Saved in:
| Main Authors: | , , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.18951 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915893988032512 |
|---|---|
| author | Bolin, David Li, Wenwen Sanz-Alonso, Daniel |
| author_facet | Bolin, David Li, Wenwen Sanz-Alonso, Daniel |
| contents | This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering the diffusion coefficient of a (fractional) elliptic equation on a metric graph from noisy measurements of the solution. Well-posedness hinges on both stability of the forward model and an appropriate choice of prior. We establish the stability of elliptic and fractional elliptic forward models using recent regularity theory for differential equations on metric graphs. For the prior, we leverage modern Gaussian Whittle--Matérn process models on metric graphs with sufficiently smooth sample paths. Numerical results demonstrate accurate reconstruction and effective uncertainty quantification. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18951 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Elliptic Bayesian Inverse Problems on Metric Graphs Bolin, David Li, Wenwen Sanz-Alonso, Daniel Analysis of PDEs Statistics Theory Computation This paper studies the formulation, well-posedness, and numerical solution of Bayesian inverse problems on metric graphs, in which the edges represent one-dimensional wires connecting vertices. We focus on the inverse problem of recovering the diffusion coefficient of a (fractional) elliptic equation on a metric graph from noisy measurements of the solution. Well-posedness hinges on both stability of the forward model and an appropriate choice of prior. We establish the stability of elliptic and fractional elliptic forward models using recent regularity theory for differential equations on metric graphs. For the prior, we leverage modern Gaussian Whittle--Matérn process models on metric graphs with sufficiently smooth sample paths. Numerical results demonstrate accurate reconstruction and effective uncertainty quantification. |
| title | Elliptic Bayesian Inverse Problems on Metric Graphs |
| topic | Analysis of PDEs Statistics Theory Computation |
| url | https://arxiv.org/abs/2507.18951 |