This study presents a geometric deep learning framework for predicting cold spray particle impact responses using finite element simulation data. A parametric dataset was generated through automated Abaqus simulations spanning a systematic range of particle velocity, particle temperature, and friction coefficient, yielding five output targets including maximum equivalent plastic strain, average contact plastic strain, maximum temperature, maximum von Mises stress, and deformation ratio. Four novel algorithms i.e. a GraphSAGE-style inductive graph neural network, a Chebyshev spectral graph convolution network, a topological data analysis augmented multilayer perceptron, and a geometric attention network were implemented and evaluated. Each input sample was treated as a node in a k-nearest-neighbour feature-space graph, enabling the models to exploit spatial similarity between process conditions during training. Three-dimensional feature space visualisations and two-dimensional contour projections confirmed the highly non-linear and velocity-dominated nature of the input-output relationships. Quantitative evaluation demonstrated that GraphSAGE and GAT consistently achieved R-square values exceeding 0.93 across most targets, with GAT attaining peak performance of R-square equal to 0.97 for maximum plastic strain. ChebSpectral and TDA-MLP performed considerably worse, yielding negative R-square values for several targets. These findings establish spatial graph-based neighbourhood aggregation as a robust and physically interpretable surrogate modelling strategy for cold spray process optimisation.

翻译：本研究提出了一种几何深度学习框架，用于基于有限元仿真数据预测冷喷涂粒子冲击响应。通过自动化Abaqus仿真生成了涵盖粒子速度、粒子温度及摩擦系数系统变化范围的参数化数据集，产生了包括最大等效塑性应变、平均接触塑性应变、最高温度、最大冯·米塞斯应力及变形比在内的五个输出目标。研究实现并评估了四种新颖算法：GraphSAGE式归纳图神经网络、切比雪夫谱图卷积网络、拓扑数据分析增强型多层感知器以及几何注意力网络。每个输入样本被视作k近邻特征空间图中的节点，使模型在训练过程中能够利用工艺条件间的空间相似性。三维特征空间可视化与二维等高线投影证实了输入-输出关系具有高度非线性且以速度为主导的特性。定量评估表明，GraphSAGE与GAT在多数目标上持续取得超过0.93的R平方值，其中GAT在最大塑性应变预测中达到峰值性能（R平方值为0.97）。ChebSpectral与TDA-MLP表现显著逊色，在多个目标上产生负R平方值。这些发现确立了基于空间图的邻域聚合方法作为冷喷涂工艺优化中一种鲁棒且具物理可解释性的代理建模策略。