Model Order Reduction Techniques for the Stochastic Finite Volume Method
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866914570266738688 |
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| author | Qu, Ray Chan, Jesse Tokareva, Svetlana |
| author_facet | Qu, Ray Chan, Jesse Tokareva, Svetlana |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05091 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Model Order Reduction Techniques for the Stochastic Finite Volume Method Qu, Ray Chan, Jesse Tokareva, Svetlana Numerical Analysis 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. |
| title | Model Order Reduction Techniques for the Stochastic Finite Volume Method |
| topic | Numerical Analysis |
| url | https://arxiv.org/abs/2507.05091 |