Recent advances in implicit neural representations show great promise when it comes to generating numerical solutions to partial differential equations. Compared to conventional alternatives, such representations employ parameterized neural networks to define, in a mesh-free manner, signals that are highly-detailed, continuous, and fully differentiable. In this work, we present a novel machine learning approach for topology optimization -- an important class of inverse problems with high-dimensional parameter spaces and highly nonlinear objective landscapes. To effectively leverage neural representations in the context of mesh-free topology optimization, we use multilayer perceptrons to parameterize both density and displacement fields. Our experiments indicate that our method is highly competitive for minimizing structural compliance objectives, and it enables self-supervised learning of continuous solution spaces for topology optimization problems.

翻译：最近隐含神经表征的进展在为局部差异方程式提供数字解决方案方面显示了巨大的希望。 与常规替代品相比,这种表征采用参数化神经网络,以无网状方式界定高度详细、连续和完全不同的信号。 在这项工作中,我们提出了一种新型的地形优化机器学习方法 -- -- 高维参数空间和高度非线性客观景观存在的一个重要反向问题。 为了在无网状表层优化背景下有效地利用神经表征,我们使用多层透视器对密度和迁移场进行参数化。 我们的实验表明,我们的方法在尽量减少结构性合规目标方面具有高度竞争力,并且能够自我监督地学习持续解决地形优化问题的空间。