Denoising Diffusion Model With Pixel‐Adaptive Convolutions for Sheet Metal Forming Analysis

ABSTRACT Traditional tool development processes in mechanical forming, especially for pressing tools, are often limited by time‐consuming trial‐and‐error cycles, which rely heavily on expert knowledge. These cycles can create bottlenecks and increase costs. Machine learning can be a useful tool to greatly speed up these processes by using advanced models. In this regard, previous research proposed and employed a denoising diffusion model (DDM) to inversely model effective tool surfaces from final product geometries. This model leverages spatial and temporal attention mechanisms to enhance its predictive capabilities. While DDM achieved commendable overall predictions, the accuracy in reconstructing individual denoised frames during later forming steps was lacking. To address this, the present research adopts a stepwise strategy focused on the late deformation state in forming simulations. The research utilizes pixel‐adaptive convolutional neural networks (PAC) to predict high‐resolution simulation output of various channels incorporated in DDM from coarse‐mesh results, using the final part geometry as high‐resolution guidance. This approach enables efficient and reliable estimation of these high‐resolution distributions for the late deformation stage, reducing reliance on computationally intensive full‐resolution simulations at this critical point. This work demonstrates the effectiveness of PAC for simulation refinement in late‐stage deformation and lays the foundation for future integration of PAC into the DDM framework, thereby contributing to ongoing efforts toward more efficient, data‐driven approaches in industrial tool design and manufacturing.