Flow field reconstruction in turbine cascades based on self-adaptive loss physics-informed neural networks under sparse data

A self-adaptive loss physics-informed neural network (SAL-PINN) method is proposed to address the challenges of limited generalization capability exhibited by purely data-driven neural networks under sparse data conditions and the insufficient accuracy of standard physics-informed neural networks in capturing complex flow details. This method enables high-fidelity reconstruction of the plane turbine cascade flow field with limited measurement points. By incorporating a dynamic weight balancing mechanism, SAL-PINN adaptively adjusts the loss function weights for regions characterized by different numerical scales within the flow field, thereby facilitating targeted reinforcement learning for critical regions. This approach yields excellent performance in predicting both global flow structures and local flow details. The results demonstrate that under sparse data conditions, SAL-PINN achieves a further reduction in prediction errors for key physical quantities across the entire field by approximately 1.5%–2.0% compared to the standard physics-informed neural networks. In boundary regions with complex flows, the error reduction is even more pronounced, reaching 12.0%–25.4%. This study also systematically evaluates the models' sensitivity to data volume, revealing that the incorporation of physical information significantly reduces their dependence on data, while the adaptive weighting mechanism further diminishes this sensitivity. This work provides an effective solution for achieving high-accuracy flow field reconstruction with minimal data, offering significant potential for engineering applications, particularly in scenarios where experimental measurements are high-cost.