Local and Sparse Kernel Operator Learning for Incompressible Flows: An Operator Lagrange Formulation

Key points

• It builds on our earlier property-preserving kernel method, whose global output reconstruction and dense operator regression scale poorly.1
• Our method replaces the global output reconstruction by local divergence-free interpolants with divergence-free polynomials of any degree, solved in parallel on the GPU.1
• A compactly supported kernel, positive semidefinite in any input dimension, makes the operator regression sparse.1
• We show that, unlike direct evaluation, Lagrange evaluation does not amplify solve errors by the cancellation among spatial coefficients.1

Sources (1)

• [1]Local and Sparse Kernel Operator Learning for Incompressible Flows: An Operator Lagrange Formulation
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 21, 12:20 AM

  We present a local and sparse kernel method for learning the solution operators of incompressible flows.

  It builds on our earlier property-preserving kernel method, whose global output reconstruction and dense operator regression scale poorly.

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