Physics-guided Mamba network for real-time force prediction in Incremental Sheet Forming: A hybrid data-physics approach

Geometric accuracy control remains a critical bottleneck limiting the industrial application of Incremental Sheet Forming (ISF). Since forming force is a key governing variable for accuracy management, establishing a high-fidelity prediction model is a prerequisite for precision manufacturing. However, traditional analytical models often compromise fidelity due to simplified contact assumptions, while pure data-driven approaches struggle with generalization and physical inconsistency. To address this, this study proposes a Physics-Guided Mamba Hybrid Modeling Framework (PG-MHMF) that synergistically integrates a Physics-based Analytical Model (PAM) with a Mamba-based Residual Correction Network (MRCN). The PAM employs a unified contact envelope strategy to efficiently establish a mechanistic baseline, while the MRCN incorporates physics-augmented inputs into a selective state-space mechanism to accurately learn nonlinear residuals. Experimental validation on a rigorous generalization dataset confirms the framework's robustness, achieving an average Root Mean Square Error (RMSE) of 36.43 N and Mean Relative Error (MRE) of 6.19% across diverse materials and geometries. Furthermore, the framework demonstrates practical engineering utility by enabling the precise offline prediction of geometric deviations for complex non-axisymmetric structures, such as cranial prostheses. This work not only enhances prediction accuracy but also provides a data-physics collaborative paradigm for optimizing manufacturing quality.