Research
My research develops mathematical and computational tools for high-dimensional problems in scientific computing and machine learning. Three themes currently organize this work.
Scientific Computing
I study scalable numerical methods for high-dimensional equations and stochastic systems. A central goal is to combine compact function representations with algorithms that preserve the structure of the underlying problem. Current applications include Fokker-Planck equations, Kolmogorov backward equations, Hamilton-Jacobi-Bellman equations, and Gibbs distributions.
Tensor Networks
Tensor networks provide efficient representations for functions and probability distributions that would otherwise be prohibitively expensive to store or compute with. I develop tensor-network methods for high-dimensional PDEs, generative modeling, density estimation, and quantum-state reconstruction, with an emphasis on algorithms that are both scalable and mathematically interpretable.
Optimal Transport
I work on fast algorithms for entropic and constrained optimal transport, including martingale-type constraints. This research combines Sinkhorn-type iterations with sparse second-order methods to improve convergence while retaining the favorable structure of entropic formulations.
Selected and current work can be found on my Google Scholar profile.
Selected Papers
- Solving high-dimensional Fokker-Planck equation with functional hierarchical tensor, with Lexing Ying. Journal of Computational Physics 511, 113110 (2024).
- Accelerating Sinkhorn algorithm with sparse Newton iterations, with Michael Shavlovsky, Holakou Rahmanian, Elisa Tardini, Kiran Koshy Thekumparampil, Tesi Xiao, and Lexing Ying. International Conference on Learning Representations (2024).
- Variational inference and density estimation with non-negative tensor train, with Rajat Dwaraknath and Lexing Ying. arXiv:2507.21519 (2025).