A new synergetic paradigm in environmental numerical modeling: Hybrid models combining deterministic and machine learning components

A new type of environmental numerical models, hybrid environmental numerical models (HEMs) based on combining deterministic modeling and machine learning components, is introduced and formulated. Conceptual and practical possibilities of developing HEM, as an optimal synergetic combination of the traditional deterministic/first principles modeling (like that used for solving PDEs on the sphere representing model dynamics of global climate models) and machine learning components (like accurate and fast neural network emulations of model physics or chemistry processes), are discussed. Examples of developed HEMs (hybrid climate models and a hybrid wind–wave ocean model) illustrate the feasibility and efficiency of the new approach for modeling extremely complex multidimensional systems.