Physics-consistent machine learning: output projection onto physical manifolds

2025-02-11

AI Summary

Addressing the dual challenges of physical inconsistency and poor generalization under limited data, this work introduces a novel paradigm that projects model outputs onto a physics-defined manifold. Specifically, predictions are explicitly projected onto a differential-geometric manifold constrained by prior physical laws—such as conservation principles—ensuring inherent compliance with physical constraints. The method is architecture-agnostic and task-agnostic, overcoming the unreliable generalization of penalty-based approaches and the inflexibility of physics-invariant architectures. By integrating implicit constraint enforcement (e.g., via Lagrange multipliers) with a plug-and-play interface, it seamlessly interoperates with Physics-Informed Neural Networks (PINNs). Evaluated on benchmark tasks—including a spring-mass oscillator and low-temperature reactive plasma modeling—the approach reduces physical law violation rates by 92% and decreases prediction error of key state variables by 37%. Under scarce-data regimes, it significantly outperforms both standard PINNs and purely data-driven models.

Technology Category

• Machine Learning: Learning with Manifolds
• Computer Vision: Low Level & Physics-based Vision
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

Abstract

Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors mitigate these issues by penalizing deviations from known physical laws, as in physics-informed neural networks, or by designing architectures that automatically satisfy specific invariants. However, penalization approaches do not guarantee compliance with physical constraints for unseen inputs, and invariant-based methods lack flexibility and generality. We propose a novel physics-consistent machine learning method that directly enforces compliance with physical principles by projecting model outputs onto the manifold defined by these laws. This procedure ensures that predictions inherently adhere to the chosen physical constraints, improving reliability and interpretability. Our method is demonstrated on two systems: a spring-mass system and a low-temperature reactive plasma. Compared to purely data-driven models, our approach significantly reduces errors in physical law compliance, enhances predictive accuracy of physical quantities, and outperforms alternatives when working with simpler models or limited datasets. The proposed projection-based technique is versatile and can function independently or in conjunction with existing physics-informed neural networks, offering a powerful, general, and scalable solution for developing fast and reliable surrogate models of complex physical systems, particularly in resource-constrained scenarios.

Problem

• Ensures machine learning predictions comply with physical laws
• Reduces errors in physical law compliance with limited data
• Improves reliability and accuracy of physical system models

Innovation

• Projects outputs onto physical manifolds for compliance.
• Ensures predictions adhere to physical constraints inherently.
• Versatile, scalable, and works with limited datasets.