# Geometric and Topological Deep Learning for Predicting Thermo-mechanical Performance in Cold Spray Deposition Process Modeling Source: [Geometric and Topological Deep Learning for Predicting Thermo-mechanical Performance in Cold Spray Deposition Process Modeling]() Collection index: [llms.txt]() Data updated: 2026-03-18T05:00:11.457Z Authors: Akshansh Mishra Published: 2026-03-15T16:46:05.000Z ## Abstract 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. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. - [Maximum equivalent plastic strain prediction on Cold spray impact simulation data](): Maximum equivalent plastic strain prediction; Cold spray impact simulation data; MSE: 0.035597. - [Maximum temperature prediction on Cold spray impact simulation data](): Maximum temperature prediction; Cold spray impact simulation data; MSE: 283.043396. - [Particle Deformation Ratio Prediction on Cold Spray Impact Simulation Data (test)](): Particle deformation ratio prediction; Cold spray impact simulation data (test); MSE: 0.000325. - [Average contact plastic strain prediction on Cold spray impact simulation](): Average contact plastic strain prediction; Cold spray impact simulation; MSE: 0.000028. ## Original sources and implementation [Original paper]() [PDF]()