Abstract Metal Powder Bed Fusion (PBF) epitomizes the complexity of modern manufacturing, where strongly coupled thermal, mechanical, and fluid-dynamic interactions evolve over multiple spatial and temporal scales. Capturing these multiscale phenomena with predictive fidelity remains a central barrier to reliable, repeatable, and certifiable metal additive manufacturing. Conventional numerical solvers such as finite element or finite volume methods provide physical rigor but are computationally prohibitive for design exploration, uncertainty quantification, or real-time control. This paper positions Scientific Machine Learning (SciML) as a unifying paradigm that bridges the interpretability of physics-based modeling with the adaptability of data-driven inference. By embedding governing physical laws directly into learning procedure, or introducing biases into the architectures, SciML enables models that are both data-efficient and physically consistent, capable of accelerating high-fidelity simulations and supporting in-situ process optimization. The review is structured around three persistent challenges: mathematical complexity stemming from coupled multiphysics interactions, training instability inherent to physics-informed optimization, and practical integration barriers that limit industrial deployment. We analyze how emerging formulations such as Physics-Informed Neural Networks and Neural Operators address these challenges and advance toward robust, generalizable process surrogates. Beyond synthesizing existing methods, the paper outlines a roadmap toward physics-grounded digital twins , signaling a transformative step toward intelligent, self-correcting metal additive manufacturing systems.
Depaoli et al. (Wed,) studied this question.