EE Systems Seminar
Our understanding and ability to compute the solutions to nonlinear partial differential equations has been strongly curtailed by our inability to effectively parameterize the inertial manifold of their solutions. I will discuss our ongoing efforts for using machine learning to advance the state of the art, both for developing a qualitative understanding of "turbulent" solutions and for efficient computational approaches. We aim to learn parameterizations of the solutions that give more insight into the dynamics and/or increase computational efficiency. I will touch on three topics: (i) using machine learning to develop models of the small scale behavior of spatio-temporal complex solutions, with the goal of maintaining accuracy albeit at a highly reduced computational cost relative to a full simulation. (ii) "larger scale" efforts to classify and understand patterns in nonlinear pdes, relating them to invariant (but unstable) solutions of the underlying equations.(iii) using these ideas to simplify and accelerate experimental measurements of complex fluid flows.