CAREER: Scalable Approaches for Large-Scale Data-driven Bayesian Inverse Problems in High Dimensional Parameter Spaces

University Of Texas At Austin, Austin TX

Investigators

Abstract

Inverse problems are contemporary tools in cyberinfrastructure and mathematical research, especially in inferring knowledge from observational and experimental data together with simulations and models. They are pervasive in scientific discovery and decision-making for complex, natural, engineered, and societal systems, and thus are of paramount importance across many disciplines including engineering mathematical and physical sciences. For inverse problems that serve as a basis for design, control, discovery, and decision-making, their solutions must be equipped with certain degree of confidence. Though the past decades have seen advances in both theories and computational algorithms for inverse problems, quantifying the uncertainty in their solution remains challenging and an open problem facing the computational science and engineering community. The drastic increase in the quantity of measurements and data holds promise for data-driven scientific discoveries. However, much data remains unused as inversion - a systematic tool to infer knowledge from data - is unable to scale up to the quantity of data being generated. This proposal develops computational and data scalable strategies to tackle the challenge of large-scale data-driven statistical inverse problems in order to continue the pace of scientific discoveries and to promote the progress of science, aligned with NSF's mission. The proposed integrated research and education program contributes uncertainty quantification (UQ) skills to modern education and training of future STEM workforce; provides scalable inverse/UQ mathematical algorithms/software that potentially advance the frontiers of computational science and engineering; provides inverse/UQ cutting-edge algorithms/software that can potentially improve oil/gas discovery in order to meet the ever-increasing demand in energy; constitutes the PI?s ongoing contribution to the pipeline of US scientists, engineers, and innovators to maintain the US global leadership in technology and sciences; and educates and supplies additional leaders/experts from underrepresented minorities to Big-Data/UQ research communities. This project develops an integrated education and cross-disciplinary research program that tackles big-data-driven large-scale uncertainty quantification (UQ) problems in high dimensional parameter spaces. The project rigorously develops a randomized misfit approach that exploits extreme computing systems to efficiently reduce the amount of ever-growing observational data. It develops a comprehensive ensemble transform approach that has potential to solves large-scale statistical Bayesian inverse problems in a scalable manner using current and future NSF computing infrastructures. The novelty of the proposed interdisciplinary approach is to bring together advances from stochastic programming, probability theory, parallel computing, and computer vision to produce a new and rigorous data reduction method for inverse/UQ problems; justifiable efficient sampling approaches for large-scale Bayesian inverse problems; and open-source software implementing these approaches. These products can enable mathematicians, scientists, and engineers in sensing-based disciplines to address challenging inverse/UQ problems that can lead to new scientific discoveries. Inverse seismic wave propagation is chosen as the demanding testbed for the developments. This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.