Learning stochastic models of dynamical systems from observed data is of interest in many scientific fields. Here, we propose a new method for this task within the family of dynamical variational autoencoders. The proposed double projection method estimates both the system state trajectories and the noise time series from data. This approach naturally allows us to perform multi-step system evolution and to learn models with a comparatively low-dimensional state space. We evaluate the performance of the method on six benchmark problems, including both simulated and experimental data. We further illustrate the effects of the teacher forcing interval of the multi-step scheme on the nature of the internal dynamics and compare the resulting behavior to that of deterministic models of equivalent architecture.

翻译：从观测数据中学习动力系统的随机模型是众多科学领域关注的问题。本文在动态变分自编码器框架内提出了一种解决该问题的新方法。所提出的双投影方法能够从数据中同时估计系统状态轨迹与噪声时间序列。该方法天然支持多步系统演化，并能学习具有相对低维状态空间的模型。我们在六个基准问题上评估了该方法的性能，包括模拟数据与实验数据。进一步地，我们阐释了多步方案中教师强制间隔对内部动力学性质的影响，并将所得行为与同等架构的确定性模型进行了对比分析。