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Abstract

Machine learning is rapidly evolving as a powerful tool in enhancing computational physics, pattern recognition, artificial intelligence, etc. In this talk we will first describe some of the basic elements of the theory of statistical learning by V. N. Vapnik and A. Chervonenkis such as support vector machine, reproducing kernel methods etc. We will then indicate possible future directions in connecting these developments to some of the latest results in statistical and stochastic Navier-Stokes equations such as invariant-ergodic measures, martingale solutions, nonlinear stochastic filtering and large deviations (all deal with the probability laws of fluid velocity), with the long term vision of developing machine learning to turbulence.