Self-Directed Online Machine Learning for Topology Optimization.

Topology optimization by optimally distributing materials in a given domain requires stochastic optimizers to solve highly complicated problems. However, with hundreds of design variables or more involved, solving such problems would require millions of Finite Element Method (FEM) calculations whose computational cost is huge and impractical. Here we report a self-directed online learning method which integrates Deep Neural Network (DNN) with FEM calculations. A DNN learns and substitutes the objective as a function of design variables. A small amount of training data are generated dynamically around the DNN's prediction of the global optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. Our algorithm was tested by compliance minimization problems and demonstrated a reduction of computational time by over two orders of magnitude than the current method. This approach enables solving very large multi-dimensional optimization problems.