Mechanism-Assisted Deep State Space Model for Dynamic System Identification

Deep state space model (DSSM) are a temporal model that is actively researched. It combines deep neural networks with classic state space model (SSM) so that it can be used for prediction and identification of dynamic system. However, DSSM treats observation as multiple 1-D variables instead of one multidimensional variable, which does not make the most of correlation information in observation. On the other hand, DSSM cannot combine the mechanism of the system. Therefore, we propose a new model called mechanism-assisted deep state space model (MA-DSSM). We use the multidimensional time-varying SSM to describe the temporal structure of system observation. System observation is assumed to be a multidimensional random variable. Two recurrent neural networks are used to extract static and dynamic features of the system. These measures enhance the prediction performance of the model. In addition, we design conditional mask which can finely and flexibly combine prior knowledge in the SSM with DSSM. So that MA-DSSM can combine data with mechanism and further improve performance. This article introduces the detailed structure of MA-DSSM, the calculation of training loss and the process of prediction. Three numerical experiments are used to verify the performance of MA-DSSM. The experimental results show that MA-DSSM has the best prediction performance with the assistance of system mechanism. The prediction performance is also better than the comparison model without the assistance of system mechanism.