Inductive bias and information fusion with concatenated neural networks

Although data-driven modeling holds promise in many applications by lowering the computational burden, training deep learning models needs a huge amount of data. This big data might not be always available for scientific problems and may lead to poorly generalizable data-driven models. Exploiting prior knowledge about the problem, this study explores a physics-guided machine learning approach to build more tailored, effective, and efficient surrogate models. For our analysis, we focus on the development of predictive models for turbulent boundary layer flows over a flat plate. In particular, we combine the power-law velocity profile (low-fidelity model) with the noisy data obtained either from experiments or computational fluid dynamics simulations (high-fidelity models) through a concatenated neural network. We illustrate how the prior knowledge from the low-fidelity model results in reducing uncertainties associated with deep learning models applied to boundary layer flow prediction problems. We demonstrate that the proposed inductive bias produces physically consistent models that attempt to achieve better generalization than data-driven models obtained purely based on data.