Research Project Title:
Polar Factorization of Maps via Optimal Transport
abstract:Optimal transport is a well-studied research area with applications as wide ranging as market allocation, machine learning, and fluid simulations. A seminal result in this field is Brenier's polar factorization theorem, which states that any nondegenerate vector field can be decomposed into an area-preserving map and a convex map. Our research will attempt to find an algorithm to approximate this factorization in the semi-discrete case. We will then explore applications of this algorithm in manipulation of smoke (and fluid) simulations and modeling of transport problems with non-uniform costs.
I am participating in the SuperUROP program because I want to gain valuable experience in the field of numerical optimization, especially as it applies to simulations. I have taken several high-level computer science and maths courses, and I am excited to apply my knowledge towards my research!