基于基因表达式编程与人工神经网络相结合的Turbulence模型开发
Turbulence Model Development based on a Novel Method Combining Gene Expression Programming with an Artificial Neural Network
摘要：
数据驱动方法被广泛应用于物理模型的开发，但仍存在一些局限性，影响其性能、可推广性和鲁棒性。将基因表达式编程（GEP）与人工神经网络（ANN）相结合，提出了一种新的符号回归方法--基因表达式编程神经网络（GEPNN）。在该方法中，进化算法生成的候选表达式在训练迭代过程中在GEP和ANN结构之间进行转换，并通过结合GEP的全局搜索和ANN的梯度优化能力，实现高效且鲁棒的收敛到准确的模型。此外，稀疏增强策略已被引入GEPNN，以提高训练模型的可解释性。GEPNN方法已经过测试，发现不同的物理定律，显示出改进的收敛模型与精确的系数。此外，对于湍流的大涡模拟，GEPNN训练的亚网格尺度应力模型显着提高了湍流统计和流动结构的预测比传统的模型，显示出优势相比，现有的GEP和人工神经网络方法在先验和后验测试。
英文摘要：
Data-driven methods are widely used to develop physical models, but there still exist limitations that affect their performance, generalizability and robustness. By combining gene expression programming (GEP) with artificial neural network (ANN), we propose a novel method for symbolic regression called the gene expression programming neural network (GEPNN). In this method, candidate expressions generated by evolutionary algorithms are transformed between the GEP and ANN structures during training iterations, and efficient and robust convergence to accurate models is achieved by combining the GEP's global searching and the ANN's gradient optimization capabilities. In addition, sparsity-enhancing strategies have been introduced to GEPNN to improve the interpretability of the trained models. The GEPNN method has been tested for finding different physical laws, showing improved convergence to models with precise coefficients. Furthermore, for large-eddy simulation of turbulence, the subgrid-scale stress model trained by GEPNN significantly improves the prediction of turbulence statistics and flow structures over traditional models, showing advantages compared to the existing GEP and ANN methods in both a priori and a posteriori tests.
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