标题： LevelSetPy：用于双曲Hamilton-Jacobi偏微分方程的GPU加速包 显示英文标题

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

摘要： 本文介绍了一个软件包的发布，用于通过水平集方法对（复数）动力系统中的\textit{安全}要求进行几何推理。 重点分析了安全性，使用哈密顿-雅可比方程。 在范围方面，我们提供了求解哈密顿-雅可比-伊萨克斯方程的数值算法实现：通过迎风法计算相关值函数的空间导数，通过拉克斯-弗里德里希斯格式计算哈密顿量，并通过总变差减小的龙格-库塔格式整体整合哈密顿-雅可比方程。 由于计算速度以及与其他现代科学计算库（通常用 Python 语言编写）的互操作性至关重要，我们利用现代计算框架如\texttt{CUPY}和\texttt{NUMPY}，并将大量计算转移到 GPU 设备以帮助并行化并在安全性分析中提高启动时间。 我们希望这个软件包能够帮助用户快速迭代想法，并通过现代工程问题中的几何仿真评估系统的各种安全性要求。 显示英文摘要

摘要： 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.