Field Inversion Symbolic Regression with Embedded Equation Learner for Interpretable Turbulence Model Correction
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2026
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| _version_ | 1866910134592077824 |
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| author | Jiazhe, Li Chenyu, Wu Zizhou, He Yufei, Zhang |
| author_facet | Jiazhe, Li Chenyu, Wu Zizhou, He Yufei, Zhang |
| contents | An interpretable, physics-consistent turbulence model correction framework, termed FISR-Equation Learner (EQL), is proposed by embedding equation learning directly into a Partial Differential Equations (PDE)-constrained field inversion process based on the adjoint method. Unlike conventional two-stage approaches, the correction model is optimized end-to-end in parameter space using an EQL architecture, enabling the direct identification of compact analytical expressions while maintaining consistency with the governing equations. The method is applied to the shear-stress-transport (SST) model and trained on two canonical separated flows, the curved backward-facing step and the NASA hump. The resulting explicit expression significantly reduces separation bubble overprediction and improves reattachment prediction, achieving performance comparable to neural-network-based end-to-end methods while retaining full interpretability. Generalization is demonstrated on unseen configurations, including periodic hills, a surface-mounted cube, and the high-lift NLR7301 airfoil. The model improves separated-flow predictions and stall characteristics without degrading attached boundary-layer performance. Overall, FISR-EQL provides a practical pathway toward optimal yet transparent data-driven turbulence model correction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_14569 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Field Inversion Symbolic Regression with Embedded Equation Learner for Interpretable Turbulence Model Correction Jiazhe, Li Chenyu, Wu Zizhou, He Yufei, Zhang Fluid Dynamics An interpretable, physics-consistent turbulence model correction framework, termed FISR-Equation Learner (EQL), is proposed by embedding equation learning directly into a Partial Differential Equations (PDE)-constrained field inversion process based on the adjoint method. Unlike conventional two-stage approaches, the correction model is optimized end-to-end in parameter space using an EQL architecture, enabling the direct identification of compact analytical expressions while maintaining consistency with the governing equations. The method is applied to the shear-stress-transport (SST) model and trained on two canonical separated flows, the curved backward-facing step and the NASA hump. The resulting explicit expression significantly reduces separation bubble overprediction and improves reattachment prediction, achieving performance comparable to neural-network-based end-to-end methods while retaining full interpretability. Generalization is demonstrated on unseen configurations, including periodic hills, a surface-mounted cube, and the high-lift NLR7301 airfoil. The model improves separated-flow predictions and stall characteristics without degrading attached boundary-layer performance. Overall, FISR-EQL provides a practical pathway toward optimal yet transparent data-driven turbulence model correction. |
| title | Field Inversion Symbolic Regression with Embedded Equation Learner for Interpretable Turbulence Model Correction |
| topic | Fluid Dynamics |
| url | https://arxiv.org/abs/2604.14569 |