Numerical Identification of Nonlocal Potentials in Aggregation

作     者：Yuchen He Sung Ha Kang Wenjing Liao Hao Liu Yingjie Liu 

作者机构：Institute of Natural SciencesShanghai Jiao Tong UniversityShanghaiChina School of MathematicsGeorgia Institute of TechnologyAtlantaGeorgiaGA 30332-0160USA Department of MathematicsHong Kong Baptist UniversityHong Kong SAR 

出 版 物：《Communications in Computational Physics》 (计算物理通讯（英文）)

年 卷 期：2022年第32卷第8期

页      面：638-670页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：supported in part by Simons Foundation grant 282311 and 584960 supported in part by NSF grant NSF-DMS 1818751 and NSF-DMS 2012652 supported in part by HKBU 162784 and 179356 supported in part by NSF grants DMS-1522585 and DMS-CDS&E-MSS-1622453 

主　　题：Aggregation equation nonlocal potential PDE identification Bregman iteration operator splitting 

摘      要：Aggregation equations are broadly used tomodel population dynamicswith nonlocal interactions,characterized by a potential in the *** paper considers the inverse problem of identifying the potential from a single noisy spatialtemporal *** identification is challenging in the presence of noise due to the instability of numerical *** propose a robust model-based technique to identify the potential by minimizing a regularized data fidelity term,and regularization is taken as the total variation and the squared Laplacian.A split Bregman method is used to solve the regularized optimization *** method is robust to noise by utilizing a Successively Denoised Differentiation *** consider additional constraints such as compact support and symmetry constraints to enhance the performance *** also apply thismethod to identify time-varying potentials and identify the interaction kernel in an agent-based *** numerical examples in one and two dimensions are included to verify the effectiveness and robustness of the proposed method.