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.

翻译：近年来，数据驱动的深度学习模型在湍流动力系统分析中受到广泛关注。在降阶模型框架下，卷积自编码器为传统方法提供了一种普适性替代方案。它们能够直接从数据中学习非线性变换，无需系统先验知识。然而，此类模型生成的特征缺乏可解释性，导致最终模型成为黑箱系统：虽能有效降低系统复杂度，却无法揭示潜在特征的内在含义。为应对这一关键问题，我们提出了一种面向高维流体流动数据的可解释卷积自编码器新方法，该方法在保持传统卷积自编码器重建质量的同时实现了特征可解释化。本方法仅需对训练过程进行微调即可轻松集成到现有卷积自编码器架构中。我们将所提方法与本征正交分解及两种现有可解释卷积自编码器方法进行对比，并将所有方法应用于三个复杂度各异的实验性湍流Rayleigh-Bénard对流数据集。实验结果表明：所提方法具有轻量化、易训练的特性，在64模态下相比本征正交分解实现最高6.4%的相对重建性能提升，且随着模态数减少，相对提升率最高可达229.8%。此外，本方法生成的可解释特征与本征正交分解具有相似性，其资源消耗显著低于现有卷积自编码器方法（参数量使用率低于2%）。现有方法往往需要在可解释性与重建性能之间进行权衡，或仅能提供有限程度的可解释性。