Self-learning PI-iTransformer: Adaptive physics modeling for forecasting real world soil temperature sensor data

Temperature monitoring and forecasting are of great significance for accurately evaluating soil thermal remediation processes. However, existing data-draven forecasting models simultaneously learn from noise, which limits the accuracy of soil temperature forecasting. If a physical model is to be introduced, it is necessary to first overcome the additional errors caused by the high uncertainty of soil internal structure and local physicochemical parameters. To address these challenges, this study proposes a self-learning physics constrained iTransformer prediction framework. This model transforms multi-scale physical constraints into regularization mechanisms embedded in the training process through autonomous learning of dynamic control equations, avoiding the rigid introduction of physical models that may cause additional errors. At the same time, it captures to some extent the transient characteristics of sensor time series and the periodic patterns of heat conduction. The experimental results show that the physical constraints reduces the average MAE and MSE of real prediction scenarios by 5%, effectively overcoming the inherent bottleneck of high noise data. This method has also achieved optimal performance on multiple industrial time series benchmarks, confirming its generalizability for predicting complex physical systems and establishing a new paradigm for temporal prediction of noisy sensor data in industrial control.