Physics-Informed Surrogates for Temperature Prediction of Multi-Tracks in Laser Powder Bed Fusion

TL;DR

The paper addresses rapid, accurate prediction of 3D temperature fields in LPBF by combining physics‑informed neural networks (PINNs) with DeepONet‑based neural operators to obtain parametric surrogates. While PI‑EnDeepONet performs well for single‑track scenarios, it struggles with multi‑track complexity due to the curse of dimensionality. A Sequential PINN framework is proposed and demonstrated to deliver substantially faster training (about 8.5× reduction) and lower errors (MAPE < 2.5%) across multi‑track paths, while accurately capturing cooling histories essential for microstructure predictions. The findings support using sequential PINNs for scalable, real‑time compatible surrogate modeling in tool‑path optimization and process monitoring in AM.

Abstract

Modeling plays a critical role in additive manufacturing (AM), enabling a deeper understanding of underlying processes. Parametric solutions for such models are of great importance, enabling the optimization of production processes and considerable cost reductions. However, the complexity of the problem and diversity of spatio-temporal scales involved in the process pose significant challenges for traditional numerical methods. Surrogate models offer a powerful alternative by accelerating simulations and facilitating real-time monitoring and control. The present study presents an operator learning approach that relies on the deep operator network (DeepONet) and physics-informed neural networks (PINN) to predict the three-dimensional temperature distribution during melting and consolidation in laser powder bed fusion (LPBF). Parametric solutions for both single-track and multi-track scenarios with respect to tool path are obtained. To address the challenges in obtaining parametric solutions for multi-track scenarios using DeepONet architecture, a sequential PINN approach is proposed to efficiently manage the increased training complexity inherent in those scenarios. The accuracy and consistency of the model are verified against finite-difference computations. The developed surrogate allows us to efficiently analyze the effect of scanning paths and laser parameters on the thermal history.

Figures (8)

• Figure 1: Schematic representation of the original DeepONet.
• Figure 2: Schematic representation of the En-DeepONet with physics-informed loss functions.
• Figure 3: (a) Outline of multiple tracks on a workpiece. (b)Tree structure representation of breaking down multi-track scenarios into $n$ times intervals. Green colored nodes indicate the track numbers.
• Figure 4: Schematic representation of the computational domain and boundary conditions.
• Figure 5: Comparison of the calculated temperature and meltpool dimensions for all single-track scenarios. R.E. stands for the relative error.(a): PINN solution vs. reference (FD) solution, (b): PI-EnDeepONet solution vs. reference (FD) solution. 5 % relative error zone is indicated by light red color. (c): Comparison of melt pool dimensions for each method. Error bars indicate 5% error with respect to FD solution.