Machine learning tools in production engineering

Machine learning methods have shown potential for the optimization of production processes. Due to the complex relationships often inherent in those processes, the success of such methods is often uncertain and unreliable. Therefore, understanding the (algorithmic) behavior and results of machine learning methods is crucial to improve the prediction of production processes. Here, mathematical tools may help. This paper shows how efficient algorithms for the training of neural networks and their retraining in the framework of transfer learning are expressed in a discrete as well as a time-continuous formulation. The latter can be analyzed and investigated using mathematical techniques from kinetic gas dynamics. The results obtained provide a first step towards explainable artificial intelligence. Based on the mathematical description, an adapted ensemble method for retraining of neural networks is proposed and compared with backpropagation algorithms. The process of training and retraining is a common task and therefore demonstrated for two very different production processes. The first one involves the prediction of specific cutting forces and the second one the prediction of particle properties in a plasma spraying coating process. For both use cases, the presented algorithms are applied and their performance is evaluated giving thereby an indication how mathematically inspired methods improve classical tasks in production processes.