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Well-posedness of Bayesian inverse problems for hyperbolic conservation laws

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arxiv 2107.09701 v1 pith:R2FUVEXP submitted 2021-07-20 math.NA cs.NAmath.AP

Well-posedness of Bayesian inverse problems for hyperbolic conservation laws

Siddhartha Mishra , David Ochsner , Adrian M. Ruf , Franziska Weber This is my paper
classification math.NA cs.NAmath.AP
keywords bayesianconservationhyperbolicinverselawsposteriorwell-posednessapproximations
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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.

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