Mathematics Colloquium - Lu Zhang
This event is in the past.
2:45 p.m. to 3:45 p.m.
Speaker: Lu Zhang (Columbia University)
Title: Coupling physics-deep learning inversion
Abstract: In recent years, there is an increasing interest in applying deep learning to geophysical/medical data inversion. However, direct application of end-to-end data-driven approaches to inversion have quickly shown limitations in the practical implementation. Indeed, due to the lack of prior knowledge on the objects of interest, the trained deep learning neural networks very often have limited generalization. In this talk, we introduce a new methodology of coupling model-based inverse algorithms with deep learning for two typical types of inversion problems. In the first part, we present an offline-online computational strategy of coupling classical least-squares based computational inversion with modern deep learning based approaches for full waveform inversion to achieve advantages that can not be achieved with only one of the components. In the second part, we present an integrated data-driven and model-based iterative reconstruction framework for joint inversion problems. The proposed method couples the supplementary data with the partial differential equation model to make the data-driven modeling process consistent with the model-based reconstruction procedure. We also characterize the impact of learning uncertainty on the joint inversion results for one typical inverse problem.