| Autor: |
He, Yuchen, Kang, Sung Ha, Liao, Wenjing, Liu, Hao, Liu, Yingjie |
| Rok vydání: |
2022 |
| Předmět: |
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| Druh dokumentu: |
Working Paper |
| DOI: |
10.4208/cicp.OA-2021-0177 |
| Popis: |
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. |
| Databáze: |
arXiv |
| Externí odkaz: |
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