On the coercivity condition in the learning of interacting particle systems
This work provides a theoretical foundation for the identifiability of interaction functions in learning interacting particle systems, which is crucial for researchers developing nonparametric regression methods in this domain.
This paper addresses the identifiability of interaction functions in learning interacting particle systems. It demonstrates that for a class of ergodic interaction functions, the integral kernel associated with the learning problem is strictly positive definite, thereby satisfying the coercivity condition.
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.