Research Interests

  • (Branched) optimal transport.
  • Computational optimal transport with applications in data science.
  • Calculus of variations and Geometric measure theory.
  • Inverse problems.
  • PDE with a focus on mixing of two-phase flows.

Research Projects.

(Under Constructions. Please refer to Posts for available short descriptions and intuitions.)

Multimariginal Optimal Transport (MMOT) [Green line project]

MMOT is a natural generalization from 2-marginal classical optimal transport problem to multi-marginals. The famous Wasserstein barycenter problem is an instance of MMOT problems. It can be used in data registrations, data fusion, etc…

Joint with Matt Parno, we introduce an exact and efficient way to compute MMOT with pairwise cost functions. This can be applied in any applications when any pairwise strictly convex relations between marginals are known.

Our python package description page can be found here MMOT2D.

The application of MMOT on predicting sea ice dynamics can be found in our group page Lagrangian Mapping.

Branched Optimal Transport and Fluids Mixing [Orange line project]

Shape Analysis [Blue line project]

Despeckle and Denoising [Purple line project]

Last updated: 2022-Oct-30