Year: 2026
Type: preprint
Abstract: Taking a variational approach, study the inverse problem of locating gas leaks from line-of-sight concentration measurements using a convection--diffusion model with the source term a Radon measure. By imposing sparsity-promoting regularisation on this measure, we recover point sources---identifying both their locations and intensities---rather than diffuse approximations. We jointly estimate the underlying physical convection (wind) and diffusion parameters. Our main theoretical contribution is the analysis of Lipschitz dependence of the forward solution of the convection--diffusion equation with respect to its parameters: the measure, and the convection and diffusion fields. Numerically, we employ a semi-grid-free optimisation approach for reconstructing the source measure. Our experiments demonstrate accurate localisation, highlighting the potential of the method for practical gas emission detection.
Source: arXiv (Cornell University)
Authors: Dang, Thi Tam, Valkonen, Tuomo
Institution: University of Helsinki
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: Jane ja Aatos Erkon Säätiö
OpenAlex ID: W7161048527