A stochastic gradient online learning and prediction method for accelerating structural topology optimization using recurrent neural network

This study presents a new stochastic gradient online learning and prediction (SGoLap) method for accelerating structural topology optimization. The new method utilizes a one-hidden-layer recurrent neural network (RNN) to learn and predict online derivative information, including the second-order derivative of the objective function, in conjunction with an online learning and prediction strategy, and saves total computational time by selectively skipping FEA and sensitivity analysis steps. In the training module, a stochastic sampling scheme is proposed to reduce the size of training datasets and the number of RNN parameters. In addition to using gradient information, the SGoLap is applied to an approximated and vectorized Hessian matrix to account for contribution of second-order derivative in design variable update and to further reduce computational time. The present numerical results of solving 2D and 3D topology optimization problems demonstrate that the implementation of SGoLap can save up to 99.3 % and 90.9 % of the total computational time respectively.