Modeling multi-agent systems on networks is a fundamental challenge in a wide variety of disciplines. Given data consisting of multiple trajectories, we jointly infer the (weighted) network and the interaction kernel, which determine, respectively, which agents are interacting and the rules of such interactions. Our estimator is based on a non-convex optimization problem, and we investigate two approaches to solve it: one based on an alternating least squares (ALS) algorithm, and another based on a new algorithm named operator regression with alternating least squares (ORALS). Both algorithms are scalable to large ensembles of data trajectories. We establish coercivity conditions guaranteeing identifiability and well-posedness. The ALS algorithm appears statistically efficient and robust even in the small data regime, but lacks performance and convergence guarantees. The ORALS estimator is consistent and asymptotically normal under a coercivity condition. We conduct several numerical experiments ranging from Kuramoto particle systems on networks to opinion dynamics in leader-follower models.

翻译：在各类学科中，对网络上的多智能体系统进行建模是一项根本性挑战。基于包含多条轨迹的数据，我们联合推断（加权）网络和交互核，这两者分别决定了哪些智能体在相互作用以及这类相互作用的规则。我们的估计量基于一个非凸优化问题，并研究了两种求解方法：一种基于交替最小二乘算法，另一种基于一种名为算子回归结合交替最小二乘的新算法。两种算法均可扩展至大规模数据轨迹集合。我们建立了保证可识别性和适定性的强制性条件。交替最小二乘算法即使在少量数据情况下也表现出统计有效性和鲁棒性，但缺乏性能和收敛性保证。而在强制性条件下，算子回归结合交替最小二乘估计量是一致且渐近正态的。我们进行了多项数值实验，范围涵盖网络上的Kuramoto粒子系统到领导者-跟随者模型中的观点动力学。