Title: Sparse Bayesian Learning Approach for Estimating Interaction Kernels in the Motsch-Tadmor Model

Abstract: This study focuses on the data-driven reconstruction of asymmetric interaction kernels within the Motsch-Tadmor model, utilizing observed trajectory data. The dynamics of the system are described by semilinear evolution equations, wherein the interaction kernel establishes a normalized, state-dependent Laplacian operator that drives collective behavior. To tackle the associated nonlinear inverse problem, we introduce a variational framework that leverages the implicit structure of the governing equations to transform the kernel identification task into a subspace identification problem. We prove an identifiability result that delineates the specific conditions required for the unique recovery of the interaction kernel, modulo a scaling factor. For robust resolution of the inverse problem, we devise a sparse Bayesian learning algorithm that utilizes informative priors for regularization, facilitates uncertainty quantification, and supports rigorous model selection. Comprehensive numerical tests on various interacting particle systems validate the proposed framework’s accuracy, robustness, and interpretability across diverse noise levels and data scenarios.

Source: arXiv Generated at: 2026-06-03 00:00:00 UTC