Uncertainly quantification
- Uncertainly propagation (Forward UQ) with multi-level Monte Carlo (MLMC) methods for hyperbolic and related PDEs.
- Dynamic load balancing for scalable-MPI implementations on leadership class HPC platforms.
- Bayesian inversion (Inverse UQ) and data assimilation for fluid flows.
Selected Publications
S. Mishra and C. Schwab, Sparse tensor multi-level Monte Carlo Finite Volume methods for hyperbolic conservation laws with random initial data. Math. Comput., 81(180), 1979-2018, 2012.
S. Mishra, Ch. Schwab and J. Sukys, Multi-level Monte Carlo Finite Volume methods for nonlinear systems of conservation laws in multi-dimensions, Jl. Comput. Phys, 231 (2012), no. 8, 3365-3388.
S. Mishra, Ch. Schwab and J. Sukys, Multi-Level Monte Carlo Finite Volume methods for uncertainty quantification of acoustic wave propagation in random heterogeneous layered medium, J. Comput. Phys., 312, 2016, 192-217.
S. Lanthaler, S. Mishra and F. Weber, On the well-posedness of Bayesian inversion for PDEs with ill-posed forward problems, Preprint 2021, arXiv:2107.07593.