[论文] Error-Conditioned Neural Solvers

论文概要

研究领域: CV 作者: Haina Jiang, Liam Wang, Peng-Chen Chen 发布时间: 2026-06-27 arXiv: 2606.27354

中文摘要

神经替代模型通常将求解视为纯统计任务，难以纠正约束违反并在训练分布之外外推。我们提出误差条件神经求解器，通过理论分析和实验验证，展示了如何使神经求解器能够检测和纠正自身错误。

原文摘要

Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution. Recent hybrid methods promote physical correctness by targeting the PDE residual via gradient descent or Gauss--Newton steps, but inherit the compute cost and instability of the underlying classical optimizers. We show, theore...

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