A General Deep Learning Method for Computing Molecular Parameters of a Viscoelastic Constitutive Model by Solving an Inverse Problem

Abstract

Prediction of molecular parameters and material functions from the macroscopic viscoelastic properties of complex fluids are of great significance for molecular and formulation design in fundamental research as well as various industrial applications. A general learning method for computing molecular parameters of a viscoelastic constitutive model by solving an inverse problem is proposed. The accuracy, convergence and robustness of a deep neural network (DNN)-based numerical solver have been validated by considering the Rolie-Poly model for modeling the linear and non-linear steady rheometric properties of entangled polymer solutions in a wide range of concentrations. The results show that as long as the DNN could be trained with a sufficiently high accuracy, the DNN-based numerical solver would rapidly converge to its solution in solving an inverse problem. The solution is robust against small white noise disturbances to the input stress data. However, if the input stress significantly deviates from the original stress, the DNN-based solver could readily converge to a different solution. Hence, the resolution of the numerical solver for inversely computing molecular parameters is demonstrated. Moreover, the molecular parameters computed by the DNN-based numerical solver not only reproduce accurately the steady viscoelastic stress of completely monodisperse linear lambda DNA solutions over a wide range of shear rates and various concentrations, but also predict a power law concentration scaling with a nearly same scaling exponent as those estimated from experimental results.

Keywords

• machine learning
• inverse problem
• deep neural network
• constitutive equation
• polymeric fluids
• viscoelasticity