Physics-Informed Machine Learning for Thermal Field Prediction in Directed Energy Deposition

Abstract

Directed Energy Deposition (DED) is an additive manufacturing process in which accurate thermal predictions are essential for understanding melt-pool behaviour. While high-fidelity simulations can provide this information, they are computationally expensive, especially when a large number of simulations are required. This motivates the development of faster predictive methods. This thesis investigates the use of machine learning (ML) surrogate models as an efficient alternative for thermal prediction in DED processes. Both data-driven and physics-informed approaches are considered, including neural networks and neural operators. The models are trained on data generated from high-fidelity simulations, with the goal of evaluating trade-offs between predictive accuracy, computational cost and the incorporation of physical constraints. A paired benchmark spans three architecture families, each with a data-only and a physics-informed variant, giving six model variants in total. Trained across four training-data fractions and three initialisation seeds, the data-only pointwise MLP achieves the best trade-off. It produces a root mean square error (RMSE) of 12.1 ± 0.3 K (approximately 0.7% of the liquidus temperature of 1928 K) on the in-distribution test set and 46.9 ± 16.6 K on the process-extreme out-of-distribution (OOD) split. At 8.6 ms per output - roughly 7 000× faster than the GPU-accelerated solver - the surrogate is sufficiently accurate for unlocking new use cases such as interactive process-parameter exploration, where rapid iteration matters more than solver-level precision. Physics-informed training through soft partial differential equation (PDE) and boundary losses does not improve overall accuracy and substantially increases training time, although it does provide some regularisation benefits at high temperatures on OOD cases. The volume-averaged RMSE is dominated by ambient voxels (87% of the domain below 400 K). Out-of-distribution generalisation remains the dominant limitation, with OOD error roughly four times larger than random-test error. These results suggest that for this fixed-domain setting, compact data-driven surrogates are preferable to more complex physics-informed or operator-based models. Future work should test whether these results hold at finer grid resolutions and explore uncertainty estimates to flag unreliable predictions.