PHYSICS-INFORMED MACHINE LEARNING UNDER SMALL-DATA CONSTRAINTS: LESSONS FROM ABRASIVE WATERJET MILLING

This paper investigates how to effectively apply machine learning to small, expensive, and material-specific datasets in manufacturing, specifically abrasive waterjet milling (AWJM). With only 155 data points, the authors examine the interplay between data curation, evaluation protocols, and the integration of physical knowledge into predictive models.

The authors propose a methodological framework that treats data preprocessing as a set of competing hypotheses rather than a fixed pipeline. They distinguish between physics-based cleaning (removing erroneous data) and statistical curation (filtering extreme values). They evaluate eight machine learning algorithms—including Gaussian Processes (GP), Gradient Boosting (GB), and Support Vector Regression (SVR)—across four levels of physics integration, ranging from pure data-driven models to hybrid models that learn residuals from a physics-based power-law baseline.

The study reveals that model rankings are highly unstable when using small hold-out sets; a model that appears to be the best performer on a single 15-point test set may drop significantly in rank when evaluated using 10-fold cross-validation. Gaussian Processes consistently occupy the top ranks in this regime. Furthermore, physics integration is highly algorithm-dependent: learning residuals on a physics baseline improves GP performance and provides interpretable decompositions, but it degrades the performance of tree-based models. Finally, the authors find that while automated hyperparameter tuning helps models with sensitive parameters, it can actually harm multi-stage hybrid pipelines because the small validation sets lead to unreliable selection.