Geometric and topological deep learning for predicting thermo-mechanical performance in cold spray deposition process modeling

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 R² values exceeding 0.93 across most targets, with GAT attaining peak performance of R² = 0.97 for maximum plastic strain. ChebSpectral and TDA-MLP performed considerably worse, yielding negative R² 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.