Data-driven physics-informed constitutive metamodeling of complex fluids: A multifidelity neural network (MFNN) framework

Abstract

In this work, we introduce a comprehensive machine-learning algorithm, namely, a multifidelity neural network (MFNN) architecture for data-driven constitutive metamodeling of complex fluids. The physics-based neural networks developed here are informed by the underlying rheological constitutive models through the synthetic generation of low-fidelity model-based data points. The performance of these rheologically informed algorithms is thoroughly investigated and compared against classical deep neural networks (DNNs). The MFNNs are found to recover the experimentally observed rheology of a multicomponent complex fluid consisting of several different colloidal particles, wormlike micelles, and other oil and aromatic particles. Moreover, the data-driven model is capable of successfully predicting the steady state shear viscosity of this fluid under a wide range of applied shear rates based on its constituting components. Building upon the demonstrated framework, we present the rheological predictions of a series of multicomponent complex fluids made by DNN and MFNN. We show that by incorporating the appropriate physical intuition into the neural network, the MFNN algorithms capture the role of experiment temperature, the salt concentration added to the mixture, as well as aging within and outside the range of training data parameters. This is made possible by leveraging an abundance of synthetic low-fidelity data that adhere to specific rheological models. In contrast, a purely data-driven DNN is consistently found to predict erroneous rheological behavior.

Probing the Rheological Properties of Liquids Under Conditions of Elastohydrodynamic Lubrication Using Simulations and Machine Learning

“…Studies have demonstrated that ML methods can classify conformations of polymer chains and characterize structural relaxations in glassy materials [37,49,50]. However, with the exception of a few recent developments [51], there is a lack of utilization of ML techniques in examining the rheological behavior of liquids. The application of ML methods in the specific context of NEMD simulations related to tribological applications has not been explored to the best of our knowledge.…”

Rheology-Informed Neural Networks (RhINNs) for forward and inverse metamodelling of complex fluids

“…With an ever-increasing computational power and the ability to process large data sets, data-driven models have become indisputable and powerful tools. With a limited number of studies utilizing ML algorithms 33 – 36 , the field of soft matter and more specifically rheology is lagging behind in leveraging such advanced methodologies. This is partially due to the ambiguous consequences of the produced meta-models and their adherence to the fundamental underlying physics.…”

“…In the case with unknown governing laws, the pathway to embedding the physical laws into the training process has to change accordingly. One such method would be to introduce the physical intuition to the NN implicitly and by means of physics-based synthetic data, generated from constitutive laws 33 .…”

Applying physics-based loss functions to neural networks for improved generalizability in mechanics problems

“…Of these fields this work is primarily interested in the development and use of PINNs [28,29,30,31,32,33,34,26,35,36,37,38,39]. The approach in PINNs is to use as an input-output pair to the neural network a fundamental variable, or set of variables for the physical problem, and use these variables to construct the quantities that appear in the governing equation of motion, such as the velocity and pressure fields in a fluids problem.…”