Data-efficient surrogate modeling using Laplace-Beltrami shape-features: a case study on a cup drawing process

Process control and optimization are important aspects of manufacturing processes. Surrogate models, i.e. data driven models obtained from numerical simulations, are often employed to predict the process outcome for given process parameters in real time. In this work, we investigate a Laplace-Beltrami shape-feature approach for constructing a surrogate model for cup drawing process simulations. The resulting surrogate model captures local changes in deformations and field quantities on mesh geometries more accurately than standard methods. However, comparing mesh distortions, especially local mesh qualities, is challenging. To address this, we introduce a measure of improvement of mesh distortion to analyse the obtained error distributions. We demonstrate the benefits of the proposed method in contrast to variance-based methods such as principal component analysis, which do not adequately model local variations.