We present a comprehensive examination of learning methodologies employed for the structural identification of dynamical systems. These techniques are designed to elucidate emergent phenomena within intricate systems of interacting agents. Our approach not only ensures theoretical convergence guarantees but also exhibits computational efficiency when handling high-dimensional observational data. The methods adeptly reconstruct both first- and second-order dynamical systems, accommodating observation and stochastic noise, intricate interaction rules, absent interaction features, and real-world observations in agent systems. The foundational aspect of our learning methodologies resides in the formulation of tailored loss functions using the variational inverse problem approach, inherently equipping our methods with dimension reduction capabilities.

翻译：我们全面审视了用于动力系统结构辨识的学习方法。这些技术旨在阐明相互作用智能体复杂系统中的涌现现象。我们的方法不仅保证了理论收敛性，而且在处理高维观测数据时展现出计算高效性。该方法能够熟练重构一阶和二阶动力系统，适应观测噪声与随机噪声、复杂交互规则、缺失交互特征以及智能体系统中的真实观测数据。我们学习方法的基础在于利用变分逆问题方法构建定制化损失函数，这自然赋予了方法降维能力。