Differentiable simulations of viscoelastic fluids for developing digital rheometers

Viscoelastic flows are widely encountered in a diverse array of industrial and biophysical processes. However, accurately modeling these flows via constitutive models remains a significant challenge. The advent of differentiable simulation methods leveraging automatic differentiation offers a promising avenue for improved computational models and addressing inverse design problems in viscoelastic fluids. In this work, we introduce a fully-differentiable computational framework incorporating a viscoelastic fluid solver implemented with JAX. This framework enables data-driven parametrization of known constitutive equations, the discovery of optimal models, and the identification of additional corrective terms to existing constitutive relations. Our approach accommodates arbitrary flow conditions and is not limited to specific experimental setups or model choices. By embedding the training of the model within the fluid solver, we can incorporate data from a multitude of flow conditions, allowing us to characterize the intrinsic fluid properties that generalize across various scenarios.