The Department of Applied Mathematics weekly seminar is given by scholars and researchers working in applied mathematics, broadly interpreted.
Title: Data-driven approaches to imaging and characterization of advanced materials from laser ultrasonic test data
Abstract: The first part of this talk highlights recent advances in the theory of inverse scattering germane to a new class of imaging functionals that enable spatiotemporal tracking of engineered (or manmade) processes in complex and/or unknown environments. More specifically, I will introduce the theory of differential imaging that is rooted in the factorization and linear sampling methods. The second part of the talk showcases an application of the sampling-based imaging indicators to laser ultrasonic imaging and characterization of additively manufactured (AM) components from limited-aperture test data. This includes a discussion of our recent efforts to (a) enhance and accelerate the waveform inversion process via deep learning in order to enable real-time remote sensing of AM processes, and (b) address challenges related to reconstructions from noisy measurements. The indicator maps from the sampling type imaging functionals are compared to those furnished by the state-of-the-art approaches to laser ultrasonic imaging. Our preliminary results highlight the unique advantages of ML-accelerated waveform tomography when applied to multi-fidelity experimental data.