Investigating the applicability of physics-based machine learning algorithms to meta-modeling of complex fluids

We briefly present three types of physics-based machine learning frameworks, to model, describe, and predict the behavior of complex fluids. In the area of data-driven constitutive meta-modeling, we present Rheology-Informed Neural Networks (RhINNs) and Multi-Fidelity Neural Network (MFNN), in which the physical intuition is being included explicitly and implicitly, respectively. We used RhINNs as an alternative solver for systems of Ordinary Differential Equations (ODEs) in a direct approach, and to learn the model/material parameters using a series of limited experimental data in an inverse platform. MFNN is also used as a data-driven constitutive meta-modeling of complex fluids and compares its rheological predictions with those of a simple Deep NN and experimental measurements. Generation of the low-fidelity data points is done using the underlying rheological constitutive models, while the high-fidelity network is trained on a limited number of experimentally measured data. We will discuss the MFNN predictions of a set of flow curves for a multi-component colloidal and wormlike micelle solution with respect to temperature, salinity, and aging of the mixture. With regards to complex fluid flow modeling, non-Newtonian physics-informed neural network (nn-PINNs) is introduced for solving systems of coupled PDEs. nn-PINNs are then employed to solve the constitutive models in conjunction with conservation of momentum while avoiding the mesh generation step, followed by validating for a number of different complex fluids with various constitutive models. These include a range of Generalized Newtonian Fluids empirical constitutive models and some phenomenological models with memory effects and thixotropic timescales, and for several flow protocols. We finally discuss the outlook and opportunities, and more importantly the limitations of science-based ML platforms in rheology and non-Newtonian fluid mechanics.