Sequential Bayesian learning-enabled thermal and material flow field prediction in additive friction stir deposition

Renowned for its capabilities of producing fully dense material that possesses forging-standard properties, additive friction stir deposition is a promising solid-state additive process whose printing outcomes are governed by the coupled thermal and material flow fields in the deposition zone. However, these fields remain challenging to predict due to sparse measurements and incomplete understanding of extreme thermomechanical processing. Here, we integrate three-dimensional computational fluid dynamics simulations with two-dimensional in situ thermal imaging through a sequential measurement-informed Bayesian learning framework. This framework enables accurate and rapid prediction of three-dimensional distributions of temperature and velocity across arbitrary processing conditions, while continuously updating predictions with reduced uncertainties as new experimental data becomes available. Leveraging both embedded physics and experimental data, this approach is shown to consistently outperform benchmark machine learning models. Moreover, it delivers high-fidelity full-field predictions within one second on a 24-core CPU, compared with roughly eight hours required by physics-based simulations.