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Well-posedness of Bayesian inverse problems for hyperbolic conservation laws

by S. Mishra and D. Ochsner and A. M. Ruf and F. Weber

(Report number 2021-24)

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.

Keywords: Inverse problem, Bayesian, Wasserstein distance, conservation laws

@Techreport{MORW21_966,
  author = {S. Mishra and D. Ochsner and A. M. Ruf and F. Weber},
  title = {Well-posedness of Bayesian inverse problems for hyperbolic conservation laws},
  institution = {Seminar for Applied Mathematics, ETH Z{\"u}rich},
  number = {2021-24},
  address = {Switzerland},
  url = {https://www.sam.math.ethz.ch/sam_reports/reports_final/reports2021/2021-24.pdf },
  year = {2021}
}

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