ODE-RSSM: Learning Stochastic Recurrent State Space Model from Irregularly Sampled Data

Abstract

For the complicated input-output systems with nonlinearity and stochasticity, Deep State Space Models (SSMs) are effective for identifying systems in the latent state space, which are of great significance for representation, forecasting, and planning in online scenarios. However, most SSMs are designed for discrete-time sequences and inapplicable when the observations are irregular in time. To solve the problem, we propose a novel continuous-time SSM named Ordinary Differential Equation Recurrent State Space Model (ODE-RSSM). ODE-RSSM incorporates an ordinary differential equation (ODE) network (ODE-Net) to model the continuous-time evolution of latent states between adjacent time points. Inspired from the equivalent linear transformation on integration limits, we propose an efficient reparameterization method for solving batched ODEs with non-uniform time spans in parallel for efficiently training the ODE-RSSM with irregularly sampled sequences. We also conduct extensive experiments to evaluate the proposed ODE-RSSM and the baselines on three input-output datasets, one of which is a rollout of a private industrial dataset with strong long-term delay and stochasticity. The results demonstrate that the ODE-RSSM achieves better performance than other baselines in open loop prediction even if the time spans of predicted points are uneven and the distribution of length is changeable. Code is availiable at https://github.com/yuanzhaolin/ODE-RSSM.