基于牛顿-克里洛夫校正的替代模型预测实现可靠且高效的稳态计算流体动力学
Reliable and efficient steady CFD from surrogate predictions through Newton-Krylov correction
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中文总结 AI 辅助
本研究提出求解器耦合的替代模型-牛顿框架，结合替代模型快速预测与牛顿-克里洛夫迭代高精度收敛，在OOD基准及实际翼型优化中提升稳态CFD的可靠性与效率，实现15.5倍生成级加速并可扩展至三维。
中文摘要 AI 辅助
神经替代模型为加速科学与工业中由偏微分方程控制的计算密集型模拟提供了有前景的途径，然而其实际应用受限于分布外（OOD）条件下的不可靠预测。我们开发了求解器耦合的替代模型-牛顿框架，该框架将替代模型预测作为牛顿-克里洛夫迭代的高质量初始猜测，从而结合快速全局流场预测与终端阶段的高精度数值收敛。在由实际跨音速翼型优化轨迹采样几何构成的OOD基准测试中，该框架将中位数残差L2比值降低了七个数量级以上，同时大幅减少了流场与气动误差。在实际超临界翼型优化中，它提升了在线预测可靠性，同时实现了比计算流体动力学（CFD）快15.5倍的生成级加速。我们进一步使用飞翼数据集测试了该框架向三维的扩展。这些研究共同证明了替代模型-牛顿耦合在工业工作流程中提供准确、高效且可扩展的稳态CFD的潜力。
英文摘要
Neural surrogates offer a promising route to accelerating computationally expensive simulations governed by partial differential equations across science and industry. Their practical deployment, however, is limited by unreliable predictions under out-of-distribution (OOD) conditions. We develop a solver-coupled surrogate-Newton framework that uses surrogate predictions as high-quality initial guesses for Newton-Krylov iterations, thereby combining rapid global flow-field prediction with high-accuracy numerical convergence at the terminal stage. On an OOD benchmark comprising geometries sampled from actual transonic airfoil optimization trajectories, the framework lowers the median residual L_2 ratio by over seven orders of magnitude while substantially reducing field and aerodynamic errors. In practical supercritical airfoil optimization, it improves online prediction reliability while achieving a 15.5-fold generation-level speedup over CFD. We further test the framework's extension to three dimensions using a flying-wing dataset. Together, these studies demonstrate the potential of surrogate-Newton coupling to deliver accurate, efficient and scalable steady CFD across industrial workflows.
