A Dual-Head ANN Architecture for Multi-objective Thermal Optimization of MHD Nanofluid Flow within a Wavy Enclosure

This study examines magnetohydrodynamic natural convection of a Cu–H₂O nanofluid inside a wavy undulating cavity and develops an artificial neural network-based dual-task learning framework for predictive heat-transfer modeling and regime classification. To analyze the coupled impacts of Rayleigh number, nanoparticle volume concentration, and wavy shape of cavity on flow motion and convection heat in the present work, a numerical simulation model is used. An ANN is trained to predict the average Nusselt number along the flat plate from the simulation dataset, and then classification of thermal regimes is performed into Low, Medium and High types using a quantile-based discretization method. The regression ANN has a high predictive accuracy, showing good correlation between the values of the simulated mean Nusselt number and R² is 0.9878. The residuals of the model are well-distributed, and its generalization to test samples is stable. Moreover, the classification ANN also achievesgood regime identification with accuracy 0.97, supported by consistent 5-fold cross-validation results and clear inter-class separation in latent-space feature projections. Overall, the integration of CFD-based simulation with ANN-driven regression and classification provides a computationally efficient surrogate modeling framework for rapid heat-transfer estimation andintelligent thermal regime mapping in complex enclosure geometries.本研究针对波浪起伏腔体内的铜-水纳米流体（Cu–H₂O nanofluid）磁流体自然对流问题展开系统分析，并构建了基于人工神经网络（artificial neural network, ANN）的双任务学习框架，用于传热预测建模与流态分类。为探究瑞利数（Rayleigh number）、纳米颗粒体积浓度以及腔体波浪形状对流动与对流换热的耦合影响，本研究采用数值模拟模型开展相关分析。研究基于模拟数据集训练人工神经网络，以预测平板表面的平均努塞尔数（average Nusselt number），并通过基于分位数的离散化方法将热流态划分为低、中、高三类。该回归人工神经网络预测精度优异，模拟平均努塞尔数与预测值的决定系数（R²）可达0.9878，二者呈现出极强的相关性。模型残差分布均匀，对测试样本的泛化性能稳定。此外，分类人工神经网络同样实现了出色的流态识别效果，识别精度达0.97，该结果得到了一致性五折交叉验证（5-fold cross-validation）结果的支撑，且在隐空间特征投影中呈现出清晰的类间分离效果。总体而言，将基于计算流体动力学（Computational Fluid Dynamics, CFD）的数值模拟与人工神经网络驱动的回归、分类任务相结合，可为复杂封闭几何结构中的快速传热估算与智能热流态映射提供高效的替代建模框架。