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A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Model.

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Title: A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Model.
Authors: Feng, Jinchao1 jcfeng@gbu.edu.cn, Tang, Sui2 suitang@math.ucsb.edu
Source: Journal of Scientific Computing. Aug2026, Vol. 108 Issue 2, p1-27. 27p.
Subjects: Kernel (Mathematics), Inverse problems
Abstract: In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch–Tadmor model based on observed trajectory data. The model under consideration is governed by a class of semilinear evolution equations, where the interaction kernel defines a normalized, state-dependent Laplacian operator that governs collective dynamics. To address the resulting nonlinear inverse problem, we propose a variational framework that reformulates kernel identification using the implicit form of the governing equations, reducing it to a subspace identification problem. We establish an identifiability result that characterizes conditions under which the interaction kernel can be uniquely recovered up to scale. To solve the inverse problem robustly, we develop a sparse Bayesian learning algorithm that incorporates informative priors for regularization, quantifies uncertainty, and enables principled model selection. Extensive numerical experiments on representative interacting particle systems demonstrate the accuracy, robustness, and interpretability of the proposed framework across a range of noise levels and data regimes. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
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Abstract:In this paper, we investigate the data-driven identification of asymmetric interaction kernels in the Motsch–Tadmor model based on observed trajectory data. The model under consideration is governed by a class of semilinear evolution equations, where the interaction kernel defines a normalized, state-dependent Laplacian operator that governs collective dynamics. To address the resulting nonlinear inverse problem, we propose a variational framework that reformulates kernel identification using the implicit form of the governing equations, reducing it to a subspace identification problem. We establish an identifiability result that characterizes conditions under which the interaction kernel can be uniquely recovered up to scale. To solve the inverse problem robustly, we develop a sparse Bayesian learning algorithm that incorporates informative priors for regularization, quantifies uncertainty, and enables principled model selection. Extensive numerical experiments on representative interacting particle systems demonstrate the accuracy, robustness, and interpretability of the proposed framework across a range of noise levels and data regimes. [ABSTRACT FROM AUTHOR]
ISSN:08857474
DOI:10.1007/s10915-026-03344-2