Manifold Learning with Implicit Physics Embedding for Reduced-Order Flow-Field Modeling
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917211380121600 |
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| author | Wang, Weiji Gong, Chunlin Jia, Xuyi Li, Chunna |
| author_facet | Wang, Weiji Gong, Chunlin Jia, Xuyi Li, Chunna |
| contents | Nonlinear manifold learning (ML) based reduced-order models (ROMs) can substantially improve the quality of nonlinear flow-field modeling. However, noise and the lack of physical information often distort the dimensionality-reduction process, reducing the robustness and accuracy of flow-field prediction. To address this problem, we propose a novel manifold learning ROM with implicit physics embedding (IPE-ML). Starting from data-driven manifold coordinates, we incorporate physical parameters (e.g., angle of attack, Mach number) into manifold coordinates system by minimizing the prediction error of Gaussian process regression (GPR) model, thereby fine-tuning the manifold structure. These adjusted coordinates are then used to construct a flow-fields prediction model that predict nonlinear flow-field more accurately. The method is validated on two test cases: transonic flow-field modeling of the RAE2822 and supersonic flow-field modeling of the hexagon airfoil. The results indicate that the proposed IPE-ML can significantly improve the overall prediction accuracy of nonlinear flow fields. In transonic case, shock-related errors have been notably reduced, while in supersonic case the method can confine errors to small local regions. This study offers a new perspective on embedding physical information into nonlinear ROMs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_13673 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Manifold Learning with Implicit Physics Embedding for Reduced-Order Flow-Field Modeling Wang, Weiji Gong, Chunlin Jia, Xuyi Li, Chunna Fluid Dynamics Nonlinear manifold learning (ML) based reduced-order models (ROMs) can substantially improve the quality of nonlinear flow-field modeling. However, noise and the lack of physical information often distort the dimensionality-reduction process, reducing the robustness and accuracy of flow-field prediction. To address this problem, we propose a novel manifold learning ROM with implicit physics embedding (IPE-ML). Starting from data-driven manifold coordinates, we incorporate physical parameters (e.g., angle of attack, Mach number) into manifold coordinates system by minimizing the prediction error of Gaussian process regression (GPR) model, thereby fine-tuning the manifold structure. These adjusted coordinates are then used to construct a flow-fields prediction model that predict nonlinear flow-field more accurately. The method is validated on two test cases: transonic flow-field modeling of the RAE2822 and supersonic flow-field modeling of the hexagon airfoil. The results indicate that the proposed IPE-ML can significantly improve the overall prediction accuracy of nonlinear flow fields. In transonic case, shock-related errors have been notably reduced, while in supersonic case the method can confine errors to small local regions. This study offers a new perspective on embedding physical information into nonlinear ROMs. |
| title | Manifold Learning with Implicit Physics Embedding for Reduced-Order Flow-Field Modeling |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2601.13673 |