Based on a physical model of a trumpet’s functioning, the numerical continuation approach is used to construct the model’s bifurcation diagram, which depends on the instrument’s acoustic characteristics and the musician’s parameters. In this article, we first identify 10 descriptors that account for the main characteristics of each bifurcation diagram. It is first shown that these descriptors can be used to classify four professional trumpets with a recognition rate close to 100%. The XGBoost algorithm is used for this purpose. Secondly, we evaluate the ability of different classical machine learning algorithms to predict the values of the 10 descriptors given the acoustic characteristics of a trumpet and the value of the musician’s parameters. The best surrogate model is obtained using the LassoLars method, trained on a dataset of 12,000 bifurcation diagrams calculated by numerical continuation. Training takes just 2 min, and real-time predictions are accurate, with an error of approximately 1%. A software interface has been developed to enable trumpet designers to predict the values of the descriptors for a trumpet being designed, without any knowledge of physics or nonlinear dynamics.