Multi-fidelity modeling to predict the rheological properties of a suspension of fibers using neural networks and Gaussian processes

Abstract

Unveiling the rheological properties of fiber suspensions is of paramount interest to many industrial applications. There are multiple factors, such as fiber aspect ratio and volume fraction, that play a significant role in altering the rheological behavior of suspensions. Three-dimensional (3D) numerical simulations of coupled differential equations of the suspension of fibers are computationally expensive and time-consuming. Machine learning algorithms can be trained on the available data and make predictions for the cases where no numerical data are available. However, some widely used machine learning surrogates, such as neural networks, require a relatively large training dataset to produce accurate predictions. Multi-fidelity models, which combine high-fidelity data from numerical simulations and less expensive lower fidelity data from resources such as simplified constitutive equations, can pave the way for more accurate predictions. Here, we focus on neural networks and the Gaussian processes with two levels of fidelity, i.e., high and low fidelity networks, to predict the steady-state rheological properties, and compare them to the single-fidelity network. High-fidelity data are obtained from direct numerical simulations based on an immersed boundary method to couple the fluid and solid motion. The low-fidelity data are produced by using constitutive equations. Multiple neural networks and the Gaussian process structures are used for the hyperparameter tuning purpose. Results indicate that with the best choice of hyperparameters, both the multi-fidelity Gaussian processes and neural networks are capable of making predictions with a high level of accuracy with neural networks demonstrating marginally better performance.

Rheology of bi-disperse dense fiber suspensions

“…11 Moreover, the rheological properties of these suspensions are complex and heavily dependent on several variables, including suspending fluid properties, fiber size distribution, shape, flexibility, roughness, and volume fractions. [12][13][14][15][16][17][18][19][20][21] Even though fiber size distributions are more commonly encountered in the applications and natural environments stated above than mono-disperse suspensions, the role of bi-or poly-dispersity on the rheology of fiber suspensions is limited in the literature.…”

“…25,26 Recently, we have developed a numerical model by incorporating short-range interactions via attractive and repulsive interactions and contact interactions in the dense fiber suspension. 12–14,27 The model presented in this study effectively describes the rheological characteristics of dense fiber suspensions as found in experimental settings. 19,20 These characteristics include the existence of a yield stress, shear thinning rheology, and normal stress differences.…”

Prediction of Proppant Settling Velocity in Fiber-Containing Fracturing Fluids

“…Shaqfeh and Fredrickson 11 analyzed the relationship between the fiber-added viscosity and fluid viscosity by studying the influence of the fiber orientation distribution on the constitutive equation of the suspension. Boodaghidizaji et al 12 studied the rheological behavior of the suspension of fibers using single-fidelity and multi-fidelity Gaussian processes and neural networks. Khan et al 13 present a constitutive model for frictional fiber suspensions in a steady shear flow.…”