Yuan Luo

PhD Candidate in Applied Math at UC Davis

My primary research interest are computational topology, geometry processing, and their applications in machine learning.

My current and previous mentors include Dr. Joel Hass, Dr. Dmitriy Morozov, Dr. Patrice Koehl, Dr. Arnur Nigmetov, Dr. Bradley J. Nelson and Dr. Li Cai.

I interned at Meta as a machine learning software engineer in summer 2025, at the International Computer Science Institute as a research intern in summers 2024 and 2026, and at Lawrence Berkeley National Laboratory as a research intern in summer 2023.

Research

Pairwise distances among five tori of revolution with increasing minor radii

Computing a Metric on the Shape Space of Tori

Yuan Luo, Yanwen Luo, Patrice Koehl, and Joel Hass

ACM Transactions on Graphics (SIGGRAPH Asia 2026)

A metric on the shape space of triangulated genus-one surfaces that do not need same mesh combinatorics.

pdf code

Hyperbolic checkerboard morphing on the Poincaré disk

Morphing Graphs on Hyperbolic Surfaces

Yanwen Luo and Yuan Luo

under review

The first algorithm to morph geometric graphs on hyperbolic surfaces, based on a generalization of Tutte’s spring embedding theorem.

arxiv pdf code gallery

A bifiltered graph and its Betti tables in the plane

Computing Betti Tables and Minimal Presentations of Zero-Dimensional Persistent Homology

Yuan Luo, Dmitriy Morozov, and Luis Scoccola

under review

Log-linear algorithms for Betti tables of zero-dimensional bigraded persistence.

arxiv pdf code

Point cloud trajectory maximizing H1 persistence

Accelerating Iterated Persistent Homology Computations with Warm Starts

Yuan Luo and Bradley J. Nelson

Computational Geometry, 2024

Update matrix factorizations across similar filtrations, handling insertion, deletion, and permutation in a single batch.

arxiv journal code

Dimension reduction of orthogonal cycles by PCA, MDS, Isomap, and persistent homology

Topology-Preserving Dimensionality Reduction via Interleaving Optimization

Bradley J. Nelson and Yuan Luo

arXiv 2022

Use persistent homology to keep clusters and holes in correspondence after projection.

arxiv pdf code

Projects

Side-by-side diffusion denoising of headphones: unguided versus H1 with delayed H0 guidance over 50 steps

Topology-Guided Diffusion

PyTorch

Guide a diffusion sampler with persistent homology losses so generated images keep prescribed loops.

Exact geodesic path between two surface points on a triangulated torus

ShapeComp

C++ · Python

Geometry processing for mesh I/O, exact geodesics, homology generators, and fundamental domains, with reusable comparison primitives and Python bindings.

github

BATS

C++ · Python

Computing and visualizing persistent homology, including the update schemes used for iterated persistence computations.

github

Wasserstein matching between initial and last H1 persistence diagrams

Torch-TDA

PyTorch

Automatic differentiation of topological features and common topological loss functions for machine-learning pipelines.

github