2026 Zhu Viscoelastic Stress Prediction

Numerical simulations of elastic turbulence in parallel shear flows of polymer solutions indicate that the phenomena is associated with the formation and instability of exact coherent states dominated by thin sheets of polymer stress. However, these “arrowhead” structures are yet to be seen directly in experiments, where simultaneous velocity and polymer conformation measurements are challenging to obtain. Motivated by these challenges, we introduce a method for the prediction of the polymer conformation field given a time series of vorticity measurements. Our approach consists of two components: the first is a convolutional neural network architecture which takes vorticity fields and outputs a positive definite conformation tensor. The second is the adaptation of an assimilation-based training algorithm which does not require a pre-generated ‘offline’ library of reference conformation fields, but is trained only using the vorticity measurements. This is particularly important in viscoelastic problems, where the appropriate model and parameters to compare to the experiments may need to be determined as part of the solution. Our method produces robust predictions of the polymer stretch, while standard, unregularised variational assimilation is ineffective.