Cartography of a multistable system using support vector machines, applied to a clarinet model

This paper presents a method to map out the behavior of a multistable dynamical system. The method outputs the boundaries of the stability regions of each multistable regime in the space of system parameters. Boundaries are produced by Support Vector Machines models. Adaptive sampling is used to improve speed and generalization to high dimensions. The method is general to any dynamical system with distinguishable multistable regimes. It is applied to a clarinet model with four distinct regimes (equilibrium and three distinct periodic notes). The cartography shows that, on the highest fingerings, the simple clarinet model only favors the expected note for very narrow ranges of reed parameters.