计算机科学
趋同(经济学)
启发式
人工神经网络
数学优化
拓扑优化
有限元法
最优化问题
人工智能
领域(数学分析)
算法
数学
经济增长
热力学
物理
数学分析
经济
作者
Changyu Deng,Yizhou Wang,Can Qin,Yun-Fei Fu,Wei Lu
标识
DOI:10.1038/s41467-021-27713-7
摘要
Abstract Topology optimization by optimally distributing materials in a given domain requires non-gradient 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 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 number of training data is generated dynamically based on the DNN’s prediction of the optimum. The DNN adapts to the new training data and gives better prediction in the region of interest until convergence. The optimum predicted by the DNN is proved to converge to the true global optimum through iterations. Our algorithm was tested by four types of problems including compliance minimization, fluid-structure optimization, heat transfer enhancement and truss optimization. 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.
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