High Dimensional Reachability

High-dimensional reachability focuses on determining the set of all possible future states of a complex system, a crucial problem for verifying the safety and performance of autonomous systems like robots and vehicles. Current research heavily utilizes deep learning methods, particularly neural networks, to approximate solutions to the computationally expensive Hamilton-Jacobi equations that govern reachability, often incorporating techniques like improved activation functions and exact boundary condition imposition to enhance accuracy. This field is vital for ensuring the safety and reliability of increasingly sophisticated autonomous systems operating in high-dimensional state spaces, impacting both theoretical verification methods and practical deployment of these technologies.