Optimal Mass Transport

Optimal mass transport (OMT) is a mathematical framework for efficiently moving mass between two probability distributions, minimizing a cost function that reflects the "effort" of transportation. Current research focuses on extending OMT to handle increasingly complex scenarios, including probabilistic constraints, dynamic systems like rigid body rotations governed by Euler equations, and high-dimensional data such as single-cell genomics data. This involves developing novel algorithms, such as those based on reduced basis methods for faster computation and Gaussian mixture models for probabilistic modeling, to solve the resulting optimization problems. OMT's applications span diverse fields, from astrodynamics and fluid dynamics to machine learning and single-cell analysis, offering powerful tools for data analysis and control system design.