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This paper treats subsampling as a source of bias in neural operator training: sampled meshes can distort boundary information, and the authors give four consistency conditions that can be checked before training. Their two modules, Boundary Quadrature Attention and Anchored Global State, are backbone-agnostic and are reported to reduce whole-mesh error on several benchmarks, though the gains are from the authors' own evaluations and need independent replication. For ML readers working on large-scale physics surrogates, the main takeaway is that how boundary data is aggregated and weighted during sampling can matter as much as the architecture.
SCANO: Restoring Boundary-Condition Completeness in Sampled Meshes with a Sliced-Cross-Attention Neural Operator for 3D Thermal Fields
arXiv:2611.04603v1 Announce Type: new Abstract: 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. We evaluate the approach on controlled and public benchmarks and a data-centre thermal simulation dataset (DCTS) containing million-cell meshes. On both benchmarks, BQA improves every backbone, reducing whole-mesh error up to 15-fold. On all three datasets, AGS aligns regional with whole-mesh predictions, cutting regional error at least tenfold for most backbones on the public benchmark. Together, the modules nearly halve the best original backbone's whole-mesh error on both benchmarks. SCANO predicts a room-scale field in under one second, over 100 times faster than whole-room anchor self-attention.
Abstract: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. We evaluate the approach on controlled and public benchmarks and a data-centre thermal simulation dataset (DCTS) containing million-cell meshes. On both benchmarks, BQA improves every backbone, reducing whole-mesh error up to 15-fold. On all three datasets, AGS aligns regional with whole-mesh predictions, cutting regional error at least tenfold for most backbones on the public benchmark. Together, the modules nearly halve the best original backbone's whole-mesh error on both benchmarks. SCANO predicts a room-scale field in under one second, over 100 times faster than whole-room anchor self-attention.
Machine Learning (cs.LG); Computational Physics (physics.comp-ph)
arXiv:2611.04603 [cs.LG]
(or arXiv:2611.04603v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2611.04603 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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