用神经网络求解核聚变中的平衡方程，验证其可靠性。
Evaluation and Verification of Physics-Informed Neural Models of the Grad-Shafranov Equation
- 将边界条件作为输入，训练可泛化到多种情况的物理信息神经网络。
- 相比傅里叶神经算子，该网络在精度和推理速度上表现更优。
- 首次对这类网络开展形式化验证，适合核聚变仿真与可信AI研究者。
我们的研究源于核聚变反应堆依赖磁流体动力学（MHD）平衡稳定运行的需求，其中等离子体压强与约束磁场需保持平衡。在轴对称托卡马克装置中，假设环向对称性下，该平衡可通过广义-沙弗兰方程（Grad-Shafranov Equation, GSE）数学建模。近期工作表明物理信息神经网络（PINNs）可用于建模GSE。但现有研究未考察单一网络在多种边界条件下的泛化能力。为此，我们评估了一种将边界点作为输入的PINN架构，并与傅里叶神经算子（FNO）模型在精度和推理速度上进行比较。结果表明，该PINN模型性能最优且准确。我们进一步使用网络验证工具Marabou执行多项验证任务。尽管在PyTorch原生评估与Marabou验证间存在部分差异，仍成功构建了实用的验证流程。本研究是首次对这类网络开展验证的探索。
原文摘要 · Abstract (English)
Our contributions are motivated by fusion reactors that rely on maintaining magnetohydrodynamic (MHD) equilibrium, where the balance between plasma pressure and confining magnetic fields is required for stable operation. In axisymmetric tokamak reactors in particular, and under the assumption of toroidal symmetry, this equilibrium can be mathematically modelled using the Grad-Shafranov Equation (GSE). Recent works have demonstrated the potential of using Physics-Informed Neural Networks (PINNs) to model the GSE. Existing studies did not examine realistic scenarios in which a single network generalizes to a variety of boundary conditions. Addressing that limitation, we evaluate a PINN architecture that incorporates boundary points as network inputs. Additionally, we compare PINN model accuracy and inference speeds with a Fourier Neural Operator (FNO) model. Finding the PINN model to be the most performant, and accurate in our setting, we use the network verification tool Marabou to perform a range of verification tasks. Although we find some discrepancies between evaluations of the networks natively in PyTorch, compared to via Marabou, we are able to demonstrate useful and practical verification workflows. Our study is the first investigation of verification of such networks.
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