Physics-Informed Neural Network Surrogate Modeling of Three-Dimensional Gas–Liquid Hydrodynamics in Aerated Double-Impeller Stirred Tanks

This study develops a physics-informed surrogate for predicting three-dimensional gas–liquid hydrodynamics in an aerated double-impeller stirred tank. Reference fields were generated using steady-state computational fluid dynamics (CFD) simulations in ANSYS Fluent at impeller speeds of 200–500 rpm. Three models with identical network architectures were examined: a supervised neural network (NN) trained on CFD data, a boundary-informed neural network (BINN) incorporating boundary constraints, and a physics-informed neural network (PINN) incorporating boundary and reduced physics constraints. At 400 and 500 rpm, the PINN outperformed the NN and BINN, achieving normalized liquid- and gas velocity errors below 10% and pressure errors of approximately 3–4%. The NN and BINN showed greater attenuation of impeller-induced gradients in high-shear regions. At the unseen intermediate speeds of 350 and 450 rpm, the PINN reproduced the principal CFD flow structures. Normalized gas velocity errors were approximately 11–14%, while normalized pressure errors ranged from 4.48% to 9.22%, depending on the operating speed and error metric. Each CFD simulation required approximately 100–140 h, whereas PINN inference at 200,000 spatial locations required approximately 2–3 h per operating condition. The initial cost of generating the CFD training data must be considered when assessing the benefit of repeated surrogate evaluations.