Physics-guided machine learning for surrogate modeling in fluid mechanics

Recently, computational modeling has shifted towards the use of statistical inference, deep learning, and other data-driven modeling frameworks. Although this shift in modeling holds promise in many applications like design optimization and real-time control by lowering the computational burden, training deep learning models needs a huge amount of data. This big data is not always available for scientific problems and leads to poorly generalizable data-driven models. This gap can be furnished by leveraging information from physics-based simplified approximations. In particular, we combine the information from simplified analytical models with the noisy data obtained either from experiments or computational fluid dynamics simulations (high-fidelity models) through a neural network. We illustrate the proposed physics-guided machine learning framework for different test cases like boundary layer flow reconstruction, airfoil force prediction, and projection-based reduced order modeling. This multi-fidelity information fusion framework produces physically consistent models that attempt to achieve better generalizability than data-driven models obtained purely based on data. This work builds a bridge between extensive simplified physics-based theories and data-driven modeling paradigm and paves the way for using hybrid physics and machine learning modeling approaches for next-generation digital twin technologies.