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] |
| Copyright of Journal of Scientific Computing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) | |
| Database: | Engineering Source |
| FullText | Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 194451936 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Model. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Feng%2C+Jinchao%22">Feng, Jinchao</searchLink><relatesTo>1</relatesTo><i> jcfeng@gbu.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Tang%2C+Sui%22">Tang, Sui</searchLink><relatesTo>2</relatesTo><i> suitang@math.ucsb.edu</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Scientific+Computing%22">Journal of Scientific Computing</searchLink>. Aug2026, Vol. 108 Issue 2, p1-27. 27p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Kernel+%28Mathematics%29%22">Kernel (Mathematics)</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+problems%22">Inverse problems</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: 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] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Scientific Computing is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.) |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1007/s10915-026-03344-2 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 27 StartPage: 1 Subjects: – SubjectFull: Kernel (Mathematics) Type: general – SubjectFull: Inverse problems Type: general Titles: – TitleFull: A Sparse Bayesian Learning Algorithm for Estimation of Interaction Kernels in Motsch-Tadmor Model. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Feng, Jinchao – PersonEntity: Name: NameFull: Tang, Sui IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2026 Type: published Y: 2026 Identifiers: – Type: issn-print Value: 08857474 Numbering: – Type: volume Value: 108 – Type: issue Value: 2 Titles: – TitleFull: Journal of Scientific Computing Type: main |
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