Uncertainties exist in almost all engineering problems, leading to significant performance degradations, system failures and safety issues. Examples include, but are not limited to, semiconductor fabrications subject to nano-scale process variations, deep neural networks vulnerable to invisible data perturbations and attacks, and autonomous systems with unknown design or environmental parameters. In order to ensure robust design and safe operations of these systems, it is highly desirable to quantify and manage the impact of these uncertainties in a possibly high-dimensional parameter space. This talk will present some of our recent theoretical and numerical results of uncertainty quantification and management, with diverse applications ranging from electronic/photonic design automation, autonomous systems and robust deep neural networks. Main topics include principled uncertainty quantification under non-Gaussian correlated uncertainties, tensor learning for high-dimensional stochastic modeling, and a close-loop control method to improve the robustness of deep neural networks against various uncertainties and perturbations.

This is a joint work with my student Zichang He, Chunfeng Cui, and our collaborator Prof. Qianxiao Li of National University of Singapore.