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| Main Authors: | , , , , , , , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.10245 |
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| _version_ | 1866911760725835776 |
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| author | Chung, Seung Whan Choi, Youngsoo Roy, Pratanu Moore, Thomas Roy, Thomas Lin, Tiras Y. Nguyen, Du Y. Hahn, Christopher Duoss, Eric B. Baker, Sarah E. |
| author_facet | Chung, Seung Whan Choi, Youngsoo Roy, Pratanu Moore, Thomas Roy, Thomas Lin, Tiras Y. Nguyen, Du Y. Hahn, Christopher Duoss, Eric B. Baker, Sarah E. |
| contents | Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the E-pilot, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. This method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about $15 - 40$ times faster with only $\sim$ $1\%$ relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_10245 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Train Small, Model Big: Scalable Physics Simulators via Reduced Order Modeling and Domain Decomposition Chung, Seung Whan Choi, Youngsoo Roy, Pratanu Moore, Thomas Roy, Thomas Lin, Tiras Y. Nguyen, Du Y. Hahn, Christopher Duoss, Eric B. Baker, Sarah E. Computational Engineering, Finance, and Science Fluid Dynamics 65F55, 65N55 (primary) 76D07 (secondary) Numerous cutting-edge scientific technologies originate at the laboratory scale, but transitioning them to practical industry applications is a formidable challenge. Traditional pilot projects at intermediate scales are costly and time-consuming. An alternative, the E-pilot, relies on high-fidelity numerical simulations, but even these simulations can be computationally prohibitive at larger scales. To overcome these limitations, we propose a scalable, physics-constrained reduced order model (ROM) method. ROM identifies critical physics modes from small-scale unit components, projecting governing equations onto these modes to create a reduced model that retains essential physics details. We also employ Discontinuous Galerkin Domain Decomposition (DG-DD) to apply ROM to unit components and interfaces, enabling the construction of large-scale global systems without data at such large scales. This method is demonstrated on the Poisson and Stokes flow equations, showing that it can solve equations about $15 - 40$ times faster with only $\sim$ $1\%$ relative error. Furthermore, ROM takes one order of magnitude less memory than the full order model, enabling larger scale predictions at a given memory limitation. |
| title | Train Small, Model Big: Scalable Physics Simulators via Reduced Order Modeling and Domain Decomposition |
| topic | Computational Engineering, Finance, and Science Fluid Dynamics 65F55, 65N55 (primary) 76D07 (secondary) |
| url | https://arxiv.org/abs/2401.10245 |