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Elliptic Bayesian inverse problems on metric graphs
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DOI：10.1088/1361-6420/ae544e.png)
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Abstract
En 中文
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-Mat & eacute;rn process models on metric graphs with sufficiently smooth sample paths. Numerical results demonstrate accurate reconstruction and effective uncertainty quantification.
Keywords:
metric graphs
(fractional) elliptic inverse problems
Bayesian approach
Gaussian Whittle-Mat & eacute
rn processes
well-posedness
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2.1
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78
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8.4K
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