Learning the hidden rheology of complex fluids through MF-RhIGNet: Multi Fidelity Rheology-Informed Graph Neural Network

Precise and reliable prediction of a structured fluids' response to an applied deformation or stress is of great interest in a variety of industries, particularly in the design of new soft materials and their processes. Nonetheless, that requires solving non-trivial time and rate-dependent constitutive equations that are commonly written in form of coupled differential equations under different flow conditions. In practice, this involves a series of experimental tests to recover model parameters and a subsequent solution of constitutive equations to predict the rheological behavior of a multi-variant thixotropic or viscoelastic material. We present a Multi Fidelity Rheology-Informed Graph Neural Network (MF-RhIGNet) for data-driven constitutive meta-modeling of these complex fluids, by combining observational and inductive biases in the neural network to adhere to constitutive laws of interest. The proposed MF-RhIGNet consists of a low-fidelity part named RhIGNets that is used to learn and recover the hidden rheology of complex constitutive models with multiple coupled ODEs, as well as a high-fidelity part that deals with a limited number of experimental data. MF-RhIGNets are found to be capable of learning and predicting non-trivial behaviors of a complex material using only a handful of data points from a single flow procedure, allowing for accurate modeling with a small number of experiments at unprecedented accuracies.