I will show an example of a highly nonconvex inverse problem, seismic inversion, and how deep learning offers a perspective on the question of initializing gradient descent in the proper basin of attraction. We think this question goes a bit beyond optimization and “landscaping”. We suggest to deal with a domain-specific signal processing question – frequency extrapolation – and then leverage it to extend the problem with extra dimensions. No prior knowledge of seismic inversion will be assumed. Joint work with Hongyu Sun.
Laurent Demanet is Professor of Applied Mathematics, in the Department of Mathematics at MIT. He holds a joint appointment with the Department of Earth, Atmospheric, and Planetary Sciences, where he is the Director of MIT's Earth Resources Laboratory.
Previously, he was Szego assistant professor (a postdoctoral position) in the Department of Mathematics at Stanford. He obtained his Ph.D. in 2006 under Emmanuel Candes, in Applied and Computational Mathematics at Caltech. He completed his undergraduate studies in mathematical engineering and theoretical physics at Universite de Louvain, Belgium.
He is the recipient of a Sloan research fellowship, a CAREER award from NSF, and a Young Investigator award from AFOSR. His research interests include applied analysis, scientific computing, machine learning, inverse problems, and wave propagation. His group studies the mathematical and numerical challenges of inverse wave scattering.