Transferability of Learned States in Neural PDE Solvers

Key points

• Our reuse contract separates solution accuracy, learning contribution, and numerical utility through paired state comparisons, matched target information and budgets, and cost accounting.1
• For a fixed linear system and residual tolerance, we construct two initial guesses with identical solution-error, energy-error, and residual norms, reaching the same solution with different conjugate-gradient (CG) iteration counts.1
• Across 240 source-training trajectories, two linear PDE families, Fourier neural operators and convolutional networks, a fixed predictor's benefit reverses across correction algorithms.1
• Independent batches confirm a 0.73 percent complete online saving for one physics-trained Fourier neural operator against zero-initialized Poisson-preconditioned CG.1

Sources (1)

• [1]Transferability of Learned States in Neural PDE Solvers
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 7, 10:49 PM

  Assessing useful reuse in neural PDE solvers is challenging: final accuracy can reflect source learning and target-time computation.

  Our reuse contract separates solution accuracy, learning contribution, and numerical utility through paired state comparisons, matched target information and budgets, and cost accounting.

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