SCANO: Restoring Boundary-Condition Completeness in Sampled Meshes with a Sliced-Cross-Attention Neural Operator for 3D Thermal Fields

Tianyu Li, Zhiwei Cao, Qingang Zhang, Ruihang Wang, Binyang Song +1

Training neural operators on million-cell meshes can exceed GPU memory limits. Models are therefore trained on subsamples and deployed on whole meshes or selected regions. However, subsampling can distort boundary information, degrading accuracy. We ask when boundary conditioning under sampling stays consistent with whole-mesh training, and how to aggregate and inject boundary data. Representing the solution as an integral of boundary data against type-dependent measures, we show that subsampling distorts this conditioning in three ways: incomplete boundary coverage or a sample-dependent global state, face weighting by count rather than area, and compression of boundary inputs into a low-dimensional vector. This analysis yields four measurable consistency conditions checkable before training. We satisfy them with two backbone-agnostic modules. Boundary Quadrature Attention (BQA) aggregates all boundary faces, typed and area-weighted, into slice tokens that every query point reads at every layer. Anchored Global State (AGS) estimates the global state from anchors independent of the sampled points. Adding both to a scalable message-passing and slice-attention backbone yields SCANO.…