Title: Uncovering Nonlinear Static Correlations in Unlabeled Data via Autoencoders with Ordered Variance

Abstract: This study introduces the Autoencoder with Ordered Variance (AEO), a model that enhances standard reconstruction loss by incorporating a variance-based regularization component. This addition enforces a structured arrangement within the latent space, where variables are sorted according to their variance calculated across the training set. Such an ordering streamlines the process of determining the appropriate dimensionality for the latent space. The framework is further expanded through the integration of residual networks, yielding the ResNet-based AEO (RAEO). Both the AEO and RAEO architectures facilitate the identification of nonlinear relationships within unlabeled datasets, effectively allowing for the extraction of static models in an unsupervised manner. From a theoretical standpoint, the paper provides formal proofs ensuring the correct ordering of latent variances. To illustrate the practical value of this approach, we apply the framework to identify nonlinear steady-state models and utilize them for real-time optimization, using a continuous stirred tank reactor as a key example.

Source: arXiv Generated at: 2026-06-02 00:00:00 UTC