EntroMesh: Mechanics-Conditioned Structural Entropy for Multi-Solid Stamping

Learned simulation of multi-solid stamping requires long-range reasoning over irregular finite-element meshes, where load, contact, material transitions, and localized plasticity govern inter-element couplings. Hierarchical mesh simulators reduce graph diameters, yet their coarse-level meshes are commonly derived from topology, geometry, algebraic connectivity, or standalone learned scores. These static coarsening schemes ignore instantaneous, state-dependent mechanical couplings and introduce substantial prediction error for evolving physical states. We introduce EntroMesh, a mechanics-conditioned structural-entropy hierarchy for multi-solid mesh prediction. EntroMesh converts each finite-element state into a dimensionless weighted graph, strengthens edges that carry stiffness, load, boundary, and strain-energy evidence, weakens edges across large stress jumps, and constructs a fixed-budget coding tree for a coarse-to-fine V-cycle graph simulator. Our hierarchy is physically interpretable, state-causal, and enables fair comparison under identical node budgets. Evaluated on the two large-scale long-time Unisoma stamping benchmarks against the state-of-the-art Unisoma model, EntroMesh reduces the sum of six-field relative-$L_2$ prediction error from 65.08 to 62.62 on BilateralStamping and from 64.19 to 53.65 on UnilateralStamping. Experiments demonstrate that mechanics-aware structural entropy is an effective hierarchical prior for large-scale multi-solid learned stamping simulation.