Monte Carlo reachability samples trajectories under sampled actions and disturbances, then builds a KDTree-backed approximation of the reachable set. ARIAA uses importance sampling to concentrate samples near the boundary, sharply reducing sample count for a given accuracy.
The engine scales to ten or more state dimensions on CPU and higher on GPU via a JAX-JIT kernel.
Related
- Reachability Analysis — Computing the set of future states a system can reach from a given initial state under bounded actions and disturbances.
- Adaptive Mesh Refinement — A reachability method that refines resolution only near the boundary of the reachable set, keeping computation tractable in 2D–5D.