Physics-Informed Machine Learning Under Small-Data Constraints: Lessons from Abrasive Waterjet Milling

2026-07-08 · Source: Machine Learning · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Engineering & Applied Sciences · Depth: Advanced, quick

Summary

This paper investigates Physics-Informed Machine Learning (PIML) challenges when applied to small, expensive, and material-specific experimental datasets, using an abrasive waterjet milling dataset ($n=155$, Inconel 718). The research makes three methodological contributions. First, it distinguishes physics-based data cleaning from statistical curation, treating the latter as competing modeling hypotheses. Second, it reveals that model rankings from a small 15-point hold-out set can be unstable, with a single-split winner dropping from rank 1 to rank 7 under 10-fold cross-validation, while Gaussian Process (GP) variants consistently rank higher. Third, the study explores various physics integration levels, finding that residual learning on a compact physics baseline benefits GP models, offering lower variance and interpretability, but degrades tree-based models. Bayesian hyperparameter tuning improved gradient boosting and SVR but harmed multi-stage hybrid pipelines at this sample size. GP uncertainty intervals showed 86% empirical coverage at a nominal 90%.

Key takeaway

For Research Scientists developing PIML models with limited experimental data, prioritize robust evaluation and explicit data curation strategies. Your model comparison should rely on methods like 10-fold cross-validation, not small hold-out sets, to avoid unstable rankings. Consider Gaussian Process variants for their stability and explore residual learning for physics integration, noting its differential impact on model types.

Key insights

Reliable PIML with small datasets requires explicit curation hypotheses, robust evaluation, and careful physics integration.

Principles

• Separate physics cleaning from statistical curation.
• Small hold-out sets yield unstable model rankings.
• Residual learning benefits GP, degrades tree models.

Method

Treat statistical data curation as competing modeling hypotheses. Evaluate models using robust methods like 10-fold cross-validation, especially with small datasets, and consider residual learning for physics integration.

In practice

• Use 10-fold cross-validation for model comparison.
• Consider Gaussian Processes for small datasets.
• Apply Bayesian tuning to parameter-sensitive models.

Topics

• Physics-Informed Machine Learning
• Small Data
• Abrasive Waterjet Milling
• Gaussian Processes
• Model Evaluation
• Data Curation

Best for: AI Scientist, Research Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by Machine Learning.