Variational Physics-Informed Neural Network for 3D Transient Melt Pool Thermal Modeling

Accurate prediction of transient melt pool thermal fields in Laser Powder Bed Fusion (LPBF) is essential for understanding melt pool geometry and defect formation mechanisms, yet conventional finite element methods (FEM) impose prohibitive computational costs for parametric process exploration. A variational physics-informed neural network (VPINN) framework is presented for 3D transient thermal modeling of a GH3536 single-track LPBF scan. The framework incorporates a continuously differentiable Goldak double-ellipsoid moving heat source, temperature-dependent thermophysical property surrogates, and an effective heat-capacity treatment of latent heat associated with solid–liquid phase change and vaporization. These components are embedded in a weak-form residual-minimization scheme with octree-adaptive domain decomposition, hierarchical Legendre test functions, and sequential sliding-window time marching. Effective absorptivity is inferred jointly with the network parameters, using sparse experimental melt pool profiles as supervision. Within a parametric study covering laser powers from 100 to 140 W and scan speeds from 1000 to 1500 mm/s, the predicted melt pool width, depth, and aspect ratio agree closely with FEM benchmarks and cross-sectional optical micrograph measurements across both supervised and held-out interpolation conditions, with total relative L2 nodal temperature errors ranging from 3.23% to 6.75%. Following a one-time offline training investment of 15,323 s that simultaneously resolves the full parametric space, surrogate inference reduces per-condition query time from 3000–4000 s (FEM) to merely 4–5 s, delivering a speedup of two to three orders of magnitude and making the framework increasingly cost-effective for high-throughput parametric studies and digital-twin integration as the number of queried conditions grows.