Tiangang Cui (Monash): Uncertainty quantification in inverse problems: a subspace approach

Speaker: Dr Tiangang Cui
Monash University

Title: Uncertainty quantification in inverse problems: a subspace approach

Date and time: Friday, 17 March 2017, 3:00-4:00pm
Location: Building 8 Level 9 Room 66 (AGR) RMIT City campus

Abstract: One of the greatest challenges in scientific computing today is how to combine complex-yet-incomplete data with large-scale models to create better estimation, prediction and decision. This challenge exists in almost every application area of scientific computing, from subsurface to astrophysics to medical imaging to biological systems to climate change and beyond. At the heart of this challenge is an inverse problem: we seek to convert indirect data into useful characterizations of unknown model parameters (e.g. physical quantities, initial or boundary conditions, model structures etc). 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 unknown parameters conditioned on the data. Unfortunately, solution of Bayesian inverse problems governed by large-scale, complex numerical models has traditionally been computationally intractable: models are complicated and computationally expensive to evaluate; available indirect data are often limited, noisy, and subject to natural variation; inversion algorithms often scale poorly to high-dimensional, or principally infinite-dimensional, model parameters.

In this talk, we will investigate the intrinsic dimensionality in both parameter space and model space by exploiting the interaction among various information sources and model structures. We will also discuss various strategies for jointly identifying low-dimensional parameter and model subspaces. The resulting subspaces naturally lead to accelerated sampling methods that can overcome two central challenges in Bayesian inverse problems: algorithmic scalability to high-dimensional parameters and computational efficiency of numerical solvers. The resulting methods also demonstrate potential reductions for problems with high-dimensional data. Examples in groundwater, glacier dynamics and atmospheric remote sensing are used to demonstrate the efficacy of our methods.

Bio: Tiangang Cui obtained all his degrees at the University of Auckland, New Zealand. He received his PhD in Engineering Science in 2010. After three years of postdoc research at the Department of Aeronautics and Astronautics at Massachusetts Institute of Technology, he joined ExxonMobil Corporation in Texas to find oil in subsurface. Tiangang left the US and joined the School of Mathematical Science at Monash University in last October as a lecturer. He will continue his research on computational inverse problems, data assimilation and computational statistics. In particular, his interest lies in exploiting intrinsic low-dimensional structures in those high dimensional problems.

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