Prediction Of Distributed Parameter Systems Based On Recurrent Neural Network

Distributed parameter systems refer to the systems whose state evolution involves both spatial and temporal information.It has been found that distributed parameter systems widely exist in many scientific and industrial areas.The predictive modeling of distributed parameter systems can not only help people better understand the internal evolutionary mechanism of spatiotemporal systems,but also allow people to control the operation of a system in a safer and more effective way.Therefore,the research on the modeling of distributed parameter systems is of great significance.To model a distributed parameter system,a traditional method is mechanism-based modeling.That is,a governing equation describing the distributed parameter system is firstly derived according to some physical theorems or chemical laws,and then the state evolution of the original system is inferred from the equation.Although such a method shows a good modeling effect on certain systems,the derivation of the governing equations highly depends on a series of strict assumptions,which are usually difficult to meet in the actual industrial scenarios.Therefore,it is very important to find a practical prediction method for modeling distributed parameter systems.From a pure data-driven perspective,this paper works on the predictive modeling of distributed parameter systems defined in one-dimensional real space,which can effectively overcome the shortcomings resulted from the lack of governing equations.Specifically,this paper constructs the historical data collected from a distributed parameter system into specific input and output forms according to certain rules,and then feeds them into an attentionbased sequence-to-sequence architecture to train a predictor that can hopefully express the future evolution of the system.Within the machine learning community,the recurrent neural network used here is originally designed for classification tasks,such as machine translation and so on.In this paper,it is adapted into a model suitable for the prediction task of a distributed parameter system,which can achieve the goal of multi-step prediction.The model is made up of an encoder cascaded after by a decoder,in which the encoder acts upon a given input sequence and stores the produced results in the network– so that it is capable of remembering the input information– and then generate the corresponding output through the decoder network.In order to verify the validity of the model,simulation experiments are carried out on four distributed parameter systems,including Korteweg-de Vries equation which admits soliton solution,Fisher Equation,Burger equation and sine-Gordon equation.It shows that good long-term prediction results are achieved with high prediction accuracy on these four distributed parameter systems.In addition,the prediction of the chaotic Lorenz system is also implemented and compared with a previously published result.Under the condition that both two models are trained with the same training data set,the experimental result shows that the method mentioned in this paper can predict Lorenz system for a longer time span than the published result.In conclusion,these experimental results sufficiently demonstrate that the predictive modeling method in this paper has certain practicability.