Physics-Informed Koopman Networks for Industrial Process Time-Series Prediction

Abstract

Industrial time series data record the dynamic changes of key parameters, and accurate prediction is crucial for real-time monitoring and production optimization. However, deep learning models encounter significant challenges in complex industrial environments, including inadequate modeling of long-term dependencies and limited generalization capabilities under varying operational conditions and noise interference. To overcome these challenges, this paper introduces a physics-informed Koopman network (PIKN) that integrates the global linearization capabilities of Koopman theory with physical prior knowledge, thereby enhancing the model’s prediction accuracy and generalization. Specifically, PIKN employs a neural network to learn the observation function, mapping the nonlinear time series to the Koopman latent space, which enables linear prediction of dynamic behavior. Additionally, a physical regularization term, derived from a simplified mechanistic equation, is incorporated into the loss function to ensure the model adheres to physical laws, thereby improving its robustness against noise and adaptability to varying operational conditions. Experimental results demonstrate that PIKN achieves superior prediction accuracy and enhanced generalization capabilities across multiple industrial data sets, thereby validating its effectiveness and advantages in industrial time series prediction.