Variational Physics Information-Adaptive Continual Learning Hybrid Probabilistic Modeling Method for Dynamic Industrial Processes

In industrial processes, the switching of working conditions, nonlinearity, dynamic characteristics, and coupling of multiple sources of uncertainty make it difficult for data-driven models to capture the complex behavior of the system, while the adaptability of mechanism-driven models is poor. To address these problems, a variational physics information-adaptive continual learning hybrid probabilistic modeling method is proposed, which achieves high-precision prediction of key parameters of industrial processes and multiple working condition adaptability. First, the time series data is expanded into a matrix containing historical time steps and input into a mixture density network to predict the parameters of the Gaussian mixture model, which not only describes the interdependence between the data but also captures the random changes in the probability distribution of the data. Second, the variational physical information loss is introduced. The physical residual is calculated by discretizing the partial differential equation, and the sampling point weight is calculated based on the difference between the model prediction value and the physical equation prediction value, so as to maintain the physical constraints in the modeling process. Finally, an adaptive continual learning loss is designed to dynamically generate the adjustment coefficient of the Fisher information matrix based on the working condition similarity, so as to measure the importance of historical working condition parameters and enhance the adaptability of the model. Verification on industrial process data sets shows that this method has significant advantages in both prediction accuracy and stability.