6 papers
Artifacts of Numerical Integration in Learning Dynamical Systems
Bing-Ze Lu, Richard Tsai
In many applications, one needs to learn a dynamical system from its solutions sampled at a finite number of time points. The learning problem is often formulated as an optimizatio…
Visibility Optimization for Surveillance-Evasion Games
Louis Ly, Yen-Hsi Richard Tsai
We consider surveillance-evasion differential games, where a pursuer must try to constantly maintain visibility of a moving evader. The pursuer loses as soon as the evader becomes…
Equivalent extensions of Hamilton-Jacobi-Bellman equations on hypersurfaces
Lindsay Martin, Richard Tsai
We present a new formulation for the computation of solutions of a class of Hamilton Jacobi Bellman (HJB) equations on closed smooth surfaces of co-dimension one. For the class of…
Greedy Algorithms for Sparse Sensor Placement via Deep Learning
Louis Ly, Yen-Hsi Richard Tsai
We consider the exploration problem: an agent equipped with a depth sensor must map out a previously unknown environment using as few sensor measurements as possible. We propose an…
A Multiscale Domain Decomposition Algorithm For Boundary Value Problems For Eikonal Equations
Lindsay Martin, Richard Tsai
In this paper, we present a new multiscale domain decomposition algorithm for computing solutions of static Eikonal equations. The new method is an iterative two-scale method that…
Growth rate of crystal surfaces with several dislocation centers
Takeshi Ohtsuka, Yen-Hsi Richard Tsai, Yoshikazu Giga
We study analytically and numerical the growth rate of a crystal surface growing by several screw dislocations. To describe several spiral steps we use the revised level set method…