We study the 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来研究SIMP方法,将坐标作为输入。在宽度的宽度范围内,我们显示DNNs的使用产生过滤效应,类似于SIMP的传统过滤技术,过滤器由神经唐氏中枢(NTK)描述。然而,这个过滤器在翻译中并不是无差别的,导致视觉文物和非最佳形状。我们建议嵌入两个输入坐标,导致NTK和过滤器的空间(近似)变异。我们从经验上确认了我们的理论观察和研究,以及过滤器大小如何受到网络结构的影响。我们的解决办法可以很容易地应用于其他基于坐标生成的方法。