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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2506.00301 |
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| _version_ | 1866918180526489600 |
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| author | Kiran, Narcicegi Pereira, Tiago |
| author_facet | Kiran, Narcicegi Pereira, Tiago |
| contents | We address the inverse problem of reconstructing both the structure and dynamics of a network from mean-field measurements, which are linear combinations of node states. This setting arises in applications where only a few aggregated observations are available, making network inference challenging. We focus on the case when the number of mean-field measurements is smaller than the number of nodes. To tackle this ill-posed recovery problem, we propose a framework that combines localized initial perturbations with sparse optimization techniques. We derive sufficient conditions that guarantee the unique reconstruction of the network's adjacency matrix from mean-field data and enable recovery of node states and local governing dynamics. Numerical experiments demonstrate the robustness of our approach across a range of sparsity and connectivity regimes. These results provide theoretical and computational foundations for inferring high-dimensional networked systems from low-dimensional observations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_00301 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Unique Reconstruction From Mean-Field Measurements Kiran, Narcicegi Pereira, Tiago Dynamical Systems Data Analysis, Statistics and Probability 37M99, 37N99, 15A29, 94A12, 65P99, 05C50, 90C25 We address the inverse problem of reconstructing both the structure and dynamics of a network from mean-field measurements, which are linear combinations of node states. This setting arises in applications where only a few aggregated observations are available, making network inference challenging. We focus on the case when the number of mean-field measurements is smaller than the number of nodes. To tackle this ill-posed recovery problem, we propose a framework that combines localized initial perturbations with sparse optimization techniques. We derive sufficient conditions that guarantee the unique reconstruction of the network's adjacency matrix from mean-field data and enable recovery of node states and local governing dynamics. Numerical experiments demonstrate the robustness of our approach across a range of sparsity and connectivity regimes. These results provide theoretical and computational foundations for inferring high-dimensional networked systems from low-dimensional observations. |
| title | Unique Reconstruction From Mean-Field Measurements |
| topic | Dynamical Systems Data Analysis, Statistics and Probability 37M99, 37N99, 15A29, 94A12, 65P99, 05C50, 90C25 |
| url | https://arxiv.org/abs/2506.00301 |