Physically constrained deep recurrent neural network for stiffness computation of plate structures

In the present study, we introduce two Neural Network (NN) enhanced methods to approximate local tangent stiffness matrix and internal force computation for a 2D Finite Element. The proposed model is based on Long-Short Term Memory (LSTM), which inherently captures required path-dependent behavior through its parameters. Furthermore, propose an training algorithm where additional loss term corresponding derivative of NN following Sobolev procedure introduced. Such learning combines data-driven approach with necessary physical constraint train NN. Thus, work focuses introducing at element level plate structures taking non-linearities into account. performance demonstrated in academic example showing maximum 90.564% boost simulation speed.