Fig. 7: The multi-level physics-informed neural network (ml-PINN) for generalization computation.

a Framework of ml-PINN for generalization learning by incorporating the physical variables related to loading conditions (u and q) as input parameters of the networks. u and q represent the displacement applied on the right boundary and the uniform load imposed on the entire region. b Direct prediction results of ml-PINN for bending beam cases under different loading conditions. FEM represents the result predicted by Finite Element Method, and Generalized PINN represents the result predicted by the proposed ml-PINN.