Accurate geomechanical parameters are key factors for stability evaluation, disaster forecasting, structural design, and supporting optimization. The intelligent back analysis method based on the monitored information is widely recognized as the most efficient and cost-effective technique for inverting parameters. To address the low accuracy of measured data, and the scarcity of comprehensive datasets, this study proposes an innovative back analysis framework tailored for small sample sizes. We introduce a multi-faceted back analysis approach that combines data augmentation with advanced optimization and machine learning techniques. The auxiliary classifier generative adversarial network (ACGAN)-based data augmentation algorithm is first employed to generate synthetic yet realistic samples that adhere to the underlying probability distribution of the original data, thereby expanding the dataset and mitigating the impact of small sample sizes. Subsequently, we harness the power of optimized particle swarm optimization (OPSO) integrated with support vector machine (SVM) to mine the intricate nonlinear relationships between input and output variables. Then, relying on a case study, the validity of the augmented data and the performance of the developed OPSO-SVM algorithms based on two different sample sizes are studied. Results show that the new datasets generated by ACGAN almost coincide with the actual monitored convergences, exhibiting a correlation coefficient exceeding 0.86. Furthermore, the superiority of the OPSO-SVM algorithm is also demonstrated by comparing the displacement prediction capability of various algorithms through four indices. It is also indicated that the relative error of the predicted displacement values reduces from almost 20% to 5% for the OPSO-SVM model trained with 25 samples and that trained with 625 samples. Finally, the inversed parameters and corresponding convergences predicted by the two OPSO-SVM models trained with different samples are discussed, indicating the feasibility of the combination application of ACGAN and OPSO-SVM in back analysis of geomechanical parameters. This endeavor not only facilitates the progression of underground engineering analysis in scenarios with limited data, but also serves as a pivotal reference for both researchers and practitioners alike.