[
    {
        "id": "osp-16500",
        "type": "article-journal",
        "title": "Transferability of Learned States in Neural PDE Solvers",
        "author": [
            {
                "family": "Wang",
                "given": "Shunye"
            },
            {
                "family": "Wen",
                "given": "Haochen"
            },
            {
                "family": "Liu",
                "given": "Shuo Li"
            },
            {
                "family": "Wang",
                "given": "Xuanyi"
            },
            {
                "family": "Liu",
                "given": "Lihao"
            },
            {
                "family": "Deng",
                "given": "Zhongying"
            }
        ],
        "URL": "https://omanscience.com/en/articles/transferability-of-learned-states-in-neural-pde-solvers",
        "language": "en",
        "issued": {
            "date-parts": [
                [
                    2026
                ]
            ]
        },
        "abstract": "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 extracts 18 version-specific protocol records from 12 papers, documenting retained states, target-time resources, and reported controls. 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. Across 240 source-training trajectories, two linear PDE families, Fourier neural operators and convolutional networks, a fixed predictor's benefit reverses across correction algorithms. 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 saves 2.50-3.33 CG iterations on held-out in-distribution tasks; matched adaptation demonstrates finite-budget pretraining value. Independent batches confirm a 0.73 percent complete online saving for one physics-trained Fourier neural operator against zero-initialized Poisson-preconditioned CG. Reuse requires matched state comparisons and downstream computational evidence."
    }
]