A bayesian inference and neural network model for predicting physical fitness consumption in table tennis athletes

Correctly predicting athletes' physical energy consumption is helpful for scientifically managing the training load to improve sports performance, especially for sports with high density and frequent movement changes, such as table tennis. This study proposes a Bayesian inference-based Autoformer temporal neural network model, termed Bayesian Autoformer (B-Autoformer), for multivariate physiological signal-based physical exertion prediction. The B-Autoformer model integrates Bayesian inference with the Autoformer temporal architecture, introducing probabilistic parameter modeling within the encoder and decoder components, and combining multi-head autocorrelation mechanisms with joint quantile loss functions to achieve both point prediction and interval prediction of VO₂-related physical exertion. The experimental data comprise two components. The Physical Activity Monitoring 2 Dataset (PAMAP2) is a publicly available multimodal physiological dataset derived from daily activity and exercise scenarios, encompassing triaxial acceleration, heart rate, and energy expenditure-related indicators, and is employed for model pre-training and generic feature learning. In this study, a special table tennis dataset was collected, including the continuous physiological signals of 18 male athletes during fixed-point technique, left and right push attack, non-fixed-point spin of the whole table and simulated competition training, and used for model fine-tuning and special verification. After filtering, time alignment and sliding window segmentation, the data are evaluated by five-fold cross-validation, combined with paired t-test and 95% confidence interval analysis. The evaluation indexes include Mean Square Error (MSE), Mean Absolute Error (MAE), coefficient of determination (R²) and interval coverage. The experimental results show that, compared with other comparison models, the MSE, MAE and R² of B-Autoformer on PAMAP2 dataset are 0.260, 0.363 and 0.906, which are significantly better than the baseline model (p < 0.05). In table tennis, MSE is 0.355, MAE is 0.435, R² is 0.875, and the highest interval coverage rate is 88%. The performance of the model remains relatively stable under different action types. The error increases slightly in complex simulated game scenes, but the trend consistency is still obvious. The results show that the model has certain advantages in representing the dynamic change and uncertainty of body movement. It can be used for training load monitoring and action intensity evaluation, thus providing reference for personalized regulation in special table tennis training.