The Cross-Twin Physics-Informed Neural Network for Wave Equations with Conserved Quantities

Physics-Informed Neural Networks (PINNs) have demonstrated significant potential in solving partial differential equations (PDEs) and modeling complex physical systems. However, when dealing with multi-scale, multi-domain scenarios and multi-physics coupled systems, PINNs face challenges such as low training efficiency and optimization instability. Based on existing PINN methods, a conservation-based Cross-Twin Network (CTN) approach is proposed for solving wave equations. By introducing interactive information-sharing and constraint mechanisms, the proposed method significantly improves the convergence speed, prediction accuracy, and training stability in multi-domain and multi-scale scenarios. Experimental results show that, compared with traditional methods, the Cross-Twin Network achieves superior performance in solving nonlinear higher-order wave PDEs and equation systems. This study provides new insights for the research and application of PINNs.