标题： 结合扩展卷积自动编码器和水库计算以实现大气流动的准确降阶预测 显示英文标题

标题： Combining Extended Convolutional Autoencoders and Reservoir Computing for Accurate Reduced-Order Predictions of Atmospheric Flows

摘要： 使用传统离散化方法（也称为全阶方法，例如有限元方法或有限体积方法）预测大气流动计算成本高昂。 我们提议通过结合扩展卷积自动编码器（E-CAE）和 reservoir computing（RC）的降阶模型（ROM）来降低计算成本。由于网络深度的扩展，E-CAE 可以将来自全阶方法的高分辨率数据编码为紧凑的潜在表示，并且能够以比标准CAE低75%的重构误差将其解码回高分辨率。压缩后的数据被输入到RC网络中，该网络预测其演化。RC网络的优势在于训练阶段相比传统预测模型具有更低的计算成本。我们通过已知的二维和三维大气流动基准测试了我们的数据驱动ROM。结果显示，我们的ROM在二维情况下未来系统动力学的重构和预测误差低于6%，在三维情况下误差低于8%，同时显著降低了全阶模拟的计算成本。与文献中的其他ROM（如动态模式分解和带插值的正交分解）相比，我们的ROM同样高效但更准确。因此，它是一种有前景的大气高维模拟替代方案。 显示英文摘要

摘要： Forecasting atmospheric flows with traditional discretization methods, also called full order methods (e.g., finite element methods or finite volume methods), is computationally expensive. We propose to reduce the computational cost with a Reduced Order Model (ROM) that combines Extended Convolutional Autoencoders (E-CAE) and Reservoir Computing (RC). Thanks to an extended network depth, the E-CAE encodes the high-resolution data coming from the full order method into a compact latent representation and can decode it back into high-resolution with 75% lower reconstruction error than standard CAEs. The compressed data are fed to an RC network, which predicts their evolution. The advantage of RC networks is a reduced computational cost in the training phase compared to conventional predictive models. We assess our data-driven ROM through well-known 2D and 3D benchmarks for atmospheric flows. We show that our ROM accurately reconstructs and predicts the future system dynamics with errors below 6% in 2D and 8% in 3D, while significantly reducing the computational cost of a full-order simulation. Compared to other ROMs available in the literature, such as Dynamic Mode Decomposition and Proper Orthogonal Decomposition with Interpolation, our ROM is as efficient but more accurate. Thus, it is a promising alternative to high-dimensional atmospheric simulations.