DRAFT-Solver: Dynamic spaRse Attention via node draFTing

Learning surrogate models for steady-state partial differential equations (PDEs) on large unstructured meshes represents a challenging task because relevant interactions may span the entire domain, while accurate predictions often require additional computation only in localized, task-dependent regions. Dense attention captures long-range dependencies but becomes impractical on large discretizations, whereas sparse and multiscale approaches commonly prescribe where fine-scale processing should occur using geometric or physical priors. To address these limitations, we introduce DRAFT-Solver (Dynamic spaRse Attention via node draFTing), a dual-scale architecture that learns its computational allocation directly from data. DRAFT-Solver combines global information exchange through softly constructed latent tokens with fine-grained self-attention over a learned, fixed-budget subset of nodes. Both token routing and node selection are trained end-to-end without predefined surface regions or manually specified masks. Across benchmarks spanning two- and three-dimensional aerodynamics, semiconductor-device simulation, and biomolecular electrostatics, DRAFT-Solver achieves competitive or improved performance relative to graph-, neural-operator-, and transformer-based baselines.