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.
A literature audit
A literature audit extracts 18 version-specific protocol records from 12 papers, documenting retained states, target-time resources, and reported controls.
Initial guesses and convergence
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.
Source-training trajectories
Across 240 source-training trajectories, two linear PDE families, Fourier neural operators and convolutional networks, a fixed predictor's benefit reverses across correction algorithms.
Relative prediction errors
Among pairs with both relative prediction errors less than or equal to 5 percent on 64 in-distribution tasks (63 by 63 interior grids), reductions in all three norms accompany more CG iterations, at mean taskwise rates of 23.5 percent and 23.9 percent in two libraries.
Work-based selection and matched adaptation
Work-based selection saves 2.50-3.33 CG iterations on held-out in-distribution tasks; matched adaptation demonstrates finite-budget pretraining value.
Independent batches and online saving
Independent batches confirm a 0.73 percent complete online saving for one physics-trained Fourier neural operator against zero-initialized Poisson-preconditioned CG.
Reuse requirements
Reuse requires matched state comparisons and downstream computational evidence.