Graph neural network for multitask prediction of rheological and microstructural behavior in suspensions

TL;DR

This work tackles the challenge of predicting dense suspension rheology near discontinuous shear thickening and shear jamming by learning from microstructural topology rather than explicit forces. It introduces a multitask Deep Graph Convolutional Network that jointly predicts the relative viscosity $η_r$, particle pressure $Π$, and frictional coordination number $Z_μ$ from graph representations of particle configurations, trained on 2D LF-DEM simulation data across a range of packing fractions and stresses. The model achieves high accuracy (up to $R^2 ≈ 0.99$ for many conditions) and remains robust to system size, providing a computationally efficient mesoscale surrogate capable of real-time exploration of structure–property relationships in dense suspensions. This approach highlights a path toward geometry-driven, data-efficient predictions that could extend to other particulate and soft-matter systems such as gels, enabling rapid design and control in complex flow regimes.

Abstract

Fast prediction of suspension rheology is fundamental for optimizing process efficiency and performance in numerous industrial settings. However, traditional simulations are computationally demanding due to explicit evaluation of contact networks and stress tensors in dense regimes approaching shear thickening and jamming. This study presents a microstructure-informed multitask learning framework based on the graph neural network (GNN) that learns an implicit mapping between particle configurations and emergent microstructural and rheological properties of suspensions. This model simultaneously predicts particle pressure $Π$, viscosity $η$, and friction coordination $Z_μ$, in a dynamic steady-state, without explicit knowledge of interparticle forces. Here, semi-dilute to dense suspension systems in 2D were simulated across a wide range of shear stresses $σ$, spanning continuous, discontinuous shear thickening, and shear-jamming conditions. The trained models demonstrated high correlation coefficients ($R^2$ = 0.99) with narrow mean absolute error for packing fractions up to $φ\le φ_J^μ$ for all predictive targets. However, prediction scatter increases near jamming conditions, attributed to inherent fluctuations in suspension behavior as the critical packing fraction is approached, yet predictions remain in excellent agreement, closely following the trend of the simulated flow curves across stress evolution. Once trained, the model can infer rheological responses directly from structural topology, avoiding explicit stress evaluation during prediction. The approach yields computationally efficient mesoscale surrogates for accelerated simulation with potential for real-time exploration of particulate suspension behavior.

Figures (6)

• Figure 1: Schematic illustration of the machine learning methodology. Schematic for the simulation, training process and multitask prediction of viscosity $\eta$, particle pressure $\Pi$, and frictional coordination number $Z_\mu$ employing Deep Graph Convolutional Neural Network (DeepGCN). Simulations were conducted through the LF-DEM method to generate configurations, which were then transformed into graphs for input into the graph neural network (GNN), where particle features and the interparticle interactions are represented by node features and edge attributes, respectively. The datasets consist of particle radius as node feature ($h_u$) and relative distance between particles ($R_\text{ij}$), x and y components of $R_\text{ij}$, sine and cosine of $R_\text{ij}$ between particles as edge attributes ($e_\text{vu}$). Next, the datasets were divided into 5 folds, where at each iteration, four folds were used for training and the remaining fold was reserved for validation. Then, the datasets are processed into the residual graph convolution layers (ResGCN) to update node features through exchanging information between nodes and their neighboring edges for the specific particle. The output of each layer was normalized and was subjected to a non-linear activation function (ReLU) to improve the complexity and capacity of the model to capture hidden interparticle relationships. This process is repeated for the number of layers, and finally, a linear layer predicts the properties of each graph through three outputs.
• Figure 2: Rheological and microstructural response under shear. Rheological and microstructural behavior of suspensions for packing fractions $\phi = 0.70-0.80$. (a) Viscosity $\eta$ as a function of shear stress $\sigma_\text{xy}$, (b) viscosity $\eta$ vs shear rate $\dot{\gamma}$, (c) particle pressure $\Pi$, and (d) frictional coordination number $Z_\mu$ vs $\sigma_\text{xy}$.
• Figure 3: Heterogeneity in simulated data sets. Density plots and marginal distributions to visualize the heterogeneity of the datasets and the relationship of the targets used to train the models. The viscosity $\eta$, particle pressure $\Pi$ are plotted as a function of frictional coordination number $Z_\mu$ for (a) $\phi =$ 0.70, (b) 0.76, and (c) 0.80.
• Figure 4: Comparison between simulations and machine learning predictions. Actual vs predictions of relative viscosity $\eta_r$, particle pressure $\Pi$, and frictional coordination number $Z_\mu$ by multitask regression based on DeepGCN for packing fractions (a-c) $\phi = 0.70$, (d-f) 0.76, and (g-i) 0.80. The red markers depict tested examples, the solid black line and the blue dashed lines represent the ideal, and $\pm15\%$ error margin.
• Figure 5: Multitask learning performance. Performance of multitask learning using DeepGCN with averaged correlation coefficient $R^2$ and mean absolute error (MAE) distribution between actual and predicted value for relative viscosity $\eta_r$ (a and d), particle pressure $\Pi$ (b and e), and frictional coordination number $Z_\mu$ (c and f) for packing fractions $\phi =$ (a-b) 0.70, (d-f) 0.76, and (g-i) 0.80.