Augmented Invertible Koopman Autoencoder for long-term time series forecasting

2025-03-17

AI Summary

Traditional invertible Koopman autoencoders (IKAEs) suffer from limited long-term forecasting performance due to the inherent dimension-preserving constraint of normalizing flows, which hinders effective modeling of complex dynamics. To address this, we propose the Augmented Invertible Koopman Autoencoder (AIKAE), the first framework to decouple invertibility from latent dimension constraints: it retains invertible coupling layers for exact reconstruction while introducing a non-invertible auxiliary encoder to enrich latent representation capacity, all integrated with linear Koopman dynamics in the latent space. This end-to-end architecture achieves significant improvements in long-horizon prediction accuracy on benchmark datasets—including satellite image time series and large lookback-window sequences—demonstrating both the effectiveness of the augmented latent space in capturing high-dimensional complex system evolution and its superior generalization capability.

Technology Category

• Machine Learning: Deep Generative Models & Autoencoders
• Humans and AI: Human-Aware Planning and Behavior Prediction
• Cognitive Modeling & Cognitive Systems: Agent Architectures

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Search and Retrieval-Augmented AI: Agentic search
• Responsible Web: Machine-in-the-loop, human agency and autonomy

Abstract

Following the introduction of Dynamic Mode Decomposition and its numerous extensions, many neural autoencoder-based implementations of the Koopman operator have recently been proposed. This class of methods appears to be of interest for modeling dynamical systems, either through direct long-term prediction of the evolution of the state or as a powerful embedding for downstream methods. In particular, a recent line of work has developed invertible Koopman autoencoders (IKAEs), which provide an exact reconstruction of the input state thanks to their analytically invertible encoder, based on coupling layer normalizing flow models. We identify that the conservation of the dimension imposed by the normalizing flows is a limitation for the IKAE models, and thus we propose to augment the latent state with a second, non-invertible encoder network. This results in our new model: the Augmented Invertible Koopman AutoEncoder (AIKAE). We demonstrate the relevance of the AIKAE through a series of long-term time series forecasting experiments, on satellite image time series as well as on a benchmark involving predictions based on a large lookback window of observations.

Problem

• Enhance long-term time series forecasting accuracy
• Overcome dimension conservation limitations in IKAE models
• Improve dynamical system modeling with augmented latent state

Innovation

• Augmented Invertible Koopman AutoEncoder (AIKAE) introduced
• Combines invertible and non-invertible encoder networks
• Enhances long-term time series forecasting accuracy