During the last decade, machine learning (ML) began to play an important role in advancing scientific discovery in domains traditionally dominated by physically based (first principle) models. The use of ML models is particularly promising in scientific problems involving processes that are not completely understood, or where it is computationally infeasible to run physically based models at desired resolutions in space and time. Numerical Weather/Climate Prediction Systems (NWPS) represent one of the most complex systems that deal with such problems. Attempts to completely substitute physically based models with even the state-of-the-art black box ML models have often met with limited success in scientific domains due to inability to provide a meaningful physical understanding of underlying processes, their large data requirements, and their limited generalizability to out-of-sample scenarios. Given that neither an ML-only nor a physically based-only approach can be considered sufficient for complex scientific and operational applications, the research community explores the continuum of hybrids of physically based and ML models, where both scientific knowledge and data are integrated in a synergistic manner. This paradigm is fundamentally different from mainstream practices in the ML community that can only work with simpler forms of heuristics and constraints. This presentation is focused on hybrid NWPSs incorporating a deeper coupling of ML methods with physical knowledge. Advantages and limitations of such an approach are discussed.
