## 3 Results
### Rules for Explaining the Results
The interactions between casting speed, Si content, and elongation are complex and can be affected by numerous factors including cooling rates, material properties, and the specifics of the casting process. The predictions given by the model are based on data and the relationships it has identified, which are represented in the form of these multiparametric graphs and matrices. Additionally, CAE ANN predicts the mean values of yield strength and corresponding local standard deviation (Figure 4), making it easier to understand how the same two input parameters in the hot extrusion process affect the output mechanical parameters of AA6082. Only the most significant portions of the explanation in the remainder of the subsection are shown, leaving out the basic explanation of the graphs (meaning of the various lines and their thicknesses, values for the output parameters, and description of the input parameters) that is typically included in the first part of the interpretation of the results. An automated explanation of the results in Figure 4 was given. The explanation also refers to the comparison of the results in Figure 3 with Figure 4:  
_To understand the reliability of the predictions, we need to consider both the predicted yield strength (Figure 4a) and the standard deviation of the prediction (Figure 4b)._  
_A higher predicted yield strength means a stronger material, while a lower standard deviation means a higher confidence in the prediction._  
_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._  
_Example Analysis:_  
_If we look at a specific silicon content of 1.00 wt.% and a casting speed of 7.3 mm/s, we find the following:_  
Figure 4: Prediction of yield strength 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). On the graph (Figure 4a), this point may lie close to the \"322.0\" line, suggesting a predicted yield strength of around 322 MPa. On the (Figure 4b) graph, the same point may lie between the \"21.0\" and \"21.5\" dotted lines, indicating a standard deviation in the yield strength prediction of between 21.0 to 21.5 MPa. So, at a Si content of 1.00 wt.% and a casting speed of 7.3 mm/s, the material is predicted to have a yield strength of approximately 322 MPa, with a standard deviation of roughly 21.0-21.5 MPa. In both graphs, data density is depicted by the gray numbers and the shading of the background. The darker the shading, the higher the data density. At the point of interest (casting speed = 7.3 mm/s and Si = 1 wt.%), the background is a lighter shade, suggesting lower data density. The exact value is not clear from the images, but it is lower than the darker regions, which means there are fewer data points contributing to the prediction and the standard deviation estimates at this location are less reliable. It's important to remember that lower data density can affect the confidence in the predictions and should be taken into account when interpreting these values. Let's delve into the provided graphs and extract information regarding yield strength and elongation based on silicon content and casting speed, keeping in mind data density for the reliability of our interpretations. Yield Strength Based on Figure 4: Yield strength predictions, represented by the solid isolines, seem to generally increase with both an increase in silicon content and casting speed. The isolines how up-wards, which suggests an interaction between the silicon content and casting speed--the effect of one may be amplified or diminished by the level of the other on yield strength. For example, at a low casting speed of around 7.2 mm/s and a silicon content of 0.89 wt.%, the yield strength is around 318 MPa.