This paper proposes a methodology to map the various acoustic regimes of wind instruments. The maps can be generated in a multi-dimensional space consisting of design, control parameters, and initial conditions. The bound- aries of the maps are obtained explicitly in terms of the parameters using a support vector machine (SVM) classifier as well as a dedicated adaptive sam- pling scheme. The approach is demonstrated on a simplified clarinet model for which several maps are generated based on different criteria. Examples of computation of the probability of occurrence of a specific acoustic regime are also provided. In addition, the approach is demonstrated on a design optimization example for optimal intonation.