用确定性自编码器实现降维模型的解耦潜空间,提升可解释性。
Disentangled Latent Spaces for Reduced Order Models using Deterministic Autoencoders
- 采用非概率方法通过正交或相关性惩罚实现潜变量解耦。
- 在周期流数据上达到与概率模型相当的性能,且超参数更鲁棒。
- 可识别关键潜变量,适合工业级仿真负载分析场景。
基于自编码器的数据驱动降维模型通常缺乏经典方法(如本征正交分解)的可解释性。通过解耦潜变量并分析其对应模态,可增强可解释性。在计算流体动力学等仿真科学中,常使用概率型β-变分自编码器(β-VAE)。本文基于一个基准周期流动数据集,证明非概率自编码器方法(通过促进潜变量正交性或惩罚相关性)也能获得竞争力的结果。相比概率模型,这些方法对损失函数中超参数的选择更具鲁棒性。进一步表明,非概率方法结合相关性惩罚项(该函数亦用于β-VAE),可有效识别出少数活跃的潜变量。所研究的概率与非概率自编码器模型最终应用于飞机迫降载荷的降维,作为本工作的工业应用场景。
原文摘要 · Abstract (English)
Data-driven reduced-order models based on autoencoders generally lack interpretability compared to classical methods such as the proper orthogonal decomposition. More interpretability can be gained by disentangling the latent variables and analyzing the resulting modes. For this purpose, probabilistic $β$-variational autoencoders ($β$-VAEs) are frequently used in computational fluid dynamics and other simulation sciences. Using a benchmark periodic flow dataset, we show that competitive results can be achieved using non-probabilistic autoencoder approaches that either promote orthogonality or penalize correlation between latent variables. Compared to probabilistic autoencoders, these approaches offer more robustness with respect to the choice of hyperparameters entering the loss function. We further demonstrate the ability of a non-probabilistic approach to identify a reduced number of active latent variables by introducing a correlation penalty, a function also known from the use of $β$-VAE. The investigated probabilistic and non-probabilistic autoencoder models are finally used for the dimensionality reduction of aircraft ditching loads, which serves as an industrial application in this work.
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