## 3 Machine Learning  
To move from the qualitative approach described above to a physically sound, quantitative one, we allow for the capability and potentiality of ML. The entire dataset relevant to the considered 144 tall building shapes is subdivided into sub-sets, a 75% of the forms for training purposes and 25% for testing. Even though the number of models in the dataset looks small, the quantity of data to feed the ML algorithm is by far larger, since the input and output parameters of each structural analysis, as described above, allow multiple patterns to be learned. The following eight quantities have been then adopted to play the role of features in the classification task: top/bottom geometry, diagrid degree, total mass, drift, expected design weight, maximum utilization, total length of the diagrid, maximum normal force. To avoid biased classification outcomes, a randomization algorithm is adopted to set the training and the testing datasets: each time the ML algorithm is used, a different pair of training and testing datasets are generated, each one possibly leading to a different classification accuracy. A procedure is then exploited to effectively learn the sought patterns in the dataset features: pairs of training and the testing datasets are generated a number of times by sorting them out of the entire dataset, and the classification accuracy is finally computed by averaging the values relevant to each single pair. Independently of the training data, in this way the most efficient generalization of the results could be achieved. We will discuss again the randomization effect at the end of Section 4.1. Since a supervised learning is adopted, a label must be defined for the structural response. As a reference case, we start by considering the label to be provided by the drift, i.e., by the lateral displacement at the top of the building as induced by the loading condition considered [36]; according to International standards [37], the drift has to be limited to a fraction (e.g., 1/300) of the total height of the building [36], in our case set around 300 m. Intuition suggests that drift provides a satisfying quantitative measure of the structural response. Accordingly, we classify all the forms in five classes, moving from worst solutions characterized by a drift close to 177 cm, up to the best ones characterized instead by a drift close to 40 cm. In this and all the other possible cases, the entire range of values in the dataset is subdivided uniformly into five classes, using labels A (best), B, C, D, E (worst) as marks. Figure 5 exemplifies how labels are distributed when the drift is plotted against the diagrid degree. The present plot is reported to show how a number of characteristics can be understood from a representation of the results like this. It looks quite obvious that using different colours for the classes helps distinguish the effects of the reported features on the classification based on the proposed label. All the results look clustered around a clear trend: even though this post-processing of the results is not going to be exploited in the following, the dashed line represents the least-squares fit of the data. It will be shown that trends like this one cannot always be recognized in the dataset; that represents a clear hurdle, if ML algorithms are not adopted to dig into the data. Furthermore, the drift is shown to decrease if the diagrid degree increases, which is indeed an intuitive result, since in this way the structure becomes stiffer. It is also worth mentioning that the considered intervals defining the labels have been assumed to be constant in size, namely that the values to bound each of them have been assumed evenly spaced between the minimum and the maximum provided by the structural analysis. Hence, the distribution of the data among the five classes is not homogeneous.