使用有序方差自编码器发现未标注数据集中的非线性静态关系
Discovering Nonlinear Static Relationships in Unlabeled Dataset using Autoencoder with Ordered Variance
AI总结：
提出一种有序方差自编码器（AEO）及其残差网络扩展（RAEO），通过方差正则化项强制潜变量有序排列，实现未标注数据中非线性关系的无监督发现与静态模型提取。
摘要：
本文提出了一种有序方差自编码器（AEO），其中传统的重建损失通过基于方差的正则化项进行增强，该正则化项促进了潜空间内的有序结构。在这种结构中，潜变量根据其在训练数据上计算的方差进行排序，有助于系统地确定潜空间维度。AEO进一步通过残差网络扩展，产生了基于ResNet的AEO（RAEO）。AEO和RAEO均能发现未标注数据集中变量间的非线性关系，从而实现无监督静态模型提取。理论贡献包括对潜变量方差排序的形式化保证。通过将框架应用于非线性稳态模型的识别及其在实时优化中的使用，以连续搅拌釜反应器过程作为代表性案例研究，展示了该框架的实际效用。
英文摘要：
This paper presents an autoencoder with ordered variance (AEO), in which the conventional reconstruction loss is augmented by a variance-based regularization term that promotes an ordered structure within the latent space. In this structure, the latent variables are ordered by their variance computed over the training data, facilitating systematic determination of the latent space dimensionality. The AEO is further extended using residual networks, resulting in a ResNet-based AEO (RAEO). Both AEO and RAEO green lead to discovery of nonlinear relationships among variables in unlabeled datasets, thereby enabling unsupervised static model extraction. Theoretical contributions include formal guarantees on the ordering of latent variances. The practical utility of the framework is demonstrated through its application to the identification of nonlinear steady-state models and their use in real-time optimization, with a continuous stirred tank reactor process serving as a representative case study.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
