Combining Stochastic Models with Machine Learning

Abstract

Machine learning has become a prevalent and powerful tool in many scientific and engineering disciplines. This last chapter presents a few methods that combine stochastic models with machine learning to advance the understanding and forecast of many complex dynamical systems. Machine learning can serve as the surrogate forecast model in data assimilation to improve the efficiency and accuracy of the ensemble forecast. Reciprocally, data assimilation helps to enhance the quality of training data and provide additional sample trajectories to train a machine learning model. In addition, machine learning facilitates the development of stochastic closures and parameterizations. It is also shown in this chapter that machine learning can be incorporated into the moment equations to improve the development of statistical reduced-order models and advance statistical forecasts. During this procedure, information measurement is utilized as the loss function for the machine learning training. Finally, if machine learning is used for the path-wise forecast of complex dynamical systems, then additional uncertainty computed from the validation error can be added to each ensemble member to build a mixture distribution that provides the forecast PDF.