On the identifiability of interaction functions in systems of interacting particles

Abstract

We address a fundamental issue in the nonparametric inference for systems of interacting particles: the identifiability of the interaction functions. We prove that the interaction functions are identifiable for a class of first-order stochastic systems, including linear systems with general initial laws and nonlinear systems with stationary distributions. We show that a coercivity condition is sufficient for identifiability and becomes necessary when the number of particles approaches infinity. The coercivity is equivalent to the strict positivity of related integral operators, which we prove by showing that their integral kernels are strictly positive definite by using Müntz type theorems.

arXiv comment25 pages

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Cited by in corpus (3)

• Learning interaction kernels in mean-field equations of 1st-order systems of interacting particles
• Learning interaction kernels in stochastic systems of interacting particles from multiple trajectories
• Learning Interaction Kernels for Agent Systems on Riemannian Manifolds