  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.
