发表机构
Plasma Science and Fusion Center, Massachusetts Institute of Technology; Computing and Mathematical Sciences, California Institute of Technology; Department of Mechanical, Aerospace, and Nuclear Engineering, Rensselaer Polytechnic Institute; Princeton Plasma Physics Laboratory（麻省理工学院等离子体科学与聚变中心; 加州理工学院计算与数学科学系; 伦斯勒理工学院机械、航空航天与核工程系; 普林斯顿等离子体物理实验室）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出方程重构方法，将参数化偏微分方程的算子学习转化为规范算子学习，实现新参数域零样本预测，在托卡马克模拟中统一多装置数据，为可复用神经PDE求解器提供新路径。
AI 中文摘要
在广泛参数范围内学习解算子需要覆盖大量输入函数和物理参数，尤其是纯数据驱动的参数化模型，且所得模型可能在训练分布之外失效。本文提出方程重构（equation recast），将参数化算子学习重构为单个规范算子的学习，从控制方程解析推导参数诱导的算子变化并将其吸收为有效源，实现对新参数 regime 的零样本预测。在多参数、非线性、奇异偏微分方程场景中，方程重构支持外推，以共享规范表示整合稀疏异构数据集，并将收敛损失作为重构迭代失效的内部警告信号。在核聚变的高保真托卡马克模拟中，该框架通过联合训练算子内的规范域映射，统一了四种装置几何结构下的电子温度数据。方程重构为可复用的神经偏微分方程求解器提供了路径，该求解器结合了方程引导的迁移、数据效率和可监控的推理。
英文摘要
Learning solution operators across broad parameter ranges can require substantial coverage of both input functions and physical parameters, particularly for purely data-driven parametric models. In addition, the resulting models may fail silently outside the training distribution. We introduce equation recast, which reformulates parametric operator learning as the learning of a single canonical operator. Parameter-induced operator variations are derived analytically from the governing equation and absorbed into effective sources, enabling zero-shot prediction across new parameter regimes. Across multi-parameter, nonlinear, and singular PDE settings, equation recast supports extrapolation, integrates sparse heterogeneous datasets in a shared canonical representation, and uses loss of convergence as an internal warning signal for failure of the recast iteration. In high-fidelity tokamak simulations for nuclear fusion, the framework unifies electron-temperature data across four device geometries through canonical-domain mapping within one jointly trained operator. Equation recast provides a route toward reusable neural PDE solvers combining equation-guided transfer, data efficiency, and monitorable inference.
