Unveiling Viscoelastic Flow Dynamics and Rheology: Data-Driven Constitutive Modeling through Differentiable Simulations

Viscoelastic flows are common in many industrial and biophysical processes, yet they are especially challenging to model in the complex geometries and flow conditions encountered in real-world applications. Differentiable simulation methods offer a promising avenue for improving computational models, particularly for inverse design problems. In this talk, we introduce a fully differentiable viscoelastic fluid solver implemented with JAX. This framework enables data-driven parametrization of viscoelastic contributions to the flow, including discovering new constitutive models or corrective terms. Our approach accommodates arbitrary flow conditions and geometries rather than being constrained to simplified setups or specific model choices. By embedding model training within the solver, we can incorporate data from numerous flow conditions and characterize intrinsic fluid properties that generalize across various scenarios. We apply our framework to flow setups where traditional constitutive models often fall short – even qualitatively – such as contracting channels. In turn, we demonstrate improved predictive accuracy and robustness over conventional methods while also uncovering mechanistic insights into these problems. This work represents a step toward creating digital rheometers capable of learning and simulating viscoelastic behavior across diverse flow conditions and geometries.