# Physics-Based Data Augmentation Enables Accurate Machine Learning Prediction of Melt Pool Geometry
## 1 Introduction  
Laser Powder Bed Fusion (L-PBF) is one of the most prominent technologies currently used in Additive Manufacturing (AM) methods for fabricating metal parts, providing unprecedented advantages for manufacturing complex-shaped metal components and dominating the metal additive manufacturing market with applications in various industries such as aerospace, automotive, pharmaceuticals, and even the energy industry [1, 2, 3, 4, 5]. In L-PBF, a laser beam selectively melts metal powders layer by layer to form melt pools, which solidify and stack into near-net-shaped parts. The quality and performance ofthe final product are affected by multiple factors, including raw powder properties, process parameters, and post-processing treatments [6; 7; 8]. The melt pool--defined as the localized region of melt powder along the laser scanning path--is central to the process. Its thermal behavior and geometric characteristics strongly influence the solidification dynamics, defect formation, and ultimately the microstructure and mechanical performance of the fabricated part [9]. However, melt pool instability can lead to serious issues such as increased porosity, poor surface finish, and mechanical degradation [10; 11; 12]. To mitigate such defects, many studies have explored the influence of process parameters--particularly laser power, scanning speed, and energy density--on melt pool geometry and quality [13; 14; 15]. While higher laser power tends to increase melt pool size, excessive energy input can lead to keyhole formation and instability. By contrast, insufficient energy may result in lack-of-fusion defects due to incomplete melting. Therefore, understanding and predicting melt pool characteristics under different processing conditions is essential for process control and defect mitigation [16]. Traditional simulation tools, such as finite element modeling (FEM), have been extensively used to capture melt pool evolution and thermal history [17; 18; 19]. Recent reviews [20] have highlighted how FEM approaches remain the primary tool for multiscale thermo-mechanical analysis in L-PBF, despite challenges in computational cost, parameter calibration, and scalability. While FEM provides valuable physical insight, its high resource demands and reliance on precise material models limit its applicability for real-time or data-intensive scenarios. To overcome these limitations, recent studies have explored data-driven approaches, particularly machine learning (ML), which can capture complex nonlinear relationships and generalize across materials and systems [21]. ML has found success in AM applications such as defect detection, topology optimization, process monitoring, and post-processing [22; 23; 24; 25; 26]. For instance, [PERSON] et al. [27] used ML to predict porosity based on chemical composition with over 90% accuracy. Similarly, [PERSON] et al. [28] applied deep learning to predict porosity and density in L-PBF-processed parts. While ML has demonstrated predictive power in AM, its application to melt pool geometry prediction remains limited [29; 30; 31]. A major challenge lies in data scarcity. High-fidelity experimental data in metal AM are difficult and expensive to obtain. Additionally, ML models often lack physical interpretability and may fail to generalize under sparse or noisy conditions [32; 33]. Combining physics-based modeling with machine learning has emerged as a promising solution. This hybrid approach improves model robustness, reduces dependency on large datasets, and enhances interpretability [34]. One effective strategy is physics-informed data augmentation. [PERSON] et al. [35] combined an analytical heat transfer model with Gaussian process regression to predict melt pool geometry under limited data conditions. [PERSON] et al. [36] employed physics-informed neural networks to simulate temperature and flow fields in L-PBF, achieving physically consistent predictions even with sparse data. [PERSON] et al.