Robust Modeling and Algorithm Design for Science and Engineering

Abstract

Efficiently extracting information from data sets is at the core of modern scientific com- puting and data-driven discovery. Modeling and algorithm design thus become crucial for research in many scientific and engineering domains. We develop formulations that fuse physics-based and data-driven models, use robust statistics to integrate information from noisy sources, and enforce the solution structure to incorporate domain knowledge. These formulations are mathematically challenging, as non-smooth structure and non-convex geom- etry make algorithm design and analysis difficult. The technical thrust of the research targets these non-convex, non-smooth problems to obtain provably convergent efficient methods. To help solve fundamental problems in science and engineering, we develop and implement methods in the context of specific applications, including phase retrieval, data decomposition, dynamic inference, and brain imaging. We have developed open source software packages, and shared them with our collaborators and the broader research community via GitHub.