Neural Operator Learning Framework for Mechanism Modeling in Industrial Process Control

In order to address the limitations of traditional modeling methods in analyzing complex multiscale dynamic systems, a new method based on frequency decomposition and neural operator learning is proposed in this paper to discover the control equations of industrial systems. The process data is decomposed into low-frequency trend components and high-frequency periodic components by Fourier transform, and then modeled using Fourier neural operators respectively. Automatic differentiation is used to directly obtain the system derivatives, eliminating the error accumulation associated with numerical differentiation. On this basis, a physical information sparse regression method is used to construct candidate function libraries with specific properties for low-frequency and high-frequency components respectively to extract explicit control equations. Experimental analysis is carried out on a chemical reactor temperature control system and a dual-axis robot arm joint control system. The results show that the proposed method has low coefficient estimation errors in equation term identification, ensuring accuracy and robustness. This method provides new insights into interpretable modeling and real-time optimization control of complex industrial systems.