Transformer neural operators stop flattening local thinning: BiLoGo lifts the rib-region smoothing index from 0.41–0.56 to 0.94
Synopsis
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.
Interpretation
BiLoGo lets a Transformer-based learned simulator for forming keep long-range information exchange without flattening the localised thinning near corners and reinforcing ribs. Earlier Transformer-based neural operators compressed the mesh into a few tokens for global interaction, which smoothed localised responses; on the ribbed case these operators reached a thinning smoothing index of only 0.41–0.56, so the predicted local variation was about half that of the finite-element result. Across the Dome, Corner and Corner+Rib cases, BiLoGo gave lower positional errors than single-level graph models, hierarchical graph models and Transformer-based neural operators; near the ribs the smoothing index was 0.87 for BiLoGo-T and 0.94 for BiLoGo-U. Its threshold-based thinning error was lowest on Corner and Corner+Rib, but on Dome CAtt-BiGNN reached 0.377% against 0.396% for BiLoGo-T, which disagrees with the abstract and conclusion statement that it is lowest on all three cases.
The model first passes messages locally on a node–element bipartite graph, then sends blank deformation and tool contact into the global module as separate streams, and finally fuses the global update with local features per entity through a gate. A bidirectional node–element GraphSAGE exchanges information along finite-element connectivity, keeping nodes and elements as separate entities so thinning is predicted on elements without interpolation; the dual-stream design keeps the relatively localised contact information from being averaged with the state of the whole blank. On the Corner+Rib case, removing the dual stream raised positional error by 7.9% and threshold-based thinning error by 20.7%; removing gated fusion raised positional error by 15.0% and thinning error by 13.0%; with any one component removed, BiLoGo-U no longer beat CAtt-BiUGNN on positional and threshold-based thinning errors.
Perspective
The evaluation covers the Dome cold-forming case, the Corner hot-stamping case and the new Corner+Rib hot-stamping case; within each dataset all simulations share one mesh topology, and material, friction coefficient, blank-holder force and stamping speed are fixed.
Thinning is treated as dominated by membrane deformation, supported on Corner+Rib by a correlation coefficient of 0.9993 between area-change thinning and the finite-element thinning; this may not hold when bending has a larger effect on thinning. Temperature and stress state are not inputs, so their influence appears only implicitly through the training data, and the model uses thinning as the formability indicator without predicting strain path or the material forming limit.