Synthetic Polynomial Surrogates for Mechanical Processes: A Comparative Study of Data-Sampling and -Modelling Methods

Abstract

To improve physical processes, domain experts use experimental test setups to gather data. After sampling, the data is analysed using a regression model, for example. The objective of this work is to investigate the performance of different combinations of sampling and machine learning methods under varying process characteristics that are previously known to the domain expert. This results in practical recommendations for users with limited expertise in machine learning. A large-scale combinatorial test setup consisting of polynomial surrogates as pseudo processes with the characteristics of variable count, complexity, process noise and position of the optimum was created. The sampling methods (Sobol, random, Bayesian optimisation and response surface methodology with additional G-optimal test points) were compared against twenty-six ML methods. The results indicate that the choice of ML method has a greater influence on global modelling accuracy than the choice of sampling method. However, strong interactions between sampling and ML method demonstrate that they should not be selected independently. Overall, the findings suggest that process noise eliminates the predictive quality of standard regression models used in statistical evaluation. Space-filling sampling methods generally provide reliable performance, while regularised polynomial, kernel-based, and additive models offer strong predictive accuracy across multiple scenarios.