Variational Augmented Invertible Koopman Autoencoder for probabilistic time series forecasting

2026-09-29

AI Summary

This study addresses the inability of deterministic neural Koopman models to quantify predictive uncertainty and perform probabilistic time series forecasting. To this end, we propose VAIKAE, which introduces variational inference into reversible Koopman autoencoders for the first time. The method models latent variables as Gaussian distributions and leverages normalizing flows to compute exact likelihoods for state-space training. Furthermore, an uncertainty-aware latent data assimilation strategy is innovatively designed to enhance forecast reliability. Experimental results demonstrate that VAIKAE significantly improves both the accuracy and reliability of probabilistic predictions across multiple long-term time series forecasting benchmarks.

Abstract

Neural Koopman autoencoder models have been shown to successfully build a latent embedding with linear dynamics for arbitrary dynamical systems, enabling strong performance in long-term time series forecasting. However, these models usually work in a deterministic setting, which does not allow the quantification of the uncertainty of their predictions. Thus, we propose the new Variational Augmented Invertible Koopman AutoEncoder (VAIKAE), in which the latent embedding follows a Gaussian distribution instead of being deterministic. A key property of the VAIKAE architecture is that it leverages normalizing flow models, enabling the use of likelihood computations in the state space of dynamical systems for training a model. We further propose new strategies for uncertainty-aware latent data assimilation with a trained VAIKAE model. The effectiveness of our methods is demonstrated in a series of experiments on long-term time series forecasting benchmarks.

Problem

• probabilistic time series forecasting
• uncertainty quantification
• Koopman autoencoder
• dynamical systems

Innovation

• Koopman Autoencoder
• Probabilistic Forecasting
• Normalizing Flow
• Uncertainty Quantification
• Data Assimilation