Probabilistic Reachable Set (PRS) plays a crucial role in many fields of autonomous systems, yet efficiently generating PRS remains a significant challenge. This paper presents a learning approach to generating 2-dimensional PRS for states in a dynamic system. Traditional methods such as Hamilton-Jacobi reachability analysis, Monte Carlo, and Gaussian process classification face significant computational challenges or require detailed dynamics information, limiting their applicability in realistic situations. Existing data-driven methods may lack accuracy. To overcome these limitations, we propose leveraging neural networks, commonly used in imitation learning and computer vision, to imitate expert methods to generate PRS approximations. We trained the neural networks using a multi-label, self-supervised learning approach. We selected the fine-tuned convex approximation method as the expert to create expert PRS. Additionally, we continued sampling from the distribution to obtain a diverse array of sample sets. Given a small sample set, the trained neural networks can replicate the PRS approximation generated by the expert method, while the generation speed is much faster.

翻译：概率可达集在自主系统的诸多领域中扮演着关键角色，然而高效生成概率可达集仍是一个重大挑战。本文提出一种为动态系统中的状态生成二维概率可达集的学习方法。传统方法如 Hamilton-Jacobi 可达性分析、蒙特卡洛方法和高斯过程分类面临显著的计算挑战或需要详细的动力学信息，这限制了它们在实际场景中的适用性。现有的数据驱动方法可能缺乏精度。为克服这些限制，我们提出利用在模仿学习和计算机视觉中常用的神经网络来模仿专家方法，以生成概率可达集的近似。我们采用多标签自监督学习方法训练神经网络。我们选择微调后的凸近似方法作为专家来创建专家概率可达集。此外，我们持续从分布中采样以获得多样化的样本集。给定一个小样本集，训练好的神经网络能够复现专家方法生成的概率可达集近似，同时生成速度显著更快。