On the convergence of PINNs for inverse source problem in the complex Ginzburg-Landau equation
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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866915409006952448 |
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| author | Cheng, Xing Li, Zhiyuan Zhang, Mengmeng Zhang, Xuezhao |
| author_facet | Cheng, Xing Li, Zhiyuan Zhang, Mengmeng Zhang, Xuezhao |
| contents | This paper addresses the problem of recovering the spatial profile of the source in the complex Ginzburg-Landau equation from regional observation data at fixed times. We establish two types of sufficient measurements for the unique solvability of the inverse problem. The first is to determine the source term by using whole data at one fixed instant. Conditional stability is established by using the eigenfunction expansion argument. Next, using the analytic continuation method, both uniqueness and a stability estimate for recovering the unknown source can be established from local data at two instants. Finally, algorithms based on the physics-informed neural networks (PINNs) are proposed, and several numerical experiments are presented to show the accuracy and efficiency of the algorithm. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18978 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the convergence of PINNs for inverse source problem in the complex Ginzburg-Landau equation Cheng, Xing Li, Zhiyuan Zhang, Mengmeng Zhang, Xuezhao Analysis of PDEs 35Q56, 35R30, 68T07 This paper addresses the problem of recovering the spatial profile of the source in the complex Ginzburg-Landau equation from regional observation data at fixed times. We establish two types of sufficient measurements for the unique solvability of the inverse problem. The first is to determine the source term by using whole data at one fixed instant. Conditional stability is established by using the eigenfunction expansion argument. Next, using the analytic continuation method, both uniqueness and a stability estimate for recovering the unknown source can be established from local data at two instants. Finally, algorithms based on the physics-informed neural networks (PINNs) are proposed, and several numerical experiments are presented to show the accuracy and efficiency of the algorithm. |
| title | On the convergence of PINNs for inverse source problem in the complex Ginzburg-Landau equation |
| topic | Analysis of PDEs 35Q56, 35R30, 68T07 |
| url | https://arxiv.org/abs/2507.18978 |