While our knowledge of Polymer Physics has greatly evolved over the past century, the complex rheology of non-Newtonian fluids remains an open area of research. In particular, we have yet to fully understand the coupling between the microscopic dynamics of the entangled polymer chains and the macroscopic flow properties of the polymer melt. Multi-scale simulations (MSS), which simultaneously couple both micro and macro degrees of freedom, have been developed to address this issue, but their computational cost has limited them to simple flows and small system sizes. In this talk, we will present a learning strategy capable of inferring the constitutive relation for the stress of polymeric flows with memory. The learned constitutive relation can then be used within macro-scale flow simulations, allowing us to update the stresses in the fluid in a manner which satisfies the dynamics of the underlying microscopic model.

We assume that the constitutive relations can be expressed in differential form, as a function 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. We tested the method on a simple microscopic model (non-interacting Hookean dumbbells) and successfully recovered the exact constitutive relation (i.e., the Maxwell model). The resulting macroscopic flow simulations give the same level of accuracy as MSS at a small fraction of the cost. This opens the door for establishing a bottom-up design framework for polymeric materials. Finally, we will discuss extensions needed to learn the constitutive relation of more complex microscopic polymer models (i.e. the Doi-Takimoto Slip-Link model of entangled polymer melts) as well as applications to other Soft Matter systems (e.g., colloidal dispersions or cellular tissues).

Ref.
Seryo N, Sato T, Molina JJ, and Taniguchi T, Physical Review Research 02, 033107 (2020)
Seryo N, Molina JJ, and Taniguchi T, Nihon Reoroji Gakkaishi (J Soc. Rheol. Jpn.), in press (2021)

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