Double projection for reconstructing dynamical systems: between stochastic and deterministic regimes

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.