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This paper presents a local and sparse kernel method for learning solution operators of incompressible flows, using divergence-free local interpolants and compactly supported kernels with Operator Lagrange weights to achieve sparse, GPU-parallel regression that outperforms neural operators on ten fluid benchmarks.
This paper proposes a minimal transverse-subspace representation that encodes a D-component divergence-free vector field as a D−1-component field, enabling end-to-end divergence-free operator learning without projection or auxiliary potentials, achieving lower error and greater robustness.