Data-driven multiscale finite-element method using deep neural network combined with proper orthogonal decomposition

In this paper, a data-driven multiscale finite-element method (data-driven FE²) is proposed using a deep neural network (DNN) and proper orthogonal decomposition (POD) to describe nonlinear heterogeneous materials. The concurrent classical FE² needs the iterative calculations of microscopic boundary-value problem for representative volume element (RVE) at all integration points of the macroscopic structures. These iterative procedures need large computational time. To overcome this limitation, the proposed data-driven FE² method solves the macroscopic problem by assigning data to all integration points that satisfy microscopic equilibrium by constructing a material genome database in which the microscopic problem of RVE is pre-calculated in online computing. Here, we developed a DNN model that can accurately and efficiently predict microscopic behavior by connecting POD for material genome database construction. Therefore, we improved the data-driven FE² technique one step further by efficiently generating available material genome database.