Deep redatuming for PDE and inverse problems

Date: Fri. June 10, 2022
Organized by: FAU DCN-AvH, Chair for Dynamics, Control and Numerics – Alexander von Humboldt Professorship at FAU Erlangen-Nürnberg (Germany)
Title: Deep redatuming for PDE and inverse problems

Speaker: Prof. Dr. Laurent Demanet
Affiliation: MIT – Massachusetts Institute of Technology (USA)

Abstract. Neural networks have been leveraged in non-trivial ways in the context of computational inverse problems over the past few years. In this talk, I will explain how deep nets can sometimes generate helpful “virtual” (unobserved) solutions of PDE, when all is known about the PDE is a set of other (observed) solutions. This estimation task is dubbed deep redatuming, and extends the reach of inversion in substantive ways. I will discuss one example in particular: symmetric autoencoders, where symmetries are the driving principle behind scientific prediction. The mathematical context for this example is a ubiquitous form of “latent rank-1” structure, which has not been formalized yet, but which is found throughout nature. Joint work with Hongyu Sun, Brindha Kanniah, Pawan Bharadwaj, and Matt Li.



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