Dynamical system reconstruction from partial observations using stochastic dynamics

Viktor Sip, Martin Breyton, Spase Petkoski, Viktor Jirsa

Keywords: Dynamical system reconstruction, State space model, Dynamical Variational Autoencoders

TL;DR: The work proposes a novel method for stochastic dynamical system reconstruction using double projection approach to system space and noise space.

Abstract: 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.

Primary Area: learning on time series and dynamical systems

Submission Number: 12489