Model Order Reduction Techniques for the Stochastic Finite Volume Method

Ray Qu; Jesse Chan; Svetlana Tokareva

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arXiv · 2507.05091

Model Order Reduction Techniques for the Stochastic Finite Volume Method

Ray Qu·Jesse Chan·Svetlana Tokareva

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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 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.

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Ray Qu, Jesse Chan, Svetlana Tokareva. 2025-07-07. Model Order Reduction Techniques for the Stochastic Finite Volume Method. https://arxiv.org/abs/2507.05091

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