Recorded 15 July 2025. Haomin Zhou of the Georgia Institute of Technology presents "A supervised learning scheme for Hamilton-Jacobi equation via density coupling" at IPAM's Sampling, Inference, and Data-Driven Physical Modeling in Scientific Machine Learning Workshop. Abstract: In this talk, I will present a supervised learning scheme for the first order Hamilton--Jacobi PDEs in high dimensions. The scheme is designed by using the geometric structure of Wasserstein Hamiltonian flows via a density coupling strategy. It can be equivalently posed as a regression problem using the Bregman divergence, which provides the loss function in learning while the data is generated through the particle formulation of Wasserstein Hamiltonian flow. We prove a posterior estimate on L1 residual of the proposed scheme based on the support of coupling density. Several numerical examples with different Hamiltonians are provided to support our findings. This presentation is based on a joint work with Jianbo Cui (HK PolyU) and Shu Liu (UCLA). Learn more online at: https://www.ipam.ucla.edu/programs/workshops/sampling-inference-and-data-driven-physical-modeling-in-scientific-machine-learning-2/