标题： 基于瘦多尺度卷积自编码器的可解释复杂动力系统特征的降阶模型 显示英文标题

标题： Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system

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（ROMs）的背景下，卷积自编码器（CAEs）为传统方法提供了一种通用的替代方案。 它们可以直接从数据中学习非线性变换，而无需了解系统的先验知识。 然而，这些模型生成的特征缺乏可解释性。 因此，得到的模型是一个黑箱，虽然有效地降低了系统的复杂性，但无法提供潜在特征的意义。 为了解决这一关键问题，我们引入了一种新的可解释的CAE方法，用于高维流体流动数据，该方法保持了传统CAEs的重建质量，并允许特征解释。 我们的方法可以轻松集成到任何现有的CAE架构中，只需对训练过程进行少量修改。 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不同复杂度的实验性湍流雷诺-贝纳德对流数据集。 我们的结果表明，所提出的方法轻量、易于训练，并且在64个模式下相对于POD的重建性能提高了高达6.4%。 当模式数量减少时，相对改进最高可达229.8%。 此外，我们的方法提供了类似于POD的可解释特征，并且比现有的CAE方法显著更少资源消耗，使用的参数不到2%。 这些方法要么以牺牲重建性能为代价来获得可解释性，要么仅能提供有限的可解释性。 显示英文摘要

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-B\'enard 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.