Well-posedness of Bayesian inverse problems for hyperbolic conservation laws

07/20/2021
by   Siddhartha Mishra, et al.
0

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.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
07/26/2023

Stability of particle trajectories of scalar conservation laws and applications in Bayesian inverse problems

We consider the scalar conservation law in one space dimension with a ge...
research
07/15/2021

On the well-posedness of Bayesian inversion for PDEs with ill-posed forward problems

We study the well-posedness of Bayesian inverse problems for PDEs, for w...
research
02/26/2019

On the well-posedness of Bayesian inverse problems

The subject of this article is the introduction of a weaker concept of w...
research
08/19/2020

Flux-stability for conservation laws with discontinuous flux and convergence rates of the front tracking method

We prove that adapted entropy solutions of scalar conservation laws with...
research
07/14/2023

A Simple Embedding Method for Scalar Hyperbolic Conservation Laws on Implicit Surfaces

We have developed a new embedding method for solving scalar hyperbolic c...
research
11/22/2022

Efficient wPINN-Approximations to Entropy Solutions of Hyperbolic Conservation Laws

We consider the approximation of weak solutions of nonlinear hyperbolic ...

Please sign up or login with your details

Forgot password? Click here to reset