With the continuous advancement in autonomous systems, it becomes crucial to provide robust safety guarantees for safety-critical systems. Hamilton-Jacobi Reachability Analysis is a formal verification method that guarantees performance and safety for dynamical systems and is widely applicable to various tasks and challenges. Traditionally, reachability problems are solved by using grid-based methods, whose computational and memory cost scales exponentially with the dimensionality of the system. To overcome this challenge, DeepReach, a deep learning-based approach that approximately solves high-dimensional reachability problems, is proposed and has shown lots of promise. In this paper, we aim to improve the performance of DeepReach on high-dimensional systems by exploring different choices of activation functions. We first run experiments on a 3D system as a proof of concept. Then we demonstrate the effectiveness of our approach on a 9D multi-vehicle collision problem.

翻译：随着自主系统的持续进步，为安全关键系统提供稳健的安全保障变得至关重要。 Hamilton-Jacobi可达性分析是一种形式化验证方法，能够保证动态系统的性能和安全性，并广泛适用于各类任务与挑战。 传统上，可达性问题通过基于网格的方法求解，其计算和内存成本随系统维度呈指数级增长。 为克服这一挑战，基于深度学习的DeepReach方法被提出，用于近似求解高维可达性问题，并展现出巨大潜力。 本文旨在通过探索不同的激活函数选择，提升DeepReach在高维系统中的性能。 我们首先在三维系统上进行实验作为概念验证，随后在九维多车碰撞问题上验证了我们方法的有效性。