Shape‐optimization of extrusion‐dies via parameterized physics‐informed neural networks

Abstract

In this paper, we present an approach to efficiently optimize the design of extrusion dies. Extrusion dies, which are relevant to the manufacturing process of plastics profile extrusion, traditionally require time‐consuming iterations between manual testing and die adjustments. As an alternative, numerical optimization can be used to obtain a high quality initial design and thereby reduce the number of adjustments to the actual die. However, numerical optimization can be computationally expensive, so the use of surrogate models can be helpful to improve efficiency. The latter is the goal of this work. Our method uses physics‐informed neural networks (PINNs) that directly incorporate a free‐form deformation (FFD) approach to allow for geometric variations. The FFD approach allows for a wide range of domain deformations, while the fully trained PINN ensures fast evaluation of the objective function. Using a two‐dimensional model of an extrusion die for demonstration, we detail the integration of the FFD method into the PINN model and discuss its potential in the three‐dimensional context.

A model hierarchy for predicting the flow in stirred tanks with physics-informed neural networks

“…Since the seminal paper of Raissi et al (2019) [31], PINNs have been successfully applied to problems across diverse domains, including solid mechanics [24,13,34], molecular dynamics [15], chemical reaction kinetics [2], the wave equation [28], hemodynamics [21,38,32], cardiac activation mapping [35], and various other fields [7]. Furthermore, PINNs have been applied to address numerous problems in fluid mechanics [19,6,18,40,12,47]. Notably, they have been employed to reconstruct the 3D wake flow past a cylinder using data from a few cross-planes [5] or as closure for Reynolds-Averaged Navier-Stokes (RANS) equations [11].…”