Speaker: Dr. Deep Ray, Assistant Professor, University of Maryland, College Park (deepray@umd.edu)
Date: Friday, September 20, 2024, 4:15 – 5:15 PM
Location: Science Engineering Hall (SCEN 404) in-person.
If you wish to receive the Zoom link, please contact Dr. Chen Liu
Title: Bayesian Inference Using Deep Generative Models
Abstract: Inverse problems arise in numerous science and engineering applications, such as medical imaging, weather forecasting and predicting the spread of wildfires. Bayesian inference provides a principled approach to solve inverse problems by considering a statistical framework, which is particularly useful when the measurement/output of the forward problem is corrupted by noise. However, Bayesian inference algorithms can be challenging to implement when the inferred field is high-dimensional, or when the known prior information is too complex.
In this talk, we will see how conditional Wasserstein generative adversarial networks (cWGANs) can be designed to learn and sample from conditional distributions in Bayesian inference problems. The proposed approach modifies earlier variants of the architecture proposed by Adler et al. (2018) and Ray et al. (2022) in two fundamental ways: i) the gradient penalty term in the GAN loss makes use of gradients with respect to all input variables of the critic, and ii) once trained, samples are generated from the posterior by considering an open ball around the measurement. These two modifications are motivated by a convergence proof that ensures the learned conditional distribution weakly approximates the true conditional distribution governing the data. Through simple examples we show that this leads to a more robust training process. We also demonstrate that this approach can be used to solve complex real-world inverse problems.
Short Bio: Dr. Deep Ray is an Assistant Professor at the University of Maryland, College Park, where he holds a joint appointment in the Department of Mathematics and the Institute for Physical Science and Technology. His research lies at the interface of conventional numerical analysis and machine learning, with a particular focus on scientific machine learning and hyperbolic conservation laws. Before joining the University of Maryland, Dr. Ray served as a Postdoctoral Research Associate in the Aerospace and Mechanical Engineering Department at the University of Southern California. In addition, he held postdoctoral positions at Computational and Applied Mathematics at Rice University and Computational Mathematics and Simulation Science, EPFL, Switzerland. He earned his Ph.D. degree from Tata Institute of Fundamental Research – Center For Applicable Mathematics.
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