Physics-consistent machine learning with output projection onto physical manifolds
M Helena Garcia Tnia S Morais Andreia Valente, Tiago Cunha Dias, Vasco Guerra, Rodrigo Ventura
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 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 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 an interpretable, general, and scalable solution for developing fast and reliable surrogate models of complex physical systems, particularly in resource-constrained scenarios. Machine learning models often struggle with limited datasets and compliance with physical laws. Here, the authors introduce a projection-based method that ensures predictions adhere to physical constraints, demonstrating enhanced accuracy and reliability in case studies with low-temperature reactive plasma and a simpler spring-mass system, offering a framework for resource-limited scenarios.