Model order reduction techniques for the stochastic finite volume method

Abstract: The stochastic finite volume method (SFV method) is a high-order accurate method for uncertainty quantification (UQ) in hyperbolic conservation laws. However, the computational cost of SFV method increases for high-dimensional stochastic parameter spaces due to the curse of dimensionality. To address this challenge, we incorporate interpolation-based reduced order modeling (ROM) techniques that reduce the cost of computing stochastic integrals in SFV method. Further efficiency gains are achieved through a Q-DEIM hyper-reduction method. Numerical experiments suggest that this approach can lower both computational cost and memory requirements for high-dimensional stochastic parameter spaces.