Machine learning method in elastic plate topology optimization problems

In this article, as an alternative to traditional methods of topology optimization of deformable solids, an approach to topology optimization based on machine learning methods is proposed. The proposed approach significantly reduces the time spent on obtaining the optimal solution and allows to avoid the use of time-consuming finite element calculations at the stage of obtaining the optimal solution. All of time-consuming calculations are performed at the network training stage. A review of the world literature on the application of machine learning methods in the problem of topology optimization of an elastic deformable solid is given. Further, as an example, a square elastic plate is considered, fixed on one side and loaded with a force on the other. For a given plate, a series of topology optimization problems (maximizing stiffness under volume constraints) are solved using the method of moving asymptotes to build a training data set. A comparative study of a neural network with one custom nonlinear layer, based on the nature of the optimal topology, and a three-layer neural network built using the standard PyTorch library features is carried out. The input parameter of the neural network is the force application point, the output parameter is the optimal topology of the plate. The network is trained using the backpropagation method. The quadratic norm of the predicted design variable values deviations compared to the true values form last optimization is minimized during neural network learning. The considered example shows the possibility of applying the approach to other problems that differ in geometry, boundary conditions, etc. The results and unsolved problems of the method are also discussed.