Students in Data Science: Machine-aided reachability analysis by solving partial differential equations

Context

In research into highly automated driving, the risk assessment of traffic situations plays a central role, especially interactions with other road users. In order to safeguard vehicle functions, it is therefore necessary to analyze the predicted states of vehicles and road users. One method for this is reachability analysis using the Hamilton-Jacobi-Bellman equation. However, previous numerical calculation approaches pose a challenge for high-dimensional systems. In this work, the numerical solution is to be approximated by using machine learning methods.

Tasks

• Approximation of the solution of a partial differential equation using machine learning methods

Requirements

• Python programming skills and initial experience in machine learning methods
• An affinity for mathematical problems
• You work independently and in a structured manner, are motivated and committed
• You have a very good command of written and spoken German and English