## 3 Results and Discussion
### Discussion  
Notably, reducing the runtime from several hours/days per CFD case to just 12 s using the above ML surrogate can transform design exploration into a truly high-throughput process. Previously, each change in the mask geometry required domain remeshing and a full CFD rerun, severely limiting the pace of innovation. Now, with the surrogate model, new geometries can be evaluated almost instantly, delivering immediate predictions of particle distribution, impact velocity, and temperature. This dramatic time savings significantly accelerate HER optimization by enabling the rapid screening of hundreds of masks or process variants in a single day. However, to fully assess and refine pin-fin architectures and roughness, this surrogate must ultimately be integrated with complementary models such as finite element analysis (FEA) and molecular dynamics (MD) [6; 30], which capture mechanical, atomistic, and interfacial phenomena beyond the scope of CFD alone. To enable high-throughput predictions across these domains, dedicated ML models should also be developed for FEA and MD simulations and coupled with the CFD-based surrogate, enabling the rapid and comprehensive estimation of pin-fin build-up, final geometry, and surface roughness.  
Beyond its computational efficiency, this ML-based surrogate model forms a critical component of a broader digital twin (DT) framework [31, 32, 33, 34, 35]. By continuously integrating real-time or simulated process data, the DT allows for predictive modeling, adaptive control, and automated optimization of cold spray additive manufacturing (CSAM) workflows [31, 33, 35]. In contrast to traditional CFD simulations--which are accurate but too slow for real-time use--the surrogate ML models bridge the gap between physical realism and computational speed. This synergy is especially vital for CSAM, where design decisions must adapt rapidly to ensure coating quality, geometric precision, and consistent performance.  
Figure 20: Predictions from the integrated first and second models for the specific test sample: inlet pressure of 4 MPa, inlet temperature of 800 \({}^{\circ}\)C, substrate SOD of 20 mm, mask SOD of 16 mm, mask wire diameter of 0.46 mm, mask opening size of 1.14 mm, and an open area of 51%.  
Furthermore, the surrogate's flexibility underscores its potential beyond the specific masked configurations studied here. With only minor parameter adjustments, the model also predicts particle distribution, impact velocity, and temperature for flat, unmasked substrates, making it broadly applicable across a range of cold spray scenarios. We anticipate that the framework can be readily extended to different powders, carrier gases, or nozzle geometries by applying the same workflow of generating CFD data followed by a two-stage machine learning training process. New CFD cases must be generated using the updated material properties or altered flow and operating conditions, after which the model can be retrained to accommodate the new parameter space.  
This machine learning framework accurately captures detailed, location-specific distributions of particle positions, velocities, and temperatures in masked cold spray processes--offering a significant improvement over traditional models that primarily predict average values (e.g., [16]). However, the model should not be extrapolated far beyond its original training envelope. If the new geometry or operating condition deviates significantly--such as incorporating mask features an order of magnitude smaller--prediction errors are likely to increase. In such scenarios, additional CFD simulations and possibly new geometric or material descriptors must be included, followed by model retraining to preserve predictive accuracy and reliability.