Learning the Constitutive Relation of Polymeric Flows with Memory

We develop a learning strategy to infer the constitutive relation for the stress of polymeric flows with memory. We assume that the relations are in differential form, functions of the velocity gradient and stress, but no assumptions are made on their functional form. The required training data is obtained from stress trajectories generated during microscopic polymer simulations. This data is then used within a Gaussian Process (GP) regression scheme, in order to infer the most likely constitutive equation. The GP prediction for the constitutive relation can then be used within macro-scale flow simulations, allowing us to update the stresses in the fluid in manner which satisfies the dynamics of the underlying microscopic model. We tested the method on a simple microscopic model (non-interacting Hookean dumbbells) and successfully recovered the exact constitutive relation. The resulting macroscopic flow simulations give the same level of accuracy as Multi-Scale descriptions at a small fraction of the cost [1].

[1] N. Seryo, T. Sato, J. J. Molina, T. Taniguchi, Phys. Rev. Res. 02, 33107 (2020)