Hybrid digital model based on Neural ODE in the task of increasing the economic efficiency of processing small-ore raw materials

The results of a study are presented, the purpose of which was to develop the structure of a hybrid digital model for managing the processes of processing small-ore raw materials, as well as an algorithm for converting technological data in accordance with this structure, ensuring improved management quality and, as a consequence, the economic efficiency of processing. The original idea underlying the hybrid digital model is the use of neural ordinary differential equations (Neural ODE) to calculate the dynamics of technological objects and the processes implemented in them. Neural ODEs are a type of physics-motivated neural networks that use physical laws during their learning process. The resulting digital intelligent machine learning system is capable of highly accurate reconstruction of the dynamics function using observational data of a technological object or process. The proposed hybrid model provides for the joint use of Neural ODE and Simulink simulation models of technological processes for processing fine ore raw materials when calculating control actions. This allows you to quickly model and analyze the reaction of dynamic objects to control inputs and quickly make the necessary changes without waiting for the reaction of the physical original. Numerical experiments have shown that the use of Neural ODE as part of a hybrid digital model accurately reproduces the dynamics of technological objects under various initial conditions. For comparison, experiments were carried out with a model in which an LSTM recurrent neural network was used instead of Neural ODE. Experiments demonstrated that in the latter case, the dynamics were simulated with high accuracy only under the original initial conditions, and when they changed, it was severely degraded. At the same time, the use of Neural ODE instead of LSTM has shown consistently high accuracy in displaying dynamics under these changes, which will help improve the quality of control of technological processes for processing fine ore raw materials and their economic efficiency.