We present a novel application of neural networks to design improved mixing elements for single-screw extruders. Specifically, we propose to use neural networks in numerical shape optimization to parameterize geometries. Geometry parameterization is crucial in enabling efficient shape optimization as it allows for optimizing complex shapes using only a few design variables. Recent approaches often utilize CAD data in conjunction with spline-based methods where the spline's control points serve as design variables. Consequently, these approaches rely on the same design variables as specified by the human designer. While this choice is convenient, it either restricts the design to small modifications of given, initial design features - effectively prohibiting topological changes - or yields undesirably many design variables. In this work, we step away from CAD and spline-based approaches and construct an artificial, feature-dense yet low-dimensional optimization space using a generative neural network. Using the neural network for the geometry parameterization extends state-of-the-art methods in that the resulting design space is not restricted to user-prescribed modifications of certain basis shapes. Instead, within the same optimization space, we can interpolate between and explore seemingly unrelated designs. To show the performance of this new approach, we integrate the developed shape parameterization into our numerical design framework for dynamic mixing elements in plastics extrusion. Finally, we challenge the novel method in a competitive setting against current free-form deformation-based approaches and demonstrate the method's performance even at this early stage.

翻译：本文提出了一种新型神经网络应用，用于改进单螺杆挤出机中的混合元件设计。具体而言，我们建议在数值形状优化中使用神经网络对几何形状进行参数化。几何参数化对于实现高效形状优化至关重要，因为它允许仅使用少量设计变量来优化复杂形状。近期的方法通常将计算机辅助设计数据与基于样条的方法结合使用，其中样条的控制点作为设计变量。因此，这些方法依赖于人类设计师指定的相同设计变量。虽然这种选择很方便，但它要么将设计限制在给定初始设计特征的微小修改上——从而有效阻止拓扑变化——要么产生过多且不理想的设计变量。在本工作中，我们脱离了计算机辅助设计和基于样条的方法，利用生成式神经网络构建了一个人工的、特征密集但低维的优化空间。使用神经网络进行几何参数化扩展了现有技术，使得所生成的设计空间不再局限于用户对特定基础形状的预设修改。相反，在相同的优化空间内，我们可以插值并探索看似不相关的设计。为了展示这一新方法的性能，我们将所开发的形状参数化集成到塑料挤出中动态混合元件的数值设计框架中。最后，我们在竞争性环境中将新方法与当前基于自由变形的方法进行对比，并展示了该方法即使在此早期阶段也具备的优异性能。