Optimal Transport for Inverse Problems and Implicit Regularization

Explore the applications of optimal transport theory in solving inverse problems and its implicit regularization effects in this virtual seminar talk from the 24th Imaging & Inverse Problems (IMAGINE) OneWorld SIAM-IS series. Delve into the historical development of optimal transport, from Monge's initial work in 1781 to Kantorovich's groundbreaking contributions in 1942. Discover how the quadratic Wasserstein distance, derived from optimal transport theory, addresses longstanding challenges in classical least-squares methods, such as nonconvexity and noise sensitivity. Learn about the adoption of this approach in the oil industry and its broader implications for data-fitting problems. Examine the preconditioning and implicit regularization effects of various mathematical metrics when used as objective functions in optimization, likelihood functions in Bayesian inference, and measures of residual in numerical PDE solutions. Gain insights from speaker Yunan Yang of New York University in this hour-long presentation that bridges theoretical concepts with practical applications in industrial and applied mathematics.