MAM-PhyGNN: A Physics-Hardcoded Graph Neural Network for fast and accurate thermal simulation in metal additive manufacturing

Accurate and efficient prediction of transient thermal fields in metal additive manufacturing (MAM) is critical for process control, but a persistent trade-off exists between fidelity and speed. High-fidelity solvers require hours of computation for a single simulation, while existing surrogates like Physics-Informed Neural Networks (PINNs) often fail in long-term predictions due to their topology-agnostic nature and soft physical constraints. To overcome these limitations, this paper introduces the Metal Additive Manufacturing Physics-Hardcoded Graph Neural Network (MAM-PhyGNN), a topology-aware Graph Neural Network (GNN) that architecturally embeds physical laws directly onto the unstructured simulation mesh. While the framework is designed for general MAM processes, its performance is validated on a challenging Laser Powder Bed Fusion (LPBF) case study. The framework formulates the heat transfer problem on an unstructured mesh as a dynamical system on a graph. Its core innovation is a dual-branch operator architecture: a deterministic, non-learnable Laplace Block hardcodes the fundamental physics of heat diffusion, providing a robust stability anchor, while a data-driven GNN learns a data-driven correction for complex nonlinear dynamics arising from temperature-dependent material properties and boundary conditions. In the LPBF case study, MAM-PhyGNN demonstrated exceptional performance. It remained stable through a 1000-step autoregressive long-term prediction on unseen data, maintaining a Pearson correlation of 0.98 with the ground truth. Crucially, MAM-PhyGNN achieved this with a computational speedup of approximately 850x over the high-fidelity solver, reducing simulation time from over 50 min to just 3.6 s. This work demonstrates that by architecturally embedding fundamental physics within a topology-aware GNN, it is possible to create surrogate models that are simultaneously fast, accurate, and stable for long-duration MAM simulations, thereby opening a viable pathway towards real-time digital twins for process optimization.