This study is focused on enhancing the computational efficiency of the solid isotropic material with penalization (SIMP) approach implemented for solving topology optimization problems. Solving such problems might become extremely time-consuming; in this direction, machine learning (ML) and specifically deep neural computing are integrated in order to accelerate the optimization procedure. The capability of ML-based computational models to extract multiple levels of representation of non-linear input data has been implemented successfully in various problems ranging from time series prediction to pattern recognition. The later one triggered the development of the methodology proposed in the current study that is based on deep belief networks (DBNs). More specifically, a DBN is calibrated on transforming the input data to a new higher-level representation. Input data contains the density fluctuation pattern of the finite element discretization provided by the initial steps of SIMP approach, and output data corresponds to the resulted density values distribution over the domain as obtained by SIMP. The representation capabilities and the computational advantages offered by the proposed DBN-based methodology coupled with the SIMP approach are investigated in several benchmark topology optimization test examples where it is observed more than one order of magnitude reduction on the iterations that were originally required by SIMP, while the advantages become more pronounced in case of large-scale problems.

这项研究的重点是通过采用罚分（SIMP）方法提高固体各向同性材料的计算效率，以解决拓扑优化问题。解决此类问题可能会非常耗时；在这个方向上，机器学习（ML）以及特别是深度神经计算被集成在一起，以加速优化过程。基于ML的计算模型提取非线性输入数据表示的多个级别的能力已成功实现，涉及从时序预测到模式识别的各种问题。后者触发了当前研究中提出的基于深度信念网络（DBN）的方法的发展。进一步来说，在将输入数据转换为新的更高级别表示形式时，将对DBN进行校准。输入数据包含SIMP方法初始步骤提供的有限元离散化的密度波动模式，输出数据对应于SIMP获得的域上所得的密度值分布。在几个基准拓扑优化测试示例中研究了所提出的基于DBN的方法与SIMP方法相结合所提供的表示能力和计算优势，在该示例中，SIMP最初要求的迭代次数减少了一个数量级以上，而在出现大规模问题时优势更加明显。输入数据包含SIMP方法初始步骤提供的有限元离散化的密度波动模式，输出数据对应于SIMP获得的域上所得的密度值分布。在几个基准拓扑优化测试示例中研究了所提出的基于DBN的方法与SIMP方法相结合所提供的表示能力和计算优势，在该示例中，SIMP最初要求的迭代次数减少了一个数量级以上，而在出现大规模问题时优势更加明显。输入数据包含SIMP方法初始步骤提供的有限元离散化的密度波动模式，输出数据对应于SIMP获得的域上所得的密度值分布。在几个基准拓扑优化测试示例中研究了所提出的基于DBN的方法与SIMP方法相结合所提供的表示能力和计算优势，在该示例中，SIMP最初要求的迭代次数减少了一个数量级以上，而在出现大规模问题时优势更加明显。