NAMEDhruv Patel | Postdoctoral Research Fellow, Mechanical Engineering, Stanford University
TITLE"Efficient Bayesian Inference using Deep Generative Priors and Multi-fidelity Modeling"
ABSTRACTBayesian inference provides a principled approach for quantifying uncertainty in various earth and environmental science applications that require the incorporation of data into a mathematical model. Despite its elegant formulation and diverse applications, it faces two challenges when applied to practical problems: (1) inferring fields of large dimensions (‘curse of dimensionality') and/or (2) characterizing appropriate prior distribution. In this talk, we will show how by leveraging ideas from deep generative modeling we can tackle both these challenges in a unified framework. Specifically, we will show how by using the approximate distribution learned by a Generative Adversarial Network (GAN) as a prior in a Bayesian update and by reformulating the resulting inference problem in the low-dimensional latent space of the GAN enable the efficient solution of large-scale stochastic inverse problems. Furthermore, to reduce the overall computational cost associated with the posterior inference with gradient-based Markov Chain Monte Carlo methods, we propose a novel multi-fidelity Hamiltonian Monte Carlo algorithm. We will demonstrate the efficacy of the proposed methods on a range of stochastic inverse problems (arising in different domains such as mechanics, material science, subsurface flow modeling, medical imaging, etc.). We will further showcase the utility of quantifying uncertainty in an optimal experimental design setting.
REFERENCESDhruv V. Patel, Deep Ray, Assad A. Oberai, "Solution of Physics-based Bayesian Inverse Problems with Deep Generative Priors", in review (Journal of Computer Methods in Applied Mechanics and Engineering), 2021, preprint: https://arxiv.org/abs/2107.02926
Dhruv V. Patel, Assad A. Oberai, "Generative Adversarial Network-based Priors for Quantifying Uncertainty in Supervised Learning", accepted (SIAM Journal of Uncertainty Quantification), 2021, preprint: https://arxiv.org/abs/2003.12597
BIODhruv Patel is the Stephen Timoshenko Distinguished Postdoctoral Fellow in the Mechanics and Computation Group (Mechanical Engineering) at Stanford. Prior to joining Stanford, he received his Ph.D. degree in Aerospace and Mechanical engineering from USC (2021) and Master of Science in Applied Mechanics from IIT Delhi (2016). He is a recipient of the Stephen Timoshenko Distinguished Postdoctoral Fellowship at Stanford and Professor Karunes Memorial award for Best Master’s thesis in applied mechanics at IIT Delhi. His research lies at the intersection of physics-based and data-driven modeling, inverse problems, and uncertainty quantification with applications to computational science and engineering. He is particularly interested in the question of how to optimally combine physics-based models with modern machine learning algorithms to develop more data-efficient and accurate hybrid models.
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