Abstract: Sudden transition is a widely existing phenomenon in engineering practice. When the state of the system experiences sudden abrupt transition, calculus-based traditional mathematical modeling methods has low accuracy. Although theoretically, machine learning algorithms, such as artificial neural networks, can approximate any nonlinear function, this type of black-box method makes no reasonable explanation for the sudden transition phenomenon. The cusp catastrophe model based on the catastrophe theory can be applied to explain the discontinuous changes in the system’s state. However, the construction of traditional cusp catastrophe models is often based on large amounts of prior knowledge to select the input variables for modeling. On the condition that there is a lack of prior knowledge and comparatively large dimensions of input variables, the model has high complexity and poor accuracy. In this paper we have put forward a two-step method for constructing a cusp catastrophe model based on the selection of variables to solve the abovementioned problems. The first step was to apply multimodel ensemble important variable selection (MEIVS) to quantify the importance of the variables to be selected and extract important variables. The second step was to use the extracted important variables to construct a cusp catastrophe model based on the framework of maximum likelihood estimation (MLE). Results indicate that on a dataset with characteristics of catastrophe, the cusp catastrophe model is simple in form using the MEIVS dimensionality reduction algorithm and outperforms the unreduced cusp catastrophe model and reduced cusp catastrophe model using other dimensionality reduction algorithms in terms of evaluation indicators. This shows that the algorithm proposed in this paper have improved the accuracy and reduced the complexity of the cusp catastrophe model. At the same time, the cusp catastrophe model exhibits higher accuracy compared with the linear and logistic models. Thus, it can be used to explain the discontinuous changes of the research object, and it has a practical engineering significance.