George Mason University
(Colloquium Tea held at 4:00 pm in 101A Crowley Hall)
PDE Constrained Optimization with Applications in Engineering, Data Science, and Machine Learning
This talk will provide an introduction to large scale (infinite dimensional) optimization problems. Special attention will be given to optimization problems constrained by partial differential equations (PDEs) with or without uncertainty. Optimization algorithms in infinite dimensions will be discussed and will be shown to have mesh independence. Reduced order modeling, tensor train decomposition and matrix sketching like tools will be employed, and further developed, to help overcome the large computational costs. Applications in imaging, fluid dynamics, complex flows, shape optimization, materials science, anomalous diffusion, drug delivery, data science and machine learning will be discussed. Especial emphasis will be given to study airflow and pathogen (such as covid-19) propagation in built environments. The developments in reduced order modeling for data science has continued to play a pivotal role in the search for gravitational waves, ever since their first discovery five years ago.