predicted elongation value of 11.95 is more reliable._
* _Data Density: The data density at this point is 0.80 This value indicates the number of data points or the amount of information from the experiments or simulations that contributed to the prediction at this specific point. A higher data density usually means that the prediction is based on more information and could be considered more reliable._  
The influence of both input parameters on the predicted elongation value is also examined in the vicinity of the point under consideration:  
Figure 3: Prediction of elongation as a function of casting speed (horizontal axis) and Si content: (**a**) mean value according to Equation (1) and (**b**) local standard deviation according to Equation (4). Influence of input parameters:
* Increasing Casting Speed (Si constant at 0.9 wt.%): At a constant silicon content of 0.9 wt.%, as the casting speed increases from 7.4 mm/s to the right, the solid lines representing elongation curve upwards. This means that elongation increases with casting speed in that range. Therefore, if you increase the casting speed while maintaining the Si content at 0.9 wt.%, the prediction for elongation will be higher. * Increasing Si Content (Casting Speed constant at 7.4 mm/s): When the casting speed is held constant at 7.4 mm/s, and we look at increasing Si content vertically on the graph, the solid isolines for elongation dip downward as we move up, which indicates that elongation decreases as the Si content increases at this casting speed.