This paper introduces a multi-level physics-informed neural network (ml-PINN) framework for solving high-order partial differential equations (PDEs) in computational structural mechanics. The framework addresses challenges posed by the fourth-order nonlinear PDEs governing bending structures by using an aggregation model combining multiple neural networks, each handling first- or second-order PDEs representing different physics. The ml-PINN shows improved accuracy and computational speed compared to classical PINNs and holds promise for real-time simulation in digital twin systems.

Weiwei He, Jinzhao Li, Xuan Kong, Lu Deng