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.

翻译：生成逼真的时间序列数据对于许多工程和科学应用至关重要。现有工作利用生成对抗网络（GANs）解决这一问题。然而，GANs在训练过程中不稳定，且易出现模式坍塌问题。尽管变分自编码器（VAEs）已知对此类问题具有更强鲁棒性，但（令人意外的是）其在时间序列生成领域的应用较少。本文提出Koopman VAE（KoVAE），一种基于模型先验创新设计的新型生成框架，能够针对规则或不规则训练数据进行优化。受Koopman理论启发，我们采用线性映射表征潜在条件先验动力学。该方法通过两个理想特性增强生成建模：（i）利用谱工具对线性映射特征值施加约束，可融入领域知识；（ii）借助动力系统理论工具，可研究系统的定性行为与稳定性。实验结果表明，在多个具有挑战性的合成及真实时间序列生成基准测试中，KoVAE显著优于现有最优GAN与VAE方法。无论训练数据规则与否，KoVAE生成的时间序列均能改善判别指标与预测指标。可视化证据亦表明，KoVAE学习到的概率密度函数能更精确地逼近经验真实分布。