On the coercivity condition in the learning of interacting particle systems

Abstract

In the learning of systems of interacting particles or agents, coercivity condition ensures identifiability of the interaction functions, providing the foundation of learning by nonparametric regression. The coercivity condition is equivalent to the strictly positive definiteness of an integral kernel arising in the learning. We show that for a class of interaction functions such that the system is ergodic, the integral kernel is strictly positive definite, and hence the coercivity condition holds true.

References in corpus (5)

• Nonparametric inference of interaction laws in systems of agents from trajectory data
• Learning interaction kernels in heterogeneous systems of agents from multiple trajectories
• Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles
• Maximum likelihood estimation of potential energy in interacting particle systems from single-trajectory data
• Parameter Estimation for the McKean-Vlasov Stochastic Differential Equation

Cited by in corpus (1)

• Identifiability of interaction kernels in mean-field equations of interacting particles