• Dr. Tiangang Cui
  • ACDL lab, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology
  • Holden Auditorium (Room 112)
  • 4:00 p.m.
  • Faculty Host: Dr. Heng Xiao

Inverse problems convert indirect measurements into useful characterizations of the unknown parameters of a physical system. Parameters are typically related to indirect measurements by mathematical models, which are complicated and expensive to evaluate numerically. Available indirect data are often limited, noisy, and subject to natural variation, while the unknown parameters of interest are often high-dimensional, or infinite-dimensional in principle. Solution of the inverse problem, along with model prediction and uncertainty assessment, can be cast in a Bayesian setting and thus naturally characterized by the posterior distribution over parameters conditioned on the data.

In this talk, I will present a set of likelihood-informed methods for overcoming the two central challenges in posterior exploration: algorithmic scalability to high-dimensional parameters and computational efficiency of numerical solvers. Our methods identify the intrinsic dimensionality in both the parameter space and the model space by exploiting the synergy between various information sources and model structures. The resulting reduced subspaces yield computationally fast posterior exploration tools that are scalable to high-dimensional parameters. Numerical examples in groundwater and atmospheric remote sensing are used to demonstrate the efficacy of our methods.

Tiangang Cui is currently a postdoc associate at the ACDL lab, Department of Aeronautics and Astronautics, Massachusetts Institute of Technology. He obtained his Bachelor in Applied Mathematics, Master in Engineering Science and PhD in Engineering Science all from the University of Auckland, New Zealand. His research interest lies in large-scale inverse problems, data assimilation, Bayesian statistics and scientific computing, with applications in subsurface, environmental fluids and imaging.