Haomin Zhou, Professor, Georgia Institute of Technology

Jialin Hong, Professor

Wasserstein Hamiltonian flow and structure preserving numerical schemes

8:30-9:30 , July 21(Thursday), ZOOM ID: 926 3601 5183

In this talk, I will present selected results from our recent studies on  Wasserstein Hamiltonian Flow (WHF). The concept, motivations, and examples of WHF are given in the first part. WHF describes a principle stating that the density of a Hamiltonian flow in sample space is a Hamiltonian flow in density manifold. It can also be derived in a control formulation as the Euler-Lagrange equation in the density space. Typical examples include the geodesic equation on Wasserstein manifold, Schrodinger equations, and Schrodinger bridge problems. In the second part, a fully discrete numerical scheme is introduced. The scheme has many desirable properties such as mass and symplectic structure preservation, time reversibility, and time transverse invariant.