Rapid AI-surrogate-based die shape compensation for Two-Point Incremental Sheet Forming

Explicit die-shape compensation for two-point incremental forming (TPIF) requires many forming-and-springback evaluations, each costing approximately 10.5 h with a high-fidelity LS-DYNA model, which makes direct FEM-in-the-loop optimization impractical. This paper replaces those evaluations with a differentiable coupled AI surrogate: a trajectory-aware Transformer Cross-Attention U-Net for forming and a U-Net for springback, trained on 4517 simulations generated by a reference model calibrated from material measurements and experimentally assessed against a 24-case TPIF campaign on DC04 sheet and optical 3D scans. Compensation is formulated as an inverse design problem in which the die correction is expressed in a reduced design space — uniform B-spline, adaptive RBF T-spline-like, or truncated hierarchical B-spline — and optimized directly through the surrogate, while the CAM toolpath is regenerated after every accepted die update so that the coupling between die shape, trajectory, forming, and springback is preserved. On two held-out freeform geometries, full-order verification of the optimized dies reduces the RMS shape error by 65% and 69%, and shrinks the fraction of the surface outside the prescribed tolerance band from 29.6% to 2.8% and from 17.7% to 0.1%, at an estimated evaluation-count-based computational cost ratio of 80 × – 1716 × .