At the heart of the work is a fundamental challenge in additive manufacturing: the properties of a 3D-printed metal part depend intimately on its grain structure, the spatial arrangement and orientation of crystalline regions separated by grain boundaries. Fine grains typically enhance strength and toughness through grain-boundary strengthening, while larger or anisotropic grains can improve ductility and creep resistance. Controlling these attributes during printing requires understanding how processing conditions such as laser scanning velocity, melt pool geometry, and heat-affected zone dimensions translate into grain evolution, a relationship complicated by vast multidimensional parameter spaces and non-linear thermal dynamics.

The research team, led by Dipayan Sanpui and Subramanian K.R.S. Sankaranarayanan, built their framework on a repository of 1,524 successfully retrieved three-dimensional polycrystalline microstructures generated with the open-source SPPARKS kinetic Monte Carlo code. These simulations modeled hundreds of laser passes over a substrate using a modified Potts Monte Carlo approach, capturing curvature-driven grain growth, melting, remelting, and nucleation in the heat-affected zone. Rather than relying on abstract statistical descriptors such as two-point statistics or chord length distributions used in earlier studies, the team extracted physically interpretable features directly from two-dimensional slices of the simulated structures.

Four descriptors formed the quantitative vocabulary of the study: average grain size, surface-to-volume ratio, sphericity, and roundness. Grain size serves as a first-order measure linked directly to mechanical performance through the Hall-Petch relationship, while surface-to-volume ratio distinguishes microstructures with similar grain dimensions but different boundary complexity. Sphericity captures overall grain compactness and elongation, whereas roundness reflects the sharpness of grain edges and corners, quantities that differ when two grains share similar elongation but diverge in boundary smoothness due to solidification dynamics. The team computed these measures directly from grain identifiers in the SPPARKS output files, streamlining integration into automated materials design pipelines.

With the features extracted, the researchers framed the problem as supervised regression, using seven processing conditions, including scanning velocity, scanning pattern, molten zone width, depth, and tail length, and heat-affected zone width and tail length, as inputs. They trained and compared multiple algorithms: Random Forest, Gradient Boosting Machine, Extreme Gradient Boosting (XGBoost), a feed-forward neural network, and a one-dimensional convolutional neural network, with hyperparameters optimized through six-fold grid search cross-validation and Keras-Tuner’s Hyperband search for the neural architectures.

Tree-based ensemble methods consistently outperformed the neural networks. XGBoost emerged as the best overall performer, achieving a coefficient of determination of 0.977 for grain size prediction, 0.946 for surface-to-volume ratio, 0.954 for sphericity, and 0.957 for roundness on test data, with a mean absolute error of just 6.62 pixels for grain size. The authors attribute grain size’s high predictability to its status as a first-order reflection of the temperature distribution across the simulation domain, while shape descriptors such as sphericity and roundness depend on secondary morphological effects, including grain boundary curvature and irregular grain interactions, that are harder to infer from processing conditions alone.

A particularly striking finding emerged from the parity plots: grain size predictions split into two distinct clusters corresponding to different microstructural regimes. The first cluster, with average grain sizes between 0 and 450 pixels, represented anisotropic structures of alternating equiaxed and elongated grains formed at higher scanning velocities and broader heat-affected zones. The second cluster, spanning 600 to 1200 pixels, arose from low-velocity, narrow-heat-affected-zone conditions that promote localized remelting and coarser, irregular grains. When trained and evaluated within the well-behaved first regime, the model reached an R² of 0.982 with an error of only 2.305 pixels; in the morphologically heterogeneous second regime, accuracy dropped to R² of 0.561, revealing where the surrogate’s reliability limits lie.

To open the black box, the team applied Shapley Additive exPlanations (SHAP), a game-theory-based framework that quantifies each input feature’s marginal contribution to predictions. The analysis showed that scanning velocity and heat-affected zone characteristics dominate grain size outcomes globally, consistent with established solidification theory in which thermal gradients, cooling rates, and grain-boundary mobility govern grain evolution. At high velocities, scanning speed and HAZ tail length controlled the outcome, with rapid cooling producing fine, anisotropic grains. At minimum velocity, scanning direction and HAZ tail length became the primary drivers: cross-hatch patterns induced multidirectional heat flux and rapid cooling that favored clusters of fine equiaxed grains, while unidirectional scanning promoted elongated, directionally aligned grains.

Beyond interpretation, the framework demonstrated practical utility for process optimization. By filtering candidate parameter combinations according to the relative error between predicted and desired grain sizes, the researchers identified viable alternative processing conditions under fixed maximum or minimum laser velocities. Under high velocity, neighboring points in parameter space with variations in melt-zone geometry yielded nearly identical grain structures, suggesting flexibility in achieving consistent microstructures. Under low velocity, HAZ tail length and scanning direction offered the most meaningful degrees of freedom. The computational payoff is substantial: simulating a single 100 × 100 × 100 site microstructure took roughly 25 minutes across four compute nodes, while the trained models deliver predictions in minutes once trained.

The authors envision their approach as a foundation for digital twins and closed-loop process control, in which sensor-derived process variables feed continuously into trained models for online quality monitoring and adaptive parameter optimization. They acknowledge limitations, notably that featurization currently operates on two-dimensional slices rather than full three-dimensional volumes, and they point toward extending the framework to experimental microscopy images, inverse design, and active-learning-based calibration as next steps. By coupling high-fidelity physics simulation with interpretable machine learning, the study illustrates how explainable AI can transform additive manufacturing from a process of empirical trial and error into a predictive, quantitatively grounded engineering discipline.

Subject of Research: Interpretable machine learning prediction of process–structure relationships in metal additive manufacturing using kinetic Monte Carlo microstructure simulations

Article Title: Data-driven discovery of process–structure relationships in additive manufacturing via featurization from kinetic Monte Carlo simulations and interpretable machine learning

Article References: Sanpui, D., Chan, H., Koneru, A., Banik, S., Manna, S., & Sankaranarayanan, S. K. (2026). Data-driven discovery of process–structure relationships in additive manufacturing via featurization from kinetic Monte Carlo simulations and interpretable machine learning. Machine Learning with Applications, 25, Article 100985. https://doi.org/10.1016/j.mlwa.2026.100985

Image Credits: AI Generated

DOI: 10.1016/j.mlwa.2026.100985

Keywords: additive manufacturing, kinetic Monte Carlo, machine learning, microstructure, XGBoost, SHAP, grain size, process-structure linkages, featurization, surrogate modeling, explainable AI, metal 3D printing