Accurate flow field prediction is crucial for solving complex fluid dynamics problems and optimizing aerodynamic structures. Although traditional computational fluid dynamics (CFD) methods are reliable, they are computationally expensive and inefficient, particularly under conditions with sparse data or uncertainty. Existing data-driven models often lack physical information constraints, which can result in predictions that violate fundamental physical laws, such as mass and momentum conservation etc. Addressing these limitations, this paper proposes a Transformer model with embedded physical information constraints named PI-Transformer. By directly incorporating the Navier-Stokes and continuity equations into the loss function, our model ensures adherence to fundamental physical laws while preserving computational efficiency. Experimental results show a 61% reduction in flow field prediction errors compared to the baseline, with enhanced robustness at higher Reynolds numbers. Despite a 20% increase in training time, PI-Transformer significantly improves prediction accuracy, reduces reliance on traditional CFD, and demonstrates substantial potential for efficient engineering applications in various industries.

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Physics-Informed Transformer for Efficient Fluid Dynamics Predictions

  • Xinzhe Hu,
  • Jinchuan Zhang,
  • Ke Yan,
  • Tianqi Wan,
  • Xu Zheng

摘要

Accurate flow field prediction is crucial for solving complex fluid dynamics problems and optimizing aerodynamic structures. Although traditional computational fluid dynamics (CFD) methods are reliable, they are computationally expensive and inefficient, particularly under conditions with sparse data or uncertainty. Existing data-driven models often lack physical information constraints, which can result in predictions that violate fundamental physical laws, such as mass and momentum conservation etc. Addressing these limitations, this paper proposes a Transformer model with embedded physical information constraints named PI-Transformer. By directly incorporating the Navier-Stokes and continuity equations into the loss function, our model ensures adherence to fundamental physical laws while preserving computational efficiency. Experimental results show a 61% reduction in flow field prediction errors compared to the baseline, with enhanced robustness at higher Reynolds numbers. Despite a 20% increase in training time, PI-Transformer significantly improves prediction accuracy, reduces reliance on traditional CFD, and demonstrates substantial potential for efficient engineering applications in various industries.