A finite-element-informed neural network for parametric simulation in structural mechanics

In this study, we propose a novel deep learning model named as the Finite-element-informed neural network (FEI-NN), inspired from finite element method (FEM) for parametric simulation of static problems in structural mechanics. The approach trains neural networks in the supervised manner, in which parametric variables of structures are considered as input features of network and spatial ones are implicitly embedded into the loss function based on a soft constraint called by finite element analysis (FEA) loss. The training process simultaneously minimizes the empirical risk function and partially respects the mechanical behaviors via the FEA loss defined as a residual calculated from the weak form of the surrogate system scaled from the actual corresponding structure. Besides, a technique developed from batch matrix multiplication is proposed to significantly reduce the time complexity for estimating the FEA loss. The method applies to some typical systems in structural mechanics including truss, beam and plate structures. Through several experiments we statistically demonstrate the superiority of the approach in terms of faster convergence and producing better DNN models in comparison to the traditional data-driven approach concerning both generalization and extrapolation performance.