Deep Learning

Justin Sirignano, University of Illinois at Urbana-Champaign

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Deep learning has had remarkable success in traditional machine learning fields such as image, text, and speech recognition. Due to this success, there is growing interest in using deep learning in science, engineering, medicine, and finance. At a high level, deep neural networks are stacks of nonlinear operations, typically with millions of parameters. This produces a highly flexible and powerful model which has proved effective in many applications. Our goal is to develop deep learning methods for applications in engineering and quantitative nance involving partial differential equations (PDEs). In particular, we will develop and test deep learning methods for solving high-dimensional PDEs (for which traditional finite difference methods are infeasible). In addition, we will develop and test deep learning models for closure terms in reduced-order PDE models (such as the LES model for the Navier-Stokes PDE).