8 research outputs found
Identifiability of interaction kernels in mean-field equations of interacting particles
We study the identifiability of the interaction kernels in mean-field
equations for intreacting particle systems. The key is to identify function
spaces on which a probabilistic loss functional has a unique minimizer. We
prove that identifiability holds on any subspace of two reproducing kernel
Hilbert spaces (RKHS), whose reproducing kernels are intrinsic to the system
and are data-adaptive. Furthermore, identifiability holds on two ambient L2
spaces if and only if the integral operators associated with the reproducing
kernels are strictly positive. Thus, the inverse problem is ill-posed in
general. We also discuss the implications of identifiability in computational
practice