Leak localisation with a measure source convection-diffusion model
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.
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BibTeX
@misc{dang2026leak,
title = {{Leak localisation with a measure source convection-diffusion model}},
author = {Thi Tam Dang and Tuomo Valkonen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2605.12095},
eprint = {2605.12095},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2605.12095},
}
RIS
TY - UNPB
TI - Leak localisation with a measure source convection-diffusion model
AU - Thi Tam Dang
AU - Tuomo Valkonen
PY - 2026
DA - 2026/10/09
PB - arXiv
DO - 10.48550/arxiv.2605.12095
UR - https://arxiv.org/abs/2605.12095
AB - 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.
ER -