Rheology-Informed Neural Networks (RhINNs) for direct and inverse complex fluid modeling

We present Rheology-Informed Neural Networks (RhINNs) architectures as alternative platforms to solve systems of Ordinary Differential Equations (ODEs) commonly used in rheological constitutive modeling of complex fluids. The proposed RhINN is employed to solve the constitutive models with multiple ODEs by benefiting from automatic differentiation in neural networks. We present direct and inverse solutions of a Thixotropic ElastoViscoPlastic (TEVP) constitutive equation for a series of different flow protocols by employing our RhINNs methodology. From a practical perspective, commonly an exhaustive list of experimentations is required to accurately parameterize a TEVP model based on a specific fluid of interest. Only then, the model can be utilized in order to predict the fluid response to a different flow protocol. Alternatively, in our inverse problem, we let the RhINN framework learn the model parameters by training on a series of limited experimental data. We show that the model can be extended to various models by including different systems of ODEs, solved for arbitrary geometries, and recover complex kymographs of kinematic heterogeneities and transient shear banding of thixotropic fluids.