Graph Neural Operator: A DeepONet-Based Framework for Learning Thermo-Mechanical Distortion in Metallic Additive Manufacturing

Recent advances in machine learning (ML) have enabled efficient modelling of process-structure-property relationships in metallic additive manufacturing (AM), offering promising alternatives to conventional simulation-based methods. However, most ML models rely on input-output regression paradigms, which limit their ability to generalize to unseen scenarios. This paper proposes a graph neural operator that integrates deep operator network (DeepONet) with graph neural networks (GNNs) to simulate the thermo-mechanical constitutive behaviour in metallic AM. The proposed DeepONet-GNN framework decouples the thermal and structural fields, leveraging sparse temperature measurements to predict full-field z-direction distortion across unseen geometries. Through layer-wise evaluations on multiple structures, the model demonstrates strong generalization, data efficiency, and robustness to variations in sensor distribution, achieving a low RMSE of 0.0881 mm. Compared to a coupled GNN, DeepONet-GNN reaches convergence with similar accuracy using 50% fewer training epochs. The proposed DeepONet-GNN model demonstrates the ability to generalize to unseen geometries while leveraging only 5% of the temperature sensor data, highlighting the potential of graph neural operators as accurate and scalable surrogates for real-time prediction in AM processes.