Generating realistic time series data is important for numerous engineering and scientific applications. Several existing works tackle this problem using generative adversarial networks, however, GANs are often unstable during training and suffer from mode collpase. While variational autoencoders (VAEs) are more robust to the above issues, surprisingly, they are considered less for time series generation. In this work, we introduce Koopman VAE (KVAE), 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 the 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 leverageing spectral tools that prescribe constraints on the eigenvalues of the linear map; and (ii) studying the qualitative behavior and stablity of the system can be performed using tools from dynamical systems theory. Our results show that KVAE 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, KVAE generates time series that improve both discriminative and predictive metrics. Further, we present visual evidence suggesting that KVAE learns probability density functions that better approximate the empirical ground truth distribution.
Generative Modeling of Regular and Irregular Time Series Data via Koopman VAEs
Ilan Naiman N. Benjamin Erichson Pu Ren Michael W. Mahoney Omri Azencot