ABSTRACT:

Many problems in physics and engineering are modeled by systems of partial differential equations such as the shallow water equations of hydrology, the Euler equations for inviscid, compressible flow, and the magnetohydrodynamic equations of plasma physics. The initial data, boundary conditions, and coefficients of these models may be uncertain due to measurement, prediction, or modeling errors.

The stochastic finite volume (SFV) method offers an efficient one-pass approach for assessing uncertainty in hyperbolic conservation laws. The SFV method has shown great promise as a weakly-intrusive PDE solver for uncertainty quantification. However, in many relevant applications, the dimension of the stochastic space can make traditional implementations of the SFV method infeasible or impossible due to the so-called curse of dimensionality. We introduce the Tensor-Train SFV (TT-SFV) method within the tensor-train framework to manage the curse of dimensionality. This integration, however, comes with its own set of difficulties, mainly due to the propensity for shock formation in hyperbolic systems. To overcome these issues, we have developed a tensor-train-adapted stochastic finite volume method that employs a global WENO reconstruction, making it suitable for such complex systems. This approach represents the first step in designing efficient tensor-train techniques for uncertainty quantification in hyperbolic systems and conservation laws involving shocks.

BIO:

Dr. Svetlana Tokareva graduated from Bauman Moscow State technical University (Russia) in 2008 with a diploma in applied mathematics. She has earned her PhD from ETH Zurich (Switzerland) in 2013. Next she spent one year in R&D for industry and joined ASCOMP, an ETH spin-off company working in computational fluid dymanics and software development for oil&gas sector, and in September 2014, she became a postdoctoral researcher in the group of Prof. Remi Abgrall at the University of Zurich. In February 2018 Dr. Tokareva joind Los Alamos National Lab where she is now a Staff Scientist in the Applied Mathematics and Plasma Physics Group (T-5).