FE-LSTM: A hybrid approach to accelerate multiscale simulations of architectured materials using Recurrent Neural Networks and Finite Element Analysis

Abstract

In the present work, a novel modeling strategy to accelerate multi-scale simulations of heterogeneous materials using deep neural networks is developed. This approach, called FE-LSTM, consists of combining the finite element method and LSTM recurrent neural networks to solve multiscale problems. In contrast to FE2 method, the finite element resolution of the microscopic problems is no longer required within FE-LSTM framework, the computation of RVE homogenized response is directly predicted by an LSTM trained on a database of offline micro simulations. The usefulness of such approach lies in the fact that once the RNN training process is performed, FE-LSTM can be applied to simulate nonlinear behaviors of any heterogeneous structure having the same microstructure used in training, considering a different Boundary Value Problem to solve. To assess the validity and reliability of the developed approach, FE-LSTM has been evaluated on several 3D architectured structures from rather simple to complex geometries under proportional and non proportional loading conditions. In terms of execution time, it has been found that FE-LSTM shows a speedup factor of nearly 40 000 as compared with legacy two-scale implementation of the FE2 method, while up to date optimized FE2 methods shows a speed up factor around 1000. Furthermore, RAM memory saving factor allow complex structures simulations to be conducted on desktop computers without requiring HPC clusters with specific additions to RAM memory.