Tong Group

Optimal Transport & Geometry

Developing efficient computational methods for optimal transport with applications to single-cell biology, trajectory inference, and generative modeling.

Optimal transport provides a principled mathematical framework for comparing probability distributions and understanding the geometry of data. Our group has contributed foundational tools to this area, including POT: Python Optimal Transport—one of the most widely used OT libraries—and theoretical advances in diffusion Earth Mover’s distance and Wasserstein Lagrangian flows.

We develop efficient computational methods for optimal transport on manifolds and graphs, with applications to single-cell biology, trajectory inference, and generative modeling. Our work on minibatch optimal transport for flow matching demonstrated how OT can improve the training of generative models by providing better couplings between source and target distributions.

Key Directions

  • Computational Frameworks: Efficient algorithms for Wasserstein flows, geodesic Sinkhorn on manifolds, and transport on graphs
  • Generative Modeling: Minibatch OT for flow matching, meta flow matching on the Wasserstein manifold
  • Biological Applications: Trajectory inference, metric flow matching for smooth interpolations on data manifolds
  • Graph Signal Processing: Diffusion EMD, unbalanced OT, and graph Fourier MMD for network data
optimal-transport differential-geometry machine-learning computational-biology

People

Alexander Tong

Alexander Tong

Principal Investigator

Katarina Petrović

Katarina Petrović

PhD Student

Selected Publications

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