Well-posedness of Bayesian inverse problems for hyperbolic conservation laws
Numerical Analysis
2021-07-23 v1 Numerical Analysis
Analysis of PDEs
Abstract
We study the well-posedness of the Bayesian inverse problem for scalar hyperbolic conservation laws where the statistical information about inputs such as the initial datum and (possibly discontinuous) flux function are inferred from noisy measurements. In particular, the Lipschitz continuity of the measurement to posterior map as well as the stability of the posterior to approximations, are established with respect to the Wasserstein distance. Numerical experiments are presented to illustrate the derived estimates.
Cite
@article{arxiv.2107.09701,
title = {Well-posedness of Bayesian inverse problems for hyperbolic conservation laws},
author = {Siddhartha Mishra and David Ochsner and Adrian M. Ruf and Franziska Weber},
journal= {arXiv preprint arXiv:2107.09701},
year = {2021}
}
Comments
26 pages, 8 figures. arXiv admin note: text overlap with arXiv:0909.2126 by other authors