Physics-informed features in supervised machine learning

2025-04-23

AI Summary

In scientific machine learning, learned features often lack physical interpretability and meaningful mechanistic grounding. Method: We propose a physics-informed nonlinear feature construction paradigm that integrates dimensional analysis with domain-specific physical constraints to enforce physical consistency in the feature mapping; it employs feature importance ranking to identify dominant physical mechanisms and supports governing-equation discovery and novel physical relation inference when first-principles laws are unknown. Contribution/Results: Experiments across multiple scientific datasets demonstrate significant improvements in regression accuracy and classification skill scores, while simultaneously achieving enhanced interpretability and mechanistic insight. The framework provides a generalizable, interpretable machine learning approach for scientific discovery—bridging data-driven modeling with physical understanding.

Technology Category

• Machine Learning: Feature Construction/Reformulation
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition
• Computer Vision: Low Level & Physics-based Vision

Application Category

• Web Mining and Content Analysis: Machine learning and data science for the Web
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

Supervised machine learning involves approximating an unknown functional relationship from a limited dataset of features and corresponding labels. The classical approach to feature-based machine learning typically relies on applying linear regression to standardized features, without considering their physical meaning. This may limit model explainability, particularly in scientific applications. This study proposes a physics-informed approach to feature-based machine learning that constructs non-linear feature maps informed by physical laws and dimensional analysis. These maps enhance model interpretability and, when physical laws are unknown, allow for the identification of relevant mechanisms through feature ranking. The method aims to improve both predictive performance in regression tasks and classification skill scores by integrating domain knowledge into the learning process, while also enabling the potential discovery of new physical equations within the context of explainable machine learning.

Problem

• Incorporating physical laws into machine learning features
• Enhancing model interpretability through physics-informed feature maps
• Discovering new physical equations via explainable machine learning

Innovation

• Physics-informed nonlinear feature maps construction
• Dimensional analysis enhances model interpretability
• Feature ranking identifies unknown physical mechanisms