@Article{CiCP-32-638,
author = {He , YuchenKang , Sung HaLiao , WenjingLiu , Hao and Liu , Yingjie},
title = {Numerical Identification of Nonlocal Potentials in Aggregation},
journal = {Communications in Computational Physics},
year = {2022},
volume = {32},
number = {3},
pages = {638--670},
abstract = {<p style="text-align: justify;">Aggregation equations are broadly used to model population dynamics with
nonlocal interactions, characterized by a potential in the equation. This paper considers the inverse problem of identifying the potential from a single noisy spatial-temporal process. The identification is challenging in the presence of noise due to the
instability of numerical differentiation. We 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 problem. Our method is robust
to noise by utilizing a Successively Denoised Differentiation technique. We consider
additional constraints such as compact support and symmetry constraints to enhance
the performance further. We also apply this method to identify time-varying potentials
and identify the interaction kernel in an agent-based system. Various numerical examples in one and two dimensions are included to verify the effectiveness and robustness
of the proposed method.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2021-0177},
url = {http://global-sci.org/intro/article_detail/cicp/21041.html}
}