Sylvia Herbert - University of California, Berkeley (UC Berkeley) Hamilton-Jacobi Reachability Analysis struggles with high-dimensional dynamic models due to the curse of dimensionality. In this talk I will discuss work to alleviate this computational burden for general nonlinear coupled systems. These techniques include (a) decomposing coupled systems by replacing coupled states with disturbances, (b) initializing computations with previous solutions or coarse approximations with guarantees for convergence, and (c) precomputing a pursuit-evasion game between high-dimensional system models and lower-dimensional reduced-order models used for fast online planning while maintaining safety with respect to the full system dynamics.