利用长短期记忆神经网络的改进POD-Galerkin降阶模型及其在流场预测中的应用

Aiming at the issue of low accuracy in rapid prediction of flow field caused by errors in the standard POD-Galerkin reduced order model, an improved POD-Galerkin model using long short-term memory (LSTM) neural networks is proposed. In this method, based on the reduced order model obtained by dimensionality reduction and projection of the flow field using proper orthogonal decomposition (POD), two LSTM neural networks are introduced to establish a corrective mapping from the POD-Galerkin model to the actual POD coefficients, and an expansion mapping between the low-order mode time coefficients and the high-order mode time coefficients, so as to eliminate the error accumulation of the standard POD-Galerkin model and extend the order of reduced order model. This method enables the construction of a hybrid reduced order model that combines physics-driven and data-driven approaches. The improved POD-Galerkin model is applied to flow field prediction of a two-dimensional flow around a cylinder. A comparison with the original standard POD-Galerkin model is performed to analyze the model accuracy and computational speed. The results show that, with the addition of neural network correction terms, the accuracy of the reduced order model is effectively improved compared with the standard POD-Galcrkin model. The root mean square error of the predicted mode time coefficients is reduced by one to two orders of magnitude compared with the original model, and the predicted flow field is closer to the original flow field. The improved model achieves a significant reduction in computation time while predicting the same order. The improved 8-ordcr improved reduced order model based on 4- and 6-ordcr expansions improves the prediction speed by approximately 56% and 25%, respectively, compared with the original 8-order POD-Galerkin model.