In the field of material shaping, traditional manual methods and physical modeling can no longer meet the precision and efficiency requirements of modern manufacturing. To address these challenges, this paper introduces a novel neural network model that leverages an advanced attention mechanism derived from Transformer architectures. Specifically, the model—termed Smart Shaping with Adaptation Physically Excited Networks (SHAPE)—is designed to predict changes in material straightness and height at multiple shaping points for various materials to ensure high-quality shaping outcomes with minimal material waste. Considering the changes in the physical properties of materials during the processing, the complex implicit deformation relationships between multiple points of material data, and the long-distance feature dependencies, we have specifically modified the multi-head attention mechanism. Combined with the adaptive attention mechanism, this allows for identifying changes in straightness and height at multiple points during shaping. Convolutional layers are added to simulate physical diffusion deformation. Considering the inherent physical constraints on materials, we have also embedded Swift’s law, which describes material deformation, into the loss function. This ensures that the intelligent shaping network aligns more closely with the actual physical laws of materials during the prediction process. Potential rebound effects are also taken into account in the network. Experimental results show that the proposed model performs excellently across various evaluation metrics, significantly outperforming existing TG-DNN and LSTM networks. Ablation experiments demonstrate that the multi-head attention mechanism and integrating Swift’s law are critical to improving the model’s performance.