# Data-Efficient Neural Network for Track Profile Modelling in Cold Spray Additive Manufacturing
###### Abstract  
Cold spray is emerging as an additive manufacturing technique, particularly advantageous when high production rate and large build sizes are in demand. To further accelerate technology's industrial maturity, the problem of geometric control must be improved, and a neural network model has emerged to predict additively manufactured geometry. However, limited data on the effect of deposition conditions on geometry growth is often problematic. Therefore, this study presents data-efficient neural network modelling of a single-track profile in cold spray additive manufacturing. Two modelling techniques harnessing prior knowledge or existing model were proposed, and both were found to be effective in achieving the data-efficient development of a neural network model. We also showed that the proposed data-efficient neural network model provided better predictive performance than the previously proposed Gaussian function model and purely data-driven neural network. The results indicate that a neural network model can outperform a widely used mathematical model with data-efficient modelling techniques and be better suited to improving geometric control in cold spray additive manufacturing. cold spray; neural network; additive manufacturing; data-efficient; model; profile; geometry; spray angle; limited data; machine learning +
Footnote †: journal: Applied Sciences  
Cold spray has recently been recognised to possess great potential as an alternative additive manufacturing technology and in this context is referred to as Cold Spray Additive Manufacturing (CSAM) [5; 6; 7; 8]. This potential is particularly important when high production rates, large build sizes and repair or building on an existing structure are in demand, e.g., in aerospace industries [8; 9]. The protective atmosphere-free environment allows for the fabrication of large components that are not possible with other additive manufacturing technologies, e.g., powder bed fusion, while providing a flexible selection of oxygen-sensitive powder materials [8; 10; 11]. These benefits have resulted in several successful demonstrations of the technology at different levels of fabrication complexity, ranging from a simple tubular structure [12], pyramidal fin array [13], to more complex parts such as topologically optimised components [14]. However, several fundamental and practical challenges need to be addressed to fully adopt the CSAM technology in commercial applications. One of these is geometric control, which is a common problem for other high production rate additive manufacturing (HPRAM) processes, including Wire and Arc Additive Manufacturing (WAAM) [15; 16] and Laser Cladding (LC) [17; 18]. Poor geometric control places many limitations on applying HPRAM technologies; examples include varying geometric quality, difficulty producing complex geometries, and geometry-induced property variations [7; 8; 19]. Hence, geometric control must be addressed to facilitate further development and commercial integration of CSAM and other HPRAM technologies. Given the track-by-track and layer-by-layer nature of HPRAM, a high-accuracy process model based on the shape of a characteristic processing unit (e.g., single-track profile) provides a promising solution to the problem and often forms a basis for the modelling of higher geometric processing units, such as overlapping and overlayer models [20; 21]. The single-track profile modelling in HPRAM was previously attempted using two distinct approaches: mathematical and data-driven modelling. In WAAM, the symmetric single-track bead profile has been approximated using various basic mathematical function models ranging from parabolic, cosine and arcs [22; 23]. These mathematical function models are often combined with another regression model to provide predictive capabilities. For example, [PERSON] et al. developed a quadratic regression model based on experimental data, computing the coefficients of the parabolic function model to describe a single-track bead profile [22].