Physics-informed hybrid conditional diffusion transformer model for cutting force prediction under param-space optimization

Accurate cutting force prediction is critical for precision machining tasks such as deformation analysis and surface quality control. However, accurate cutting force prediction remains challenging due to the difficulty of jointly modeling fine-grained temporal dynamics and global statistical characteristics, the ineffective use of sparse and heterogeneous inputs (e.g., limited machining parameters), and the lack of robustness under small-sample conditions in highly complex machining processes. To address these issues, a physics-informed hybrid conditional Diffusion Transformer, termed PPS-PIHCDiT, is introduced. It features Physical Parameter Space optimization that refines the optimization landscape by incorporating a data-driven semi-empirical physical model, thereby grounding the physics-based constraints in real machining mechanics. Our method introduces three tightly aligned components: (1) a non-autoregressive diffusion architecture with time-block segmentation and historical statistical embedding, which enables balanced modeling of local temporal features and global distributional trends; (2) a hybrid embedding module that coherently integrates machining parameters and statistical context to provide rich conditional guidance; (3) a dual-constraint training framework that combines physics-informed residuals and MMD-based distributional regularization to enhance physical consistency and generalization under data scarcity. Moreover, the diffusion process naturally captures the intrinsic stochasticity of machining operations while avoiding error accumulation across time steps—offering advantages over deterministic or autoregressive alternatives. Evaluated on a real-world dataset from five-axis CNC precision machining of engine blades, PPS-PIHCDiT achieves state-of-the-art performance in prediction accuracy (RMSE = 0.015, MAE = 0.027) and temporal–distributional fidelity (= 98.84%, = 93.14%, etc.), significantly outperforming existing methods.