2021 Volume 35 Issue 3 Pages 426-436
We have recently developed a machine learning method capable of inferring the constitutive equation for the stress of a fluid with memory (e.g., polymeric fluid) from microscopic simulations. For this, we used a Gaussian Process regression scheme to learn the constitutive relation, given as the time-derivative of the stress, as a function of the local stress and velocity strain tensors. Crucially, no assumptions are made regarding the functional form of this relation. We have applied our method to the Hookean dumbbell model, for which the exact analytical constitutive relation (Maxwell equation) is known, in order to validate the approach. Our results are in excellent agreement with the analytical solution, showing that we are able to capture the history dependence of the flow, as well as the elastic effects in the fluid. Compared to full multi-scale simulations, in which the micro and macro degrees of freedom are directly coupled, our method provides a similar degree of accuracy, at a small fraction of the cost. In addition, the method can be easily generalized to more complex and realistic polymer models. (As part of this article, we include a Japanese summary of our main results, published in [7], CC BY 4.0 (https://creativecommons.org/licenses/by/4.0/).)
