论文标题
基于复发性神经网络和正交分解的非感性替代模型的数值评估：Rayleigh Benard对流
Numerical assessments of a nonintrusive surrogate model based on recurrent neural networks and proper orthogonal decomposition: Rayleigh Benard convection
论文作者
论文摘要
诊断和计算技术的最新发展提供了从数据中利用多种形式的非感官建模方法，可以使用机器学习来构建计算廉价且准确的替代模型。为此，我们提出了一个非线性正交分解（POD）框架，称为NLPOD，以为BousSinesQ方程制造非感官的还原模型。在我们的NLPOD方法中，我们首先采用POD过程来获取一组全局模式来构建线性拟合潜在空间，并利用自动编码器网络通过POD系数的非线性无监督的映射来压缩此潜在空间的投影。然后，使用长期的短期记忆（LSTM）神经网络体系结构来发现这种低级别的歧管中的时间模式。在对LSTM模型的超参数进行详细的灵敏度分析时，精确分析了准确性和效率之间的权衡，以求解规范的Rayleigh-Benard对流系统。
Recent developments in diagnostic and computing technologies offer to leverage numerous forms of nonintrusive modeling approaches from data where machine learning can be used to build computationally cheap and accurate surrogate models. To this end, we present a nonlinear proper orthogonal decomposition (POD) framework, denoted as NLPOD, to forge a nonintrusive reduced-order model for the Boussinesq equations. In our NLPOD approach, we first employ the POD procedure to obtain a set of global modes to build a linear-fit latent space and utilize an autoencoder network to compress the projection of this latent space through a nonlinear unsupervised mapping of POD coefficients. Then, long short-term memory (LSTM) neural network architecture is utilized to discover temporal patterns in this low-rank manifold. While performing a detailed sensitivity analysis for hyperparameters of the LSTM model, the trade-off between accuracy and efficiency is systematically analyzed for solving a canonical Rayleigh-Benard convection system.
