Graph neural network based model of hydrodynamic closure laws in non-spherical particle–laden flows

We introduce a deep neural network framework that combines machine learning with domain knowledge to model particle–laden flows, specifically focusing on suspensions of non-spherical polyhedral particles. Building upon our flow configuration knowledge, our model leverages Graph Neural networks (GNNs) to capture the intricate spatial, geometrical and relational interactions between particles. The particles are represented as nodes in a directed graph, with pairwise interactions encoded as directed edges, capturing both the local microstructure and inherent symmetries of the flow configuration. A multi-layer perceptron (MLP) function is employed for message passing, and a multi-headed attention mechanism is integrated to weigh the importance of neighboring nodes and edge features in the aggregation process. We define the directed edges between the nodes using the incidence function ψ G such that the k th nearest neighbors of each particle v i are identified using the neighborhood defined by N k ( v i ) and we test different values of k to assess the impact of varying the number of neighbors. The convergence of predictions improves with an increasing number of neighbors ( k ), highlighting the importance of refining the neighborhood structure for better model performance. Our results demonstrate the effectiveness of the GNN in predicting streamwise drag forces, with R 2 values consistently exceeding 0.90 for Δ F x , and exceeding 0.80 for transverse lift force Δ F y and torque Δ T z at all κ values for low R e and ϕ . However, the model’s performance decreases as R e and ϕ increase, particularly for transverse forces and torques. We show that the GNN outperforms the literature-reported models that lack incorporation of local physical properties as input parameters and provides comparable or superior performance to Convolutional Neural Networks (CNNs), even when local velocity is included. The GNN excels in capturing the complex interactions in particle suspensions, whereas CNNs struggle unless local physical properties are incorporated. Our findings also highlight the challenges faced by the GNN in predicting hydrodynamic forces and torque at high Reynolds numbers and high particle angularity. Despite these challenges, the study suggests that integrating domain knowledge with hybrid algorithms, such as GNNs and CNNs, could improve model accuracy and robustness, particularly in scenarios with limited data. This approach holds promise for addressing the complexities of particle–laden flows, offering a more adaptable and predictive framework for suspensions with varying configurations and flow conditions.

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