Uncertainty quantification for hyperbolic systems of conservation laws
- Speaker: Prof. Dr. Siddhartha Mishra
- Place: Seminar room 1.067, Building 20.30
- Time: 6.6.2019, 14:00 - 15:00
- Invited by: CRC 1173
Hyperbolic systems of conservation laws are nonlinear PDEs that arise in a large number of models in physics and engineering. There is inherent uncertainty in inputs to the PDE such as initial and boundary data, flux and diffusion coefficients etc. This uncertainty propagates into the solution and finding efficient numerical algorithms for UQ in conservation laws is very challenging. In this lecture, we present different solution frameworks for uncertain conservation laws, namely random entropy solutions, measure-valued solutions and statistical solutions. Sampling methods such as multi-level Monte Carlo and Quasi-Monte Carlo are presented. Moreover, we present state of the machine learning algorithms for efficient UQ for some systems of conservation laws.