# BiLoGo

In sheet-forming simulation, Transformer-based neural operators move information efficiently across the mesh but tend to smooth the localised thinning near deep-drawn corners and reinforcing ribs, the regions that often decide whether a part can be formed. BiLoGo couples local node–element message passing on a bipartite graph with a dual-stream Transformer neural operator, compressing the blank state and the tool contact into separate tokens and keeping local features through gated fusion. On a ribbed hot-stamping case, BiLoGo-U raises the thinning smoothing index near the ribs from 0.41–0.56 for Transformer-based operators to 0.94, and cuts mean positional error by 8.3% relative to the most accurate hierarchical graph network, CAtt-BiUGNN.

In sheet-forming simulation, Transformer-based neural operators move information efficiently across the mesh but tend to smooth the localised thinning near deep-drawn corners and reinforcing ribs, the regions that often decide whether a part can be formed. BiLoGo couples local node–element message passing on a bipartite graph with a dual-stream Transformer neural operator, compressing the blank state and the tool contact into separate tokens and keeping local features through gated fusion. On a ribbed hot-stamping case, BiLoGo-U raises the thinning smoothing index near the ribs from 0.41–0.56 for Transformer-based operators to 0.94, and cuts mean positional error by 8.3% relative to the most accurate hierarchical graph network, CAtt-BiUGNN.