{"slug": "transferability-of-learned-states-in-neural-pde-solvers", "title": "Transferability of Learned States in Neural PDE Solvers", "summary": "A literature audit of 12 papers produced 18 version-specific protocol records showing that reuse in neural PDE solvers cannot be judged by final accuracy alone, according to an arXiv paper (2610.10972v1). Across 240 source-training trajectories spanning two linear PDE families, Fourier neural operators and convolutional networks, a fixed predictor's benefit reversed across correction algorithms, and work-based selection saved 2.50-3.33 conjugate-gradient iterations on held-out in-distribution tasks. Independent batches confirmed a 0.73 percent complete online saving for one physics-trained Fourier neural operator against zero-initialized Poisson-preconditioned CG.", "body_md": "arXiv:2610.10972v1 Announce Type: new \nAbstract: 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.", "url": "https://wpnews.pro/news/transferability-of-learned-states-in-neural-pde-solvers", "canonical_source": "https://www.machinebrief.com/news/transferability-of-learned-states-in-neural-pde-solvers-x46k", "published_at": "2026-10-09 04:00:00+00:00", "updated_at": "2026-10-09 04:46:47.546997+00:00", "lang": "en", "topics": ["machine-learning", "ai-research", "neural-networks"], "entities": ["arXiv", "Fourier neural operators", "conjugate-gradient", "Poisson-preconditioned CG"], "also_reported_by": [], "alternates": {"html": "https://wpnews.pro/news/transferability-of-learned-states-in-neural-pde-solvers", "markdown": "https://wpnews.pro/news/transferability-of-learned-states-in-neural-pde-solvers.md", "text": "https://wpnews.pro/news/transferability-of-learned-states-in-neural-pde-solvers.txt", "jsonld": "https://wpnews.pro/news/transferability-of-learned-states-in-neural-pde-solvers.jsonld"}}