AKGNN: When Adaptive Graph Neural Network Meets Kolmogorov-Arnold Network for Industrial Soft Sensors

Data-driven soft sensors, which estimate quality variables from process variables, are very important to industrial processes. However, there remains significant room for enhancement in terms of accuracy in the deep learning (DL) era, and one of the promising solutions is embedding graph structure to delineate process variable relationships for feature extraction part and modify network architecture for label inference to make it as close to those industrial (semi-)empirical equations as possible. However, the ground-truth: 1) graph structure and 2) (semi-)empirical equations are unavailable in industrial practice. To alleviate these challenges, this article introduces a novel DL-based soft sensor model termed adaptive Kolmogorov-Arnold-based graph neural network (AKGNN). Specifically, for issue 1), the AKGNN first formulates the graph structure construction as a constrained optimization problem, reformulates the metric space with the help of the entropy function, and derives a novel DL-backend compatible graph construction strategy. Consequently, for issue 2), the Kolmogorov-Arnold network (KAN) is then designed to enable the label inference to be consistent with the (semi-)empirical equations. Finally, the detailed algorithm for AKGNN is summarized and various experiments are conducted to demonstrate the effectiveness of the proposed AKGNN.