发表机构
University of Ioannina; Democritus University of Thrace; Shandong University（伊奥安尼纳大学; 色雷斯德谟克利特大学; 山东大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出结合KAN架构、引导训练与自缩放Broyden优化的物理信息网络，高效求解固定边界Grad-Shafranov平衡并识别剖面参数。
AI 中文摘要
我们采用方程驱动、物理约束的深度学习来解决固定边界Grad-Shafranov（GS）平衡问题，构建具有托卡马克相关特征的轴对称磁流体动力学平衡。使用物理信息Kolmogorov-Arnold网络（KANs）构建跨越线性（Solov'ev）和非线性剖面函数的平衡，该网络在满足适当边界条件的同时近似GS解。还考虑了一个高度非线性的压力剖面，以重现高约束模式现象，如压力台基和显著的自举电流分量。为了实现高效收敛，采用了引导训练方案，具体为基于同伦的连续课程学习和通过预训练网络的迁移学习。虽然在标准多层感知器下采用无引导的物理信息训练来计算非线性平衡仍然是一项难以实现或计算效率低下的任务，但我们的框架克服了这一限制。具体来说，我们证明了三个关键要素的组合，即KAN架构、引导训练方案和自缩放Broyden优化方法，能够实现稳定、高效且准确的平衡计算，并在平衡约束下同时进行剖面参数识别。
英文摘要
We employ equation-driven, physics-constrained deep learning to solve the fixed-boundary Grad-Shafranov (GS) equilibrium problem, constructing axisymmetric magnetohydrodynamic equilibria with tokamak-relevant characteristics. Equilibria across linear (Solov'ev) and nonlinear profile functions are constructed using Physics-Informed Kolmogorov-Arnold Networks (KANs) that approximate GS solutions while satisfying appropriate boundary conditions. A highly nonlinear pressure profile recreating high-confinement mode phenomenology, such as pressure pedestals and significant bootstrap current components, is also considered. To enable efficient convergence, guided training schemes are employed, specifically homotopy-based continuation curriculum learning and transfer learning via pretrained networks. While computing nonlinear equilibria employing standard Multi-Layer Perceptrons under unguided physics-informed training remains an elusive or computationally inefficient task, our framework overcomes this limitation. Specifically, we demonstrate that the combination of three key elements, namely KAN architecture, guided training schemes, and the self-scaled Broyden optimization method, enables stable, efficient, and accurate equilibrium computation with simultaneous profile parameter identification in view of equilibrium constraints.
