Model Order Reduction Techniques for the Stochastic Finite Volume Method
For researchers in uncertainty quantification for hyperbolic PDEs, this work offers a method to mitigate the curse of dimensionality, though it is an incremental extension of existing ROM techniques.
The paper tackles the high computational cost of the stochastic finite volume method for uncertainty quantification in hyperbolic conservation laws, particularly in high-dimensional stochastic spaces. By incorporating interpolation-based reduced order models and hyper-reduction via Q-DEIM, they achieve reduced computational cost and memory requirements.
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 model (ROM) techniques that reduce the cost of computing stochastic integrals in the SFV method. Further efficiency gains are achieved through hyper-reduction with a QR factorization-based discrete empirical interpolation method (Q-DEIM). Numerical experiments suggest that this approach can lower both computational cost and memory requirements for high-dimensional stochastic parameter spaces.