CMX Lunch Seminar
My research interests center around utilizing mathematical modeling and computational techniques to address challenges spanning a range of disciplines, such as epidemiology, optimization, data science, machine learning, mean-field games, optimal control, partial differential equations, and related areas.
This presentation explores optimization strategies for improving both partial differential equation (PDE) computations and score-based generative models (SGM). In the realm of numerical computations, we introduce a saddle point framework that capitalizes on the inherent structure of PDEs. Integrated seamlessly with existing discretization schemes, this framework eliminates the necessity for nonlinear inversions, paving the way for efficient parallelization. Shifting focus to SGM, we delve into the Wasserstein proximal operator (WPO) to understand the mathematical foundations of SGM - it can be written as the Wasserstein proximal operators of cross-entropy. Leveraging PDE formulation of WPO, we propose an WPO-informed score model which showcases accelerated training and reduced data requirements.