Conférence donnée dans le cadre de la procédure d’appel en mathématiques, Professor Position in Mathematics.

Summary: Machine learning methods have shown impressive empirical performance in applications in engineering, economics, science, and technology. In many applications the core problem consists in learning the dynamics of a stochastic process or the solution of a partial differential equation. However, in this context machine learning methods often still lack theoretical convergence guarantees, which may entail substantial risks when using them in practice. In this talk we discuss mathematical foundations of deep learning and reservoir computing, two common machine learning methods. We highlight key challenges and present recent results that showcase the benefits of randomization.