Development of Spatiotemporal Recurrent Neural Network for Modeling of Spatiotemporal Processes

摘要

Modeling distributed parameter systems (DPSs) are usually challenging due to their infinite dimension nature and strong nonlinearity. As a result, the commonly used DPS modeling methods often do not represent this kind of DPSs well due to model reduction and its neglect of nonlinear dynamics. Here, a novel spatiotemporal recurrent neural network (SRNN) modeling method was proposed for nonlinear DPSs. Generally, the space neighboring the points in a DPS interact each other by means of energy transfer, also known as spatial dynamics. In this SRNN model, its hidden layer at each time is designed to represent the spatial dynamics using a bidirectional RNN (BRNN). The BRNN has the ability to represent this complex interaction since its neighboring hidden layers are used to represent these adjacent spatial points and using a forward step and a backward step represents the interaction between neighboring hidden layers. Then, with the combination of all hidden layers of the SRNN over time, the temporal dynamics of the snapshots is exhibited and represented. In this way, this SRNN integrates the spatial temporal dynamics together and is without requirement of model reduction. A solving approach is then proposed to find its solution, and a convergence analysis further proves that the proposed method can effectively reconstruct the nonlinear spatiotemporal dynamics of the nonlinear DPS. The article not only demonstrate the effectiveness of the proposed method, but also demonstrate its superior modeling performance as compared to several common methods.