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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.
The paper presents VIOT, a variational incompressible optimal transport operator that uses a Fourier Neural Operator to predict divergence-free velocity fields for efficient incompressible density transport, achieving orders of magnitude speedup over traditional optimization methods.