Implicit Neural Representations of Sheet Stamping Geometries with Small-Scale Features

Abstract

Geometric deep learning models, like Convolutional Neural Networks (CNNs), show promise as surrogate models for predicting sheet stamping manufacturability but lack design variables essential for inverse problems like geometric optimisation. Recent developments in deep learning have enabled geometry generation from compact latent spaces that are suitable for optimisation. However, current methods do not accurately model small-scale geometric features that are crucial for stamping performance. This study proposes a new deep learning-based method to address this limitation and generate detailed stamping geometries for optimisation. Specifically, neural networks are trained to generate Signed Distance Fields (SDFs) for stamping geometries, where the zero-level-set of each SDF implicitly represents the generated geometry. A new training approach is proposed for generating SDFs of stamping geometries, which involves supervising geometric properties of the SDFs. A novel loss function is introduced that directly acts on the zero-level-set and places high emphasis on learning small-scale features. This approach is compared with the state-of-the-art approach DeepSDF by Park et al. (2019), which explicitly supervises SDF values using ground truth data. The geometry generation performance of networks trained using both approaches is evaluated quantitatively and qualitatively. The results demonstrate significantly greater geometric accuracy with the proposed approach, which can faithfully generate small-scale features. Further analysis of the new approach reveals an organised learned latent space and varying the network input generates high-quality geometries from this space. By integrating with CNN-based manufacturability surrogate models by Attar et al. (2021), this work could enable the first-ever manufacturability-constrained optimisation of arbitrary sheet stamping geometries, potentially reducing geometry design time and cost.