As natural gas pipeline networks expand, the complexity of pipeline scheduling models grows, making feasibility analysis increasingly difficult. This study focuses on the feasibility analysis of optimization models for natural gas distribution network scheduling, treating it as a classification problem. Models grounded in traditional neural networks, parallel branch neural net-works, and graph neural networks are developed and assessed. Two distinct scales of natural gas distribution networks are explored by collecting a limited dataset of sample cases to train and validate the proposed feasibility analysis models through empirical case studies. The results demonstrate that the parallel branch neural network exhibits superior predictive performance. Additionally, this study introduces an innovative methodology for traceability diagnosis of infeasible cases, offering a practical framework for engineering applications.