Uncertainty-aware multi-output Gaussian-process autoregression for melt-pool dynamics and microstructural implications

We present a machine learning modeling framework for predicting melt-pool dynamics and their microstructural consequences in laser powder bed fusion (LPBF). A latent multi-output Gaussian-process autoregressive model (L-MOGPAR) is introduced to emulate coupled time-evolving temperature fields and melt-pool morphology while providing calibrated, spatially resolved uncertainty estimates. High-fidelity training data were generated with an Arbitrary Lagrangian Eulerian–finite element method multiphysics model (incorporating free-surface Navier–Stokes with vapor-recoil pressure and temperature-dependent surface tension, enthalpy-based phase change, radiative losses, and a Gaussian heat source) run on a 51 × 162 grid for a single-pass scan of 316L stainless steel. The dataset spans 498 simulations over a power range of 60–75 W, scan speeds of 1.0–1.5 m/s, and a beam radius range of 125–155μm. L-MOGPAR was trained on 473 trajectories (10 snapshots over 800μs) after principal component analysis (PCA) compression to 25 modes with a linear model of coregionalization and temporal coupling with Markov order 1. A deterministic UNet baseline was also trained on the same data. Both surrogates reproduced temperature evolution and melt-pool geometry across the process window. UNet attained higher point accuracy (R²: T = 0.986, ∂_xT = 0.918, ∂_yT = 0.938) than L-MOGPAR (R²: T = 0.931, ∂_xT = 0.746, ∂_yT = 0.85). L-MOGPAR, however, yielded field-level uncertainty that concentrated near high-gradient melt-pool boundaries and correlated with absolute error, facilitating risk-aware usage. To assess downstream implications, we propagated the machine learning-predicted thermal histories through a grand-potential-based phase-field model for solidification. Across multiple phase-field simulations, both models produced single-digit average errors in dendrite growth. UNet was consistently better in the growth normal to laser pass direction, while L-MOGPAR achieved a lower worst-case error in selected growth cases along the laser pass. This work demonstrates an end-to-end pipeline that links process-level predictions to microstructure. With it, process to microstructure relationships can be explored quickly for robust design and performance evaluation of LPBF products.