Nonlinear System Prediction Method of Physical Neural Networks Based on Frequency Domain Control Constraints

To address the problems of high computational cost and boundary condition limitations associated with the existing physical information neural network using numerical simulation to approximate the physical control equations, a nonlinear system prediction method of physical neural networks based on frequency domain control constraints is proposed. Firstly, a nonlinear prediction network model with alternating updates of temporal features is constructed, followed by a physical control equation constraint based on the Fourier spectrum method (FSM) in the frequency domain, and then the spatio-temporal data are trained without labels under the coupling of the network model and the frequency domain control constraint to complete the system evolution learning. The experimental results show that the proposed method can achieve unlabeled nonlinear complex modeling under physical rule constraints, and has faster learning speed and prediction accuracy compared with the mainstream Physics Informed Neural Network (PINN) model and its variants. In the case of t≤0.25 s and t≤0.5 s short-time prediction, the Mean Square Error (MSE) of the system is reduced by 86% and 95% compared with that of the mainstream baseline model in the same period of time after 20 times of pre-training, and the MSE of the system can be reduced by 80% in the case of t≤2 s long-time prediction after sufficient training.