A peridynamic-informed neural network for continuum elastic displacement characterization

Abstract

Physics-informed neural networks have attracted considerable attention for solving scientific and engineering problems because of their low data dependence and physical outputs. The most popular way to embed the laws of physics into neural networks is to apply partial differential equations. However, many complex mechanical problems, such as displacements near the phase interface in heterogeneous plates, are difficult to solve using differential equations expressed by higher-order derivatives. In this work, peridynamic (PD)-informed neural networks are established to characterize the displacement of homogeneous and especially heterogeneous elastic plates. The networks are directly constrained by the integro-differential equations of bond-based PD, thus avoiding higher-order derivatives. The networks are trained without labeled data, and the convergence of the training process is accelerated by a gradual-refinement sampling method. Four simulation experiments show that the displacements of two-dimensional plates with homogeneous or heterogeneous structures are globally approximated by the proposed network with small deviations compare to those obtained with peridynamic numerical solutions. Further investigations show that sampling refinement can significantly increase the prediction accuracy of the networks for complex heterogeneous plates.