Long term evolution analysis of complex systems based on physics-informed machine learning
Physics-informed neural networks(PINN)can use physical information in numerical prediction,which is a promising application of machine learning in numerical solutions of nonlinear partial differential equations(PDEs).However,the original PINN method has inherent defects in the prediction of complex nonlinear systems and the stable and accurate prediction of long-term range.To make the PINN method to effectively predict the complex nonlinear PDEs for a long time,the PINN is improved and a new adaptive PINN method is proposed.This method decomposes the long time-domain system integral into short-term with different initial states.By collecting the numerical solution of nonlinear PDEs in short time domain with random initial conditions as training data,so that the method has good generalization,and can effectively predict the long-term evolution of complex systems.In addition,the proposed method establishes adaptive weights to automatically learn which regions of the solution are difficult,and force to focus on these regions,so as to solve the problem that the network gradient disappears when the original PINN method deals with complex systems,and improve the prediction accuracy of PINN method for complex nonlinear PDEs.Finally,the proposed method is applied to the long-period evolution analysis of complex nonlinear partial differential kinematics equations of aircrafts to verify the algorithm effectiveness.
万方数据
维普
