A Spatiotemporal Neural Network Modeling Method for Nonlinear Distributed Parameter Systems

Neural network (NN) has been widely used in the field of modeling of lumped parameter systems. However, an NN approach cannot be used to model complex nonlinear distributed parameter systems (DPSs) because it does not account for this type of system's relationship with space. In this article, we propose a novel spatiotemporal NN (SNN) method to model nonlinear DPSs, which considers not only nonlinear dynamics regarding time, but also a nonlinear relationship with space. A temporal NN model was first constructed to represent the nonlinear temporal dynamics of each sensor's position. A spatial distribution function was then developed to represent the nonlinear relationship between spatial points. This strategy results in inherent consideration of any spatial dynamics. Finally, by integrating both the temporal NN model and the spatial distribution function, a novel SNN model was created to represent the spatiotemporal dynamics of the nonlinear DPSs. A two-step solving approach was further developed to learn the model. Additional analysis and proof of concept showed the effectiveness of this proposed method. This proposed method is different from traditional data-driven modeling methods in that it uses full information from all sensors and does not require model reduction technology. Case studies not only demonstrate the effectiveness of this proposed method, but also its superior modeling performance as compared with several commonly used methods.