Inference of interacting kernel in the mean-field regime
Fuente:
arXiv
Saved in:
| Main Authors: | , , , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866917379840147456 |
|---|---|
| author | Chen, Peiyi Li, Qin Wang, Li Yang, Yunan |
| author_facet | Chen, Peiyi Li, Qin Wang, Li Yang, Yunan |
| contents | We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction procedure depends on the formulation of the forward model, which may be given either by a finite-dimensional coupled ODE system tracking individual agent trajectories or by a mean-field PDE describing the evolution of the agent density. We investigate the similarities and differences between these two formulations in the mean-field regime. While the first variation derived from the particle system does not provide an unbiased estimator of the first variation associated with the limiting PDE, we prove that, under mild assumptions, the two are close in a weak sense with a convergence rate $\mathcal{O}(N^{-1/2})$. This rate is further confirmed by numerical evidences. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14211 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inference of interacting kernel in the mean-field regime Chen, Peiyi Li, Qin Wang, Li Yang, Yunan Numerical Analysis 65C05, 65K10, 65M75, 70F17 We study the problem of reconstructing interaction kernels in systems of interacting agents from macroscopic measurements when posed as an optimization problem. The reconstruction procedure depends on the formulation of the forward model, which may be given either by a finite-dimensional coupled ODE system tracking individual agent trajectories or by a mean-field PDE describing the evolution of the agent density. We investigate the similarities and differences between these two formulations in the mean-field regime. While the first variation derived from the particle system does not provide an unbiased estimator of the first variation associated with the limiting PDE, we prove that, under mild assumptions, the two are close in a weak sense with a convergence rate $\mathcal{O}(N^{-1/2})$. This rate is further confirmed by numerical evidences. |
| title | Inference of interacting kernel in the mean-field regime |
| topic | Numerical Analysis 65C05, 65K10, 65M75, 70F17 |
| url | https://arxiv.org/abs/2603.14211 |