Abstract: In process industries, the coupling of multiple complex devices makes it challenging for independent device models to effectively guide actual production. Pure data-driven models often face out- of-distribution generalization issues, resulting in poor data efficiency and generalization capabilities. In response to this, a physics-informed neural differential equation model is proposed for flotation, a typical process industry system. The model considers the coupling relationships between devices and global characteristics, utilizing physical priors to reconstruct neural differential equations to model an environment-aware single intelligent agent. The proposed model consists of a sequence encoder, an interpolation module, a neural differential equation inference module, and a state decoder. The gradient network computational graph structure of the neural differential equations is designed based on physical priors. By establishing different systems according to the actual process topology, the multi-agent model can achieve long-term liquid level prediction for the entire flotation process and assist in multi-agent collaborative control as an online simulation environment. The model was validated using an industrial dataset collected from a flotation plant. The results show that the proposed model demonstrates superior data efficiency and generalization capability compared with the discrete-time models and baseline models without leveraging physical information to reconstruct gradient network.

Key words: process industries, systematic system modeling, neural ordinary differential equations, theory-guided model reconstruction