Dynamical system reconstruction from partial observations using stochastic dynamics
This work addresses a common challenge in scientific fields for researchers needing to model stochastic dynamical systems from incomplete data, though it appears incremental as it builds on existing autoencoder frameworks.
The authors tackled the problem of reconstructing stochastic dynamical systems from partial observations by proposing a novel method based on variational autoencoders that estimates both state trajectories and noise time series, demonstrating its performance on six test problems with simulated and experimental data.
Learning stochastic models of dynamical systems underlying observed data is of interest in many scientific fields. Here we propose a novel method for this task, based on the framework of variational autoencoders for dynamical systems. The method estimates from the data both the system state trajectories and noise time series. This approach allows to perform multi-step system evolution and supports a teacher forcing strategy, alleviating limitations of autoencoder-based approaches for stochastic systems. We demonstrate the performance of the proposed approach on six test problems, covering simulated and experimental data. We further show the effects of the teacher forcing interval on the nature of the internal dynamics, and compare it to the deterministic models with equivalent architecture.