Neural networks vs. splines: advances in numerical extruder design

Abstract

In this paper, we present a novel approach to geometry parameterization that we apply to the design of mixing elements for single-screw extruders. The approach uses neural networks of a specific architecture to automatically learn an appropriate parameterization. This stands in contrast to the so far common user-defined parameterizations. 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 computer-aided design (CAD) data in conjunction with spline-based methods where the spline’s control points serve as design variables. Consequently, these approaches rely on the design variables specified by the human designer. This approach results in a significant amount of manual tuning to define a suitable parameterization. In addition, despite this effort, many times the optimization space is often limited to shapes in close proximity to the initial shape. In particular, topological changes are usually not feasible. In this work, we propose a method that circumvents this dilemma by providing low-dimensional, yet flexible shape parametrization using a neural network, which is independent of any computational mesh or analysis methods. 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.