GraphTransportation.jl
GraphTransportation.jl was the computational core of my dissertation. I implemented the Chambolle–Pock routine to solve the continuity-equation discretization of the graph transportation problem outlined in Erbar et al. (2020), then used the first-order information already sitting in those solutions to build an intrinsic gradient-descent scheme — this part was my own contribution — to locate optima of a variance functional and form the quadratic programs of Werenski et al. (2022) to synthesize and analyze barycenters of measures in the transport geometry.
Over the summer I worked with Fable, which suggested two real improvements: writing the objective as a second-order cone program (SOCP) instead, and reworking the original approach to solve the geodesic equations directly rather than route through Chambolle–Pock.
The library now carries several solver backends — the SOCP, Hamiltonian shooting, and entropic Sinkhorn among them — validated against closed-form solutions and results published in the papers below. Sinkhorn is not a drop-in alternative to the others; it solves a regularized version of the same problem, not the same object.