SAGE-PINN：用于柱坐标轴对称多物理场流动的无奇异性轴对称几何编码物理信息神经网络
SAGE-PINN: A Singularity-free Axisymmetric Geometry-Encoded Physics-Informed Neural Network for Axisymmetric Multiphysics Flow in Cylindrical Coordinates
- Indian Institute of Technology Mandi（曼迪印度理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
提出SAGE-PINN，通过变量替换和流函数表示消除轴对称柱坐标奇异性，无需标记数据即可模拟多物理场流动，在狭窄动脉纳米流体流动中验证，速度和温度误差分别低于1.6%和9.1%。
AI中文摘要：
物理信息神经网络（PINNs）为多物理场建模提供了无网格框架，然而轴对称柱坐标下的流体流动在很大程度上仍未得到探索，因为控制算子在轴线上存在奇异性，且动量与能量通过平流和浮力强耦合。我们针对此类问题提出了SAGE-PINN，一种无奇异性轴对称几何编码物理信息神经网络。SAGE-PINN通过构造消除坐标奇异性：保持奇偶性的变量$s=r^2$和修正的流函数表示从训练残差中消除了显式的$1/r$项，并恒等地满足质量守恒。边界拟合的解析拟设精确施加边界条件，而分阶段的动量-热-联合训练、残差归一化、Péclet数和Richardson数延拓以及物理尺度漂移防护稳定了耦合优化。该框架无需标记数据，仅使用物理和边界约束进行训练，其预测结果与通过狭窄动脉的稳态纳米流体流动和传热的有限元参考解进行了验证，覆盖广泛的流动和热状态，无需针对特定案例调整。质量守恒保持在单精度舍入误差水平，在中心工作范围内，轴向速度和温度的相对$L_2$误差分别小于$1.6\%$和$9.1\%$。主要退化仅发生在强浮力影响的慢流动和高度平流主导的传热等极限状态。将柱坐标几何、守恒结构和边界物理直接嵌入网络，为轴对称多物理场流动的PINN模拟提供了一条稳健的途径。
英文摘要：
Physics-informed neural networks (PINNs) provide a mesh-free framework for multiphysics modeling, yet fluid flow in axisymmetric cylindrical coordinates remains largely unexplored because the governing operators are singular at the axis and momentum and energy are strongly coupled through advection and buoyancy. We introduce SAGE-PINN, a Singularity-free Axisymmetric Geometry-Encoded Physics-Informed Neural Network for this class of problems. SAGE-PINN removes the coordinate singularity by construction: the parity-preserving variable $s=r^2$ and a modified stream-function representation eliminate explicit $1/r$ terms from the trained residuals and satisfy mass conservation identically. Boundary-fitted analytical ansätze enforce the boundary conditions exactly, while staged momentum-thermal-joint training, residual normalization, Péclet- and Richardson-number continuation, and a physics-scaled drift guard stabilize the coupled optimization. The framework is trained without labelled data, using only physics and boundary constraints, and its predictions are validated against finite-element reference solutions for steady nanofluid flow and heat transfer through a stenosed artery over a wide range of flow and thermal regimes, without case-specific tuning. Mass conservation remains at single-precision round-off, and over the central operating range the axial velocity and temperature are reproduced within $1.6\%$ and $9.1\%$ relative $L_2$ error, respectively. The main deterioration occurs only in the limiting regimes of strongly buoyancy-influenced slow flow and highly advection-dominated heat transfer. Embedding cylindrical geometry, conservation structure, and boundary physics directly into the network provides a robust route to PINN simulation of axisymmetric multiphysics flows.
