We propose a direct mesh-free method for performing topology optimization by integrating a density field approximation neural network with a displacement field approximation neural network. We show that this direct integration approach can give comparable results to conventional topology optimization techniques, with an added advantage of enabling seamless integration with post-processing software, and a potential of topology optimization with objectives where meshing and Finite Element Analysis (FEA) may be expensive or not suitable. Our approach (DMF-TONN) takes in as inputs the boundary conditions and domain coordinates and finds the optimum density field for minimizing the loss function of compliance and volume fraction constraint violation. The mesh-free nature is enabled by a physics-informed displacement field approximation neural network to solve the linear elasticity partial differential equation and replace the FEA conventionally used for calculating the compliance. We show that using a suitable Fourier Features neural network architecture and hyperparameters, the density field approximation neural network can learn the weights to represent the optimal density field for the given domain and boundary conditions, by directly backpropagating the loss gradient through the displacement field approximation neural network, and unlike prior work there is no requirement of a sensitivity filter, optimality criterion method, or a separate training of density network in each topology optimization iteration.

翻译：我们提出了一种直接无网格方法，通过将密度场逼近神经网络与位移场逼近神经网络相结合，来实现拓扑优化。研究表明，这种直接集成方法能够获得与传统拓扑优化技术相当的结果，且额外具备与后处理软件无缝集成的优势，并在网格划分及有限元分析（FEA）代价高昂或不适用时，为以特定目标为驱动的拓扑优化提供可能。我们的方法（DMF-TONN）以边界条件和域坐标为输入，寻找最优密度场以最小化柔度与体积分数约束违反的损失函数。其无网格特性源于一种物理信息驱动的位移场逼近神经网络，该网络用于求解线弹性偏微分方程，并替代传统用于计算柔度的有限元分析。我们证明，采用合适的傅里叶特征神经网络架构与超参数后，密度场逼近神经网络能通过直接反向传播经由位移场逼近神经网络的损失梯度，学习权重以表征给定域和边界条件下的最优密度场；且与先前工作不同，本方法无需灵敏度滤波器、最优准则法或每次拓扑优化迭代中单独训练密度网络。