DIRESA, a distance-preserving nonlinear dimension reduction technique based on regularized autoencoders

TL;DR

This work introduces DIRESA, a distance-regularized Siamese twin autoencoder for nonlinear dimensionality reduction of high-volume climate data, enabling efficient analog retrieval in a latent space. By incorporating a distance loss, a covariance loss, and reconstruction loss with annealing, DIRESA preserves input-space distances, yields independent latent components, and produces faithful reconstructions. Evaluated on Lorenz '63' and MAOOAM, DIRESA outperforms PCA, KPCA, UMAP, and standard AEs in distance-ordering metrics while recovering physically meaningful modes of variability and maintaining reconstruction fidelity. The approach is implemented as an open-source Python package, designed to handle complex data types and facilitate downstream tasks such as analog search, data assimilation, and climate attribution. This method has practical potential to distill large climate archives into compact, interpretable latent representations that preserve the ordering of similarity among patterns.

Abstract

In meteorology, finding similar weather patterns or analogs in historical datasets can be useful for data assimilation, forecasting, and postprocessing. In climate science, analogs in historical and climate projection data are used for attribution and impact studies. However, most of the time, those large weather and climate datasets are nearline. This means that they must be downloaded, which takes a lot of bandwidth and disk space, before the computationally expensive search can be executed. We propose a dimension reduction technique based on autoencoder (AE) neural networks to compress the datasets and perform the search in an interpretable, compressed latent space. A distance-regularized Siamese twin autoencoder (DIRESA) architecture is designed to preserve distance in latent space while capturing the nonlinearities in the datasets. Using conceptual climate models of different complexities, we show that the latent components thus obtained provide physical insight into the dominant modes of variability in the system. Compressing datasets with DIRESA reduces the online storage and keeps the latent components uncorrelated, while the distance (ordering) preservation and reconstruction fidelity robustly outperform Principal Component Analysis (PCA) and other dimension reduction techniques such as UMAP or variational autoencoders.

Figures (14)

• Figure 1: DIRESA: Distance regularized siamese twin AE
• Figure 2: (a) Requirement for the AE: Reconstructed data as close as possible to the original. (b) DR requirements: Distance in original space is related to distance in latent space, and latent components are independent and ordered in terms of importance.
• Figure 3: Lorenz test dataset (blue) next to the decoded random uniform latent components (orange) for the different DR techniques
• Figure 4: Encoded Lorenz test dataset for the different DR techniques
• Figure 5: Scatter plots of 50 closest distances for 200 random samples of the Lorenz test dataset for for the different DR techniques