Koopman Invertible Autoencoder: Leveraging Forward and Backward Dynamics for Temporal Modeling

TL;DR

The paper introduces Koopman Invertible Autoencoders (KIA), a novel approach leveraging Koopman operator theory to improve long-term predictions by modeling system dynamics bidirectionally, demonstrating significant accuracy gains on physical datasets.

Contribution

It presents a new invertible autoencoder framework based on Koopman theory that captures forward and backward dynamics for enhanced long-term temporal modeling.

Findings

300% improvement in pendulum prediction accuracy

Robustness against noise in long-term predictions

Effective climate data forecasting

Abstract

Accurate long-term predictions are the foundations for many machine learning applications and decision-making processes. However, building accurate long-term prediction models remains challenging due to the limitations of existing temporal models like recurrent neural networks (RNNs), as they capture only the statistical connections in the training data and may fail to learn the underlying dynamics of the target system. To tackle this challenge, we propose a novel machine learning model based on Koopman operator theory, which we call Koopman Invertible Autoencoders (KIA), that captures the inherent characteristic of the system by modeling both forward and backward dynamics in the infinite-dimensional Hilbert space. This enables us to efficiently learn low-dimensional representations, resulting in more accurate predictions of long-term system behavior. Moreover, our method's invertibility design guarantees reversibility and consistency in both forward and inverse operations. We illustrate the utility of KIA on pendulum and climate datasets, demonstrating 300% improvements in long-term prediction capability for pendulum while maintaining robustness against noise. Additionally, our method excels in long-term climate prediction, further validating our method's effectiveness.