Domain decomposition for data-driven reduced modeling of large-scale systems
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917785841434624 |
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| author | Farcas, Ionut-Gabriel Gundevia, Rayomand P. Munipalli, Ramakanth Willcox, Karen E. |
| author_facet | Farcas, Ionut-Gabriel Gundevia, Rayomand P. Munipalli, Ramakanth Willcox, Karen E. |
| contents | This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may be too inaccurate or may overfit and hence generalize poorly. Moreover, processing large-scale datasets typically requires significant memory and computing resources which can render single-domain approaches computationally prohibitive. To address these challenges, we introduce a domain decomposition formulation into the construction of a data-driven reduced model. In doing so, the basis functions used in the reduced model approximation become localized in space, which can increase the accuracy of the domain-decomposed approximation of the complex dynamics. The decomposition furthermore reduces the memory and computing requirements to process the underlying large-scale training dataset. We demonstrate the effectiveness and scalability of our approach in a large-scale three-dimensional unsteady rotating detonation rocket engine simulation scenario with over $75$ million degrees of freedom and a sparse training dataset. Our results show that compared to the single-domain approach, the domain-decomposed version reduces both the training and prediction errors for pressure by up to $13 \%$ and up to $5\%$ for other key quantities, such as temperature, and fuel and oxidizer mass fractions. Lastly, our approach decreases the memory requirements for processing by almost a factor of four, which in turn reduces the computing requirements as well. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_00883 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Domain decomposition for data-driven reduced modeling of large-scale systems Farcas, Ionut-Gabriel Gundevia, Rayomand P. Munipalli, Ramakanth Willcox, Karen E. Numerical Analysis Computational Engineering, Finance, and Science This paper focuses on the construction of accurate and predictive data-driven reduced models of large-scale numerical simulations with complex dynamics and sparse training datasets. In these settings, standard, single-domain approaches may be too inaccurate or may overfit and hence generalize poorly. Moreover, processing large-scale datasets typically requires significant memory and computing resources which can render single-domain approaches computationally prohibitive. To address these challenges, we introduce a domain decomposition formulation into the construction of a data-driven reduced model. In doing so, the basis functions used in the reduced model approximation become localized in space, which can increase the accuracy of the domain-decomposed approximation of the complex dynamics. The decomposition furthermore reduces the memory and computing requirements to process the underlying large-scale training dataset. We demonstrate the effectiveness and scalability of our approach in a large-scale three-dimensional unsteady rotating detonation rocket engine simulation scenario with over $75$ million degrees of freedom and a sparse training dataset. Our results show that compared to the single-domain approach, the domain-decomposed version reduces both the training and prediction errors for pressure by up to $13 \%$ and up to $5\%$ for other key quantities, such as temperature, and fuel and oxidizer mass fractions. Lastly, our approach decreases the memory requirements for processing by almost a factor of four, which in turn reduces the computing requirements as well. |
| title | Domain decomposition for data-driven reduced modeling of large-scale systems |
| topic | Numerical Analysis Computational Engineering, Finance, and Science |
| url | https://arxiv.org/abs/2311.00883 |