Learning Density Distribution of Reachable States for Autonomous Systems
This work addresses safety verification for autonomous systems by providing a probabilistic approach, though it is incremental as it builds on existing neural network reachability tools.
The paper tackles the problem of quantifying risk for autonomous systems by learning the density distribution of reachable states from trajectory data, resulting in a method that produces more accurate density estimates and less conservative risk quantification compared to worst-case analysis.
State density distribution, in contrast to worst-case reachability, can be leveraged for safety-related problems to better quantify the likelihood of the risk for potentially hazardous situations. In this work, we propose a data-driven method to compute the density distribution of reachable states for nonlinear and even black-box systems. Our semi-supervised approach learns system dynamics and the state density jointly from trajectory data, guided by the fact that the state density evolution follows the Liouville partial differential equation. With the help of neural network reachability tools, our approach can estimate the set of all possible future states as well as their density. Moreover, we could perform online safety verification with probability ranges for unsafe behaviors to occur. We use an extensive set of experiments to show that our learned solution can produce a much more accurate estimate on density distribution, and can quantify risks less conservatively and flexibly comparing with worst-case analysis.