提出可解释的轻量级卷积自编码器,让流体动力系统降维模型既准确又易懂。
Slim multi-scale convolutional autoencoder-based reduced-order models for interpretable features of a complex dynamical system
- 基于卷积自编码器改进,通过训练微调实现特征可解释性
- 在64个模态下重构误差比POD降低6.4%,模态减少时提升达229.8%
- 参数量不足现有方法2%,适合资源受限场景下的物理系统分析
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。在降维模型(ROM)领域,卷积自编码器(CAE)为传统方法提供了通用替代方案,能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,导致模型成为黑箱,虽有效降低系统复杂度,却无法揭示潜在特征的物理意义。为解决这一关键问题,本文提出一种新型可解释的CAE方法,适用于高维流体流动数据,在保持传统CAE重构质量的同时实现特征可解释。该方法可轻松集成至任意现有CAE架构,仅需微调训练过程。我们在三个不同复杂度的实验性瑞利-贝纳德对流数据集上,与本征正交分解(POD)及两种现有可解释CAE方法进行对比。结果表明,所提方法轻量、易训练,在64个模态下相对重构性能较POD提升最高达6.4%;当模态数减少时,提升可达229.8%。此外,该方法生成的特征与POD相似且具有可解释性,同时资源消耗显著低于现有CAE方法,参数量不足2%。现有方法或牺牲可解释性以换取性能,或仅部分实现可解释性。
原文摘要 · Abstract (English)
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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