Gas sensor arrays (GSAs) usually encounter challenges due to the cross-contamination of mixed gases, leading to reduced accuracy in measuring gas mixtures. However, with the advent of artificial intelligence, there is a promising avenue for addressing this issue effectively. In pursuit of more accurate mixed gas measurements, we proposed a measurement model leveraging neural networks. Our approach involved employing the encoder of an autoencoder network (AEN) to extract features from experimental data, while fully connected layers were utilized for predicting concentrations of mixed gases. To refine the neural network parameters, we employed a variational autoencoder to generate additional data resembling the distribution of experimental data. Subsequently, we designed a domain difference maximum entropy technique to identify optimal concentration points for the calibration data. These calibration points were instrumental in training the fully connected layers, enhancing the model's accuracy. During practical usage, with the AEN configuration fixed, the model can be fine-tuned by using a small subset of test points across large-scale GSA deployments. Simulation and practical measurement results demonstrated the efficacy of our proposed measurement model, boasting high accuracy, with confidence intervals for relative errors of the four gas measurements below 3% at the 95% confidence level. Besides, the calibration scheme reduced the number of test points compared with traditional methods, reducing the cost of labor and equipment.