Transport information geometric computations
Abstract
The project develops new computational algorithms with theoretical guarantees for machine learning-induced scientific computations of partial differential equations. It involves interactive studies among optimal transport, information geometry, and mean-field games, which can construct parametric approximations of evolutionary partial differential equations in nonlinear models. This approach introduces fast, efficient, and mathematical-safe variational schemes for computational fluid dynamics. Typical examples include linear, nonlinear Fokker-Planck equations and mean-field control problems. Besides, it offers new models and efficient algorithms for studying a large number of population behaviors. In applications, it helps predict and control the evolution of pandemics in a spatial domain.
Document Details
- Document Type
- DoD Grant Award
- Publication Date
- Feb 29, 2024
- Source ID
- FA95502310087
Entities
People
- Wuchen Li
Organizations
- Air Force Office of Scientific Research
- United States Air Force
- University of South Carolina