Operator learning with point-set local transformer

Scaling neural operators to high-resolution physical fields on irregular geometries requires efficient processing of large point sets. We introduce the Point-Set Local Transformer (PLT), which combines quadrature-weighted local attention with sampled global communication to capture both local structure and long-range dependencies – without dense point-to-point attention. Its separation of source processing and query decoding enables memory-efficient prediction at independently specified output locations. We evaluate PLT on several benchmarks, including HiLiftAeroML, where full-field aircraft predictions cover 126–151 million native surface points. PLT provides accurate full-field predictions for high-lift aircraft configurations, achieving a 6.47% mean relative error in the pre-stall benchmark. On the Plasticity benchmark, PLT achieves the lowest prediction error among all considered methods, improving the state-of-the-art by 41.46%. On the SuperWing benchmark, PLT achieves a 2.91% mean relative error for the surface pressure coefficient, while chunked full-field inference reduces peak memory by 45.6%. In scaling tests, PLT supports training with 4.19 million input points using 41.4 GiB on a single GPU and achieves the lowest peak memory among the evaluated implementations. These results demonstrate accurate physical-field prediction and memory-efficient evaluation of PLT at industrial resolution.