In this study, we analyze the nature of the \(T_{c\bar{c}1}(3900)\) state using a uniformization approach, with a particular focus on different pole configurations. The \(T_{c\bar{c}1}(3900)\) was observed in the \(J/\psi \pi ^\pm \) invariant mass spectrum near the \(D\bar{D}^*\) threshold, suggesting its possible interpretation as a \(D\bar{D}^*\) hadronic molecule. We investigate this structure by modeling the coupled-channel interaction between \(J/\psi \pi \) and \(D\bar{D}^*\) using a fitting function where the pole-based interpretation is embedded. With this, we are able to generate arbitrary pole structures and extract physical insight from the resulting line shapes. These synthetic line shapes are then used to generate a training dataset for a machine learning model. Since the signal appears above the \(D\bar{D}^*\) threshold, our analysis primarily focuses on pole configurations with at least one pole on the third Riemann Sheet. Once the machine has been trained on a synthetic dataset and has demonstrated good generalization capabilities, an inference will be done on the BESIII dataset. With this method, our technique was able to infer that the signal observed by the BESIII collaboration has a pole-shadow pair configuration, which implies the presence of a large non-molecular component.
