This study investigates the generalization capabilities and robustness of purely deep learning (DL) models and hybrid models based on physical principles in fluid dynamics applications, specifically focusing on iteratively forecasting the temporal evolution of flow dynamics. Three autoregressive models were compared: a convolutional autoencoder combined with a convolutional LSTM (ConvLSTM), a variational autoencoder (VAE) combined with a ConvLSTM and a hybrid model that combines proper orthogonal decomposition (POD) with a LSTM (POD-DL). These models were tested on two high-dimensional, nonlinear datasets representing the velocity field of flow past a circular cylinder in both laminar and turbulent regimes. The study used latent dimension methods, enabling a bijective reduction of high-dimensional dynamics into a lower-order space to facilitate future predictions. While the VAE and ConvLSTM models accurately predicted laminar flow, the hybrid POD-DL model outperformed the others across both laminar and turbulent flow regimes. This success is attributed to the model's ability to incorporate modal decomposition, reducing the dimensionality of the data, by a non-parametric method, and simplifying the forecasting component. By leveraging POD, the model not only gained insight into the underlying physics, improving prediction accuracy with less training data, but also reduce the number of trainable parameters as POD is non-parametric. The findings emphasize the potential of hybrid models, particularly those integrating modal decomposition and deep learning, in predicting complex flow dynamics.

翻译：本研究探讨了在流体动力学应用中，纯深度学习模型与基于物理原理的混合模型的泛化能力和鲁棒性，特别关注对流动动力学时间演化的迭代预测。我们比较了三种自回归模型：卷积自编码器与卷积长短期记忆网络结合的模型、变分自编码器与卷积长短期记忆网络结合的模型，以及将本征正交分解与长短期记忆网络结合的混合模型。这些模型在两个代表圆柱绕流速度场的高维非线性数据集上进行了测试，涵盖了层流和湍流两种流态。研究采用了潜在维度方法，将高维动力学双射降维至低阶空间，以促进未来预测。虽然变分自编码器和卷积长短期记忆网络模型能准确预测层流，但混合模型在层流和湍流流态下均表现更优。这一成功归因于该模型能够通过非参数方法融入模态分解，从而降低数据维度并简化预测组件。通过利用本征正交分解，该模型不仅深入理解了底层物理机制，以更少的训练数据提高了预测精度，而且由于本征正交分解的非参数特性，减少了可训练参数的数量。研究结果强调了混合模型，特别是那些整合了模态分解与深度学习的方法，在预测复杂流动动力学方面的潜力。