Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs

TL;DR

This paper introduces KoVAE, a novel variational autoencoder framework based on Koopman theory, designed to generate realistic regular and irregular time series data more effectively than existing GAN and VAE methods.

Contribution

The paper proposes KoVAE, a new generative model that leverages spectral constraints and dynamical systems tools to improve time series generation, especially for irregular data.

Findings

KoVAE outperforms state-of-the-art GAN and VAE models on synthetic and real-world benchmarks.

KoVAE generates time series with better discriminative and predictive metrics.

KoVAE learns probability densities closer to ground truth distributions.

Abstract

Generating realistic time series data is important for many engineering and scientific applications. Existing work tackles this problem using generative adversarial networks (GANs). However, GANs are unstable during training, and they can suffer from mode collapse. While variational autoencoders (VAEs) are known to be more robust to the these issues, they are (surprisingly) less considered for time series generation. In this work, we introduce Koopman VAE (KoVAE), a new generative framework that is based on a novel design for the model prior, and that can be optimized for either regular and irregular training data. Inspired by Koopman theory, we represent the latent conditional prior dynamics using a linear map. Our approach enhances generative modeling with two desired features: (i) incorporating domain knowledge can be achieved by leveraging spectral tools that prescribe constraints on the eigenvalues of the linear map; and (ii) studying the qualitative behavior and stability of the system can be performed using tools from dynamical systems theory. Our results show that KoVAE outperforms state-of-the-art GAN and VAE methods across several challenging synthetic and real-world time series generation benchmarks. Whether trained on regular or irregular data, KoVAE generates time series that improve both discriminative and predictive metrics. We also present visual evidence suggesting that KoVAE learns probability density functions that better approximate the empirical ground truth distribution.