AI 中文总结
该研究针对高分辨率CFD模拟成本过高的问题，提出AI驱动的CFD工作流，采用MLP与POD-SINDy分别处理标量响应与降阶动力学，通过横流喷流示例验证了方法的有效性与适用场景。
AI 中文摘要
高分辨率计算流体动力学（CFD）模拟对设计至关重要，但对于密集设计空间采样而言成本过高。本章提出一种AI驱动的CFD工作流，结合标量响应建模与降阶动力学，以横流喷流为示例。首先采用反应型氢气横流喷流研究训练多层感知器（MLP），实现喷射器间距到未燃氢通量、壁面传热及整体温度浓度的映射，以保形插值为基线。CFD样本显示间距响应呈非单调特性，MLP识别出8倍喷管直径附近的中宽有利区域。留一法样本验证显示结果对预测量存在强依赖性：整体温度浓度预测稳健，而传热与未燃氢通量预测难度显著更高。随后采用稀疏非线性动力学识别（SINDy）作为场导出雷诺应力统计量的降阶建模框架。参数化SINDy模型可在模拟及样本外间距下提供紧凑的场级预测，不过因部分工况性能下降，其间距平均雷诺应力误差比POD基重构高6.7%。更广泛的结论是，AI驱动CFD并非单一模型方案：MLP对快速标量响应有效，而POD-SINDy更适用于瞬态降阶动力学及场导出统计量为核心的问题。
英文摘要
Highly resolved computational fluid dynamics (CFD) simulations are essential for design but too expensive for dense design-space sampling. This chapter presents an AI-driven CFD workflow that combines scalar-response modeling and reduced-order dynamics using jet-in-cross-flow examples. A reacting hydrogen jet-in-cross-flow study is first used to train a multilayer perceptron (MLP) mapping injector spacing to unburnt hydrogen throughput, wall heat transfer, and bulk temperature concentration, with shape-preserving interpolation as a baseline. The CFD samples show a non-monotonic spacing response, and the MLP identifies an intermediate-to-wide favorable region near eight jet diameters. Leave-one-sample-out validation shows strong dependence on the predicted quantity: the bulk temperature concentration is robust, while heat transfer and unburnt hydrogen throughput are substantially harder to predict. Sparse Identification of Nonlinear Dynamics (SINDy) is then used as a reduced-order modeling framework for field-derived Reynolds-stress statistics. The parametric SINDy model provides compact field-level predictions at simulated and out-of-sample spacings, though its aggregate spacing-mean Reynolds-stress error is $6.7\%$ higher than the POD-basis reconstruction because of degradation at selected cases. The broader conclusion is that AI-driven CFD is not a single-model prescription: MLPs are effective for fast scalar responses, while POD--SINDy is better suited when transient reduced dynamics and field-derived statistics are central to the question.
Comments18 pages, 4 figures. Book chapter manuscript. Companion Python/JAX software available at https://github.com/KjayJunIOR/parametric-sindy-jax-gridsearch
