23 citations · 74 across the 38 of their papers we have counts for
5 papers · 1 filter
Optimal Mesh Size for Inverse Medium Scattering Problems
Habib Ammari, Yat Tin Chow, Keji Liu
An optimal mesh size of the sampling region can help to reduce computational burden in practical applications. In this work, we investigate optimal choices of mesh sizes for the id…
Multilevel Optimal Transport: a Fast Approximation of Wasserstein-1 distances
Jialin Liu, Wotao Yin, Wuchen Li +1
We propose a fast algorithm for the calculation of the Wasserstein-1 distance, which is a particular type of optimal transport distance with homogeneous of degree one transport cos…
Optimal Human Navigation in Steep Terrain: a Hamilton-Jacobi-Bellman Approach
Christian Parkinson, David Arnold, Andrea L. Bertozzi +2
We present a method for determining optimal walking paths in steep terrain using the level set method and an optimal control formulation. By viewing the walking direction as a cont…
Algorithm for Hamilton-Jacobi equations in density space via a generalized Hopf formula
Yat Tin Chow, Wuchen Li, Stanley Osher +1
We design fast numerical methods for Hamilton-Jacobi equations in density space (HJD), which arises in optimal transport and mean field games. We overcome the curse-of-infinite-dim…
A Splitting Method For Overcoming the Curse of Dimensionality in Hamilton-Jacobi Equations Arising from Nonlinear Optimal Control and Differential Games with Applications to Trajectory Generation
Alex Tong Lin, Yat Tin Chow, Stanley Osher
Recent observations have been made that bridge splitting methods arising from optimization, to the Hopf and Lax formulas for Hamilton-Jacobi Equations with Hamiltonians . Thi…