Theory-guided hard constraint projection (HCP): A knowledge-based data-driven scientific machine learning method

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 experimental observation data. The application of knowledge-based symbolic AI represented by an expert system is limited the expressive ability model, data-driven connectionism neural networks prone produce predictions that violate physical mechanisms. In order fully integrate with observations, make full use prior information strong fitting networks, this study proposes theory-guided hard constraint projection (HCP). This converts constraints, such as governing equations, into form easy handle through discretization, then implements optimization projection. Based on rigorous mathematical proofs, HCP can ensure strictly conform mechanisms patch. performance verified experiments based heterogeneous subsurface flow problem. Due compared connected soft models, physics-informed requires fewer data, achieves higher prediction accuracy stronger robustness noisy observations.