Optimization-Based Uncertainty Quantification

This lecture by the instructor focuses on optimization-based uncertainty quantification for ill-posed inverse problems, using examples from the physical sciences. The talk covers the challenges of unfolding detector smearing in differential cross-section measurements at the Large Hadron Collider and space-based inference of carbon dioxide concentrations and fluxes with the Orbiting Carbon Observatory-2. The instructor explains the problem formulation, discretization techniques, and the linearized surrogate model for the Orbiting Carbon Observatory-2. Various regularization methods for handling ill-posed problems are discussed, along with the concept of regularization-based uncertainty quantification. The lecture concludes with a comparison of different interval constructions and decision-theoretic uncertainty quantification approaches.