Theory-guided hard constraint projection (HCP): a knowledge-based data-driven scientific machine learning method
This method addresses the challenge of integrating domain knowledge with data-driven models for scientists and engineers, particularly in fields requiring strict adherence to physical laws, offering an incremental improvement over existing physics-informed neural networks.
This paper introduces Theory-guided Hard Constraint Projection (HCP), a method that integrates domain knowledge and experimental data by converting physical constraints into a discrete form for hard constraint optimization via projection. It ensures model predictions strictly adhere to physical mechanisms, demonstrating higher accuracy and robustness with less data compared to soft constraint models and fully connected neural networks in subsurface flow problems.
Machine learning models have been successfully used in many scientific and engineering fields. However, it remains difficult for a model to simultaneously utilize domain knowledge and experimental observation data. The application of knowledge-based symbolic AI represented by an expert system is limited by the expressive ability of the model, and data-driven connectionism AI represented by neural networks is prone to produce predictions that violate physical mechanisms. In order to fully integrate domain knowledge with observations, and make full use of the prior information and the strong fitting ability of neural networks, this study proposes theory-guided hard constraint projection (HCP). This model converts physical constraints, such as governing equations, into a form that is easy to handle through discretization, and then implements hard constraint optimization through projection. Based on rigorous mathematical proofs, theory-guided HCP can ensure that model predictions strictly conform to physical mechanisms in the constraint patch. The performance of the theory-guided HCP is verified by experiments based on the heterogeneous subsurface flow problem. Due to the application of hard constraints, compared with fully connected neural networks and soft constraint models, such as theory-guided neural networks and physics-informed neural networks, theory-guided HCP requires fewer data, and achieves higher prediction accuracy and stronger robustness to noisy observations.