物理信息神经算子代理用于二维磁流体动力学重联
Physics-Informed Neural Operator Surrogate for 2D Magnetohydrodynamic Reconnection
- Indian Institute of Technology Bhilai（印度理工学院比莱分校）
- Plasma Science and Fusion Center, Massachusetts Institute of Technology（麻省理工学院等离子体科学与聚变中心）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出基于傅里叶神经算子的物理信息神经算子代理，用于二维磁流体动力学重联模拟，在宽Lundquist数范围内高精度预测状态，速度比直接数值模拟快两个数量级。
中文摘要 AI 辅助
磁重联的直接数值模拟受限于电阻磁流体动力学的尺度分离。在大的 Lundquist 数 $S$ 下，电流层厚度随 $S^{-1/2}$ 变薄，迫使使用精细网格和短时间步长，使得参数扫描代价高昂。深度学习神经算子通过学习函数空间之间的映射而非单个解，提供了一种替代方案，使得单个训练模型在推理成本下返回任意参数和时间的状态。我们开发了一个基于傅里叶神经算子（FNO）的物理信息神经算子（PINO）代理，用于壁面有界域中的二维可压缩、粘性、电阻重联。我们以初始状态、Lundquist 数和连续查询时间为条件。预测磁通函数使得 $\grad\\!\cdot\\!\bB=0$ 精确成立，直接时间查询消除了自回归误差累积，奇偶感知的谱微分与参考求解器的壁面处理相匹配。在 $10^{3}\le S\le2\times10^{5}$ 范围内训练，并保留两个值不参与训练，该代理恢复密度、压力和引导场的误差优于 $0.2\\%$，速度误差为 $3.2$ 至 $3.9\\%$，磁通函数误差为 $1.0\\%$，谱电流密度误差为 $7.5\\%$。它解析了薄而窄的电流片、Alfvén 喷流以及超出模式截断的谱分辨率。我们的代理在 $S=1.1\times10^{4}$ 范围内再现了层平均重联率，误差在 $3\\%$ 以内，恢复的重联时间指数为 $0.497$，与 Sweet-Parker 标度一致。当在 $2049^{2}$ 求解器网格上进行零样本查询时，完整轨迹运行在单个 GPU 上约为几秒，而 DNS 需要数小时，速度提升超过两个数量级，确立了学习算子作为在参数空间中调查重联的实用途径。
英文摘要
Direct numerical simulation of magnetic reconnection is limited by the scale separation of resistive magnetohydrodynamics. At large Lundquist numbers $S$ the current layer thins as $S^{-1/2}$, forcing fine grids and short time steps that make parameter scans prohibitively expensive. Deep learning neural operators offer an alternative by learning the map between function spaces rather than individual solutions, so that a single trained model returns the state for any parameter and time at inference cost. We have developed a Fourier Neural Operator (FNO) based Physics-Informed Neural Operator (PINO) surrogate for two-dimensional compressible, viscous, resistive reconnection in a wall bounded domain. We condition on the initial state, the Lundquist number, and a continuous query time. Predicting the magnetic flux function makes $\grad\!\cdot\!\bB=0$ exact, direct time queries remove autoregressive error accumulation, and parity-aware spectral differentiation matches the wall treatment of the reference solver. Trained across $10^{3}\le S\le2\times10^{5}$ with two values withheld, the surrogate recovers density, pressure, and guide field to better than $0.2\%$, velocity to $3.2$ to $3.9\%$, the flux function to $1.0\%$, and the spectral current density to $7.5\%$. It resolves the thin, narrow current sheet, Alfvénic jets, and spectral resolution beyond mode cutoff. Our surrogate reproduces the layer-averaged reconnection rate to within $3\%$ through $S=1.1\times10^{4}$, recovering a reconnection time exponent of $0.497$ consistent with Sweet-Parker scaling. When queried zero-shot on the $2049^{2}$ solver mesh, a full trajectory run is on the order of seconds on one GPU against several hours for the DNS, over two orders of magnitude faster, establishing learned operators as a practical route to surveying reconnection across parameter space.
