We present a review of a series of learning methods used to identify the structure of dynamical systems, aiming to understand emergent behaviors in complex systems of interacting agents. These methods not only offer theoretical guarantees of convergence but also demonstrate computational efficiency in handling high-dimensional observational data. They can manage observation data from both first- and second-order dynamical systems, accounting for observation/stochastic noise, complex interaction rules, missing interaction features, and real-world observations of interacting agent systems. The essence of developing such a series of learning methods lies in designing appropriate loss functions using the variational inverse problem approach, which inherently provides dimension reduction capabilities to our learning methods.

翻译：我们综述了一系列用于识别动力系统结构的学习方法，旨在理解相互作用智能体复杂系统中的涌现行为。这些方法不仅提供了收敛性的理论保证，还在处理高维观测数据时展现出计算效率。它们能够处理来自一阶和二阶动力系统的观测数据，考虑观测/随机噪声、复杂交互规则、缺失的交互特征以及实际世界中交互智能体系统的观测。发展此类学习方法的本质在于利用变分逆问题方法设计适当的损失函数，这天然地为我们的学习方法提供了降维能力。