We study the Solid Isotropic Material Penalisation (SIMP) method with a density field generated by a fully-connected neural network, taking the coordinates as inputs. In the large width limit, we show that the use of DNNs leads to a filtering effect similar to traditional filtering techniques for SIMP, with a filter described by the Neural Tangent Kernel (NTK). This filter is however not invariant under translation, leading to visual artifacts and non-optimal shapes. We propose two embeddings of the input coordinates, which lead to (approximate) spatial invariance of the NTK and of the filter. We empirically confirm our theoretical observations and study how the filter size is affected by the architecture of the network. Our solution can easily be applied to any other coordinates-based generation method.

翻译：我们用一个完全连接的神经网络生成的密度字段,以坐标作为输入。在宽度的宽度范围内,我们显示使用DNN可产生类似于SIMP传统过滤技术的过滤效应,过滤器由神经中肯内尔(NTK)描述。然而,这个过滤器在翻译中不是无差异的,导致视觉文物和非最佳形状。我们建议两个输入坐标嵌入两个嵌入点,导致NTK和过滤器的空间(近似)变异。我们从经验上确认我们的理论观察和研究如何影响过滤器的大小受到网络结构的影响。我们的解决方案可以很容易地应用于其他基于坐标的生成方法。