Topology optimization by optimally distributing materials in a given domain requires gradient-free 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 Optimization (SOLO) 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 is generated dynamically based on 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 fluid-structure optimization problems. It reduced the computational time by 2~5 orders of magnitude compared with directly using heuristic methods, and outperformed all state-of-the-art algorithms tested in our experiments. This approach enables solving large multi-dimensional optimization problems.

翻译：通过在特定领域最佳分配材料优化地形学需要无梯度优化来解决非常复杂的问题。然而,如果涉及数百个设计变量或更多的问题,解决这些问题需要数百万个计算成本巨大且不切实际的有限元素方法(FEM)计算。这里我们报告了一个将深神经网络(DNN)与FEM计算相结合的自导在线学习优化(SOLO)报告。DNN将目标作为设计变量的函数来学习和替代。少量的培训数据是根据DNN对全球最佳的预测动态生成的。DNN适应新的培训数据,并在达到趋同之前对感兴趣的区域作出更好的预测。我们的算法通过遵守最小化问题和流体结构优化问题来测试。它将计算时间减少2~5级,与直接使用超常方法相比,并超越了我们实验中测试的所有最先进的算法。这个方法可以解决大型多维优化问题。