Supervised Surrogate Modeling for Hagen-Poiseuille and Womersley flows

Computational fluid dynamics plays an important role to solve real-world flow systems, but a heavy computation burden often causes a trade-off with physical accuracy. Surrogate flow models have the potential to achieve both computational efficiency and physical accuracy. We develop a numerical procedure, using neural network (NN) and Gaussian Process (GP) methods, to demonstrate the potential of machine learning approaches in building efficient and accurate surrogate models with limited runs of the original flow models and apply it to Hagen-Poiseuille and Womersley flows that involve spatial and spatial-tempo responses, respectively. Training points are generated by calling the analytical solutions multiple times with evenly discretized spatial or spatial-temporal variables. Then NN and GP surrogate models are built using supervised machine learning regression. We compare the NN and GP methods and examine the unique feature of the GP model, which also provides confidence in the prediction. The results indicate that the surrogate models can accurately represent both Hagen-Poiseuille and Womersley flow models. Our further work will be developing surrogate models for more realistic flows.