LevelSetPy: A GPU-Accelerated Package for Hyperbolic Hamilton-Jacobi Partial Differential Equations

Abstract

This article introduces a software package release for geometrically reasoning about the \textit{safety} desiderata of (complex) dynamical systems via level set methods. In emphasis, safety is analyzed with Hamilton-Jacobi equations. In scope, we provide implementations of numerical algorithms for the resolution of Hamilton-Jacobi-Isaacs equations: the spatial derivatives of the associated value function via upwinding, the Hamiltonian via Lax-Friedrichs schemes, and the integration of the Hamilton-Jacobi equation altogether via total variation diminishing Runge-Kutta schemes. Since computational speed and interoperability with other modern scientific computing libraries (typically written in the Python language) is of essence, we capitalize on modern computational frameworks such as \texttt{CUPY} and \texttt{NUMPY} and move heavy computations to GPU devices to aid parallelization and improve bring-up time in safety analysis. We hope that this package can aid users to quickly iterate on ideas and evaluate all possible safety desiderata of a system via geometrical simulation in modern engineering problems.