A hierarchical physics-enhanced neural network based ensemble learning for finite element modeling of granular materials

The application of classical neural networks based surrogate models to implicit finite element modeling of boundary value problems is limited by numerical stability issues stemming from their inherent strong nonlinearity and smoothness characteristics. To overcome this limitation, this study proposed a novel surrogate model framework that combines a Hierarchical Physics-Enhanced Neural Network (HPENN) and ensemble learning. Based on this framework, a surrogate model is trained on data generated from coupled Finite Element Method-Discrete Element Method (FEMDEM) multiscale simulations of granular materials. The trained surrogate model is then employed to replace the meso-scale DEM computation in conventional multi-scale modeling, thus a FEMHPENN multi-scale computation scheme is formulated. The performance of the trained surrogate model and the FEM-HPENN scheme is illustrated through a numerical biaxial compression test and simulation of localization in a retaining wall. The biaxial compression test examines the effects of the number of base learners, the modulus matrix, and surrogate models trained on different meshes on the solution accuracy and convergence. Numerical results show the modulus matrix significantly impacts convergence, however, the number of base learners and mesh-dependent surrogate models primarily affect solution accuracy with only minor influence on convergence. The simulation of localization in retaining-wall further verifies that the trained surrogate model and the FEM-HPENN scheme can effectively solve BVPs related to granular materials.