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Teaching Old Preconditioners New Tricks: How GNNs Supercharge Linear Solvers

  • Large linear systems in computational science often use iterative solvers with preconditioners.
  • A novel approach using graph neural networks (GNNs) for preconditioner construction outperforms classical methods and neural network-based preconditioning.
  • The approach involves learning correction for well-established preconditioners from linear algebra with GNNs.
  • Extensive experiments demonstrate the superiority of the proposed approach and loss function over classical preconditioners.

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