基于Slim多尺度卷积自编码器的降阶模型，用于复杂动力系统的可解释特征
Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system
AI总结：
针对卷积自编码器降阶模型潜在特征不可解释的问题，提出一种轻量、可嵌入现有CAE的可解释多尺度方法，并在Rayleigh-Bénard对流数据上验证其重建与参数效率优势。
摘要：
近年来，数据驱动的深度学习模型在湍流动力系统分析中引起了广泛关注。在降阶模型（ROM）的背景下，卷积自编码器（CAE）是传统方法的一种普遍适用的替代方案。它们可以直接从数据中学习非线性变换，而无需系统的先验知识。然而，此类模型生成的特征缺乏可解释性。因此，所得模型是一个黑箱，虽然能有效降低系统复杂度，但无法提供对潜在特征含义的洞察。为解决这一关键问题，我们提出了一种新颖的可解释CAE方法，用于高维流体流动数据，该方法保持了传统CAE的重建质量，并允许特征解释。我们的方法只需对训练过程进行微小修改，即可轻松集成到任何现有CAE架构中。我们将该方法与本征正交分解（POD）以及两种现有的可解释CAE方法进行了比较。我们将所有方法应用于三个复杂度不同的实验性湍流Rayleigh-Bénard对流数据集。结果表明，所提方法轻量且易于训练；在64个模态下，其重建性能相比POD最高提升6.4%。随着模态数量减少，相对提升最高增至229.8%。此外，我们的方法可提供与POD相似的可解释特征，并且与现有CAE方法相比资源消耗显著更低，使用的参数不到其2%。这些现有方法要么以可解释性换取重建性能，要么只能在有限程度上提供可解释性。
英文摘要：
In recent years, data-driven deep learning models have gained significant interest in the analysis of turbulent dynamical systems. Within the context of reduced-order models (ROMs), convolutional autoencoders (CAEs) pose a universally applicable alternative to conventional approaches. They can learn nonlinear transformations directly from data, without prior knowledge of the system. However, the features generated by such models lack interpretability. Thus, the resulting model is a black-box which effectively reduces the complexity of the system, but does not provide insights into the meaning of the latent features. To address this critical issue, we introduce a novel interpretable CAE approach for high-dimensional fluid flow data that maintains the reconstruction quality of conventional CAEs and allows for feature interpretation. Our method can be easily integrated into any existing CAE architecture with minor modifications of the training process. We compare our approach to Proper Orthogonal Decomposition (POD) and two existing methods for interpretable CAEs. We apply all methods to three different experimental turbulent Rayleigh-Bénard convection datasets with varying complexity. Our results show that the proposed method is lightweight, easy to train, and achieves relative reconstruction performance improvements of up to 6.4% over POD for 64 modes. The relative improvement increases to up to 229.8% as the number of modes decreases. Additionally, our method delivers interpretable features similar to those of POD and is significantly less resource-intensive than existing CAE approaches, using less than 2% of the parameters. These approaches either trade interpretability for reconstruction performance or only provide interpretability to a limited extend.
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