A physics-inspired neural network to model higher order hydrodynamic interactions in heterogeneous suspensions

Abstract

We propose a novel physics-inspired, data-driven framework for modeling particle-laden flows that conceptually overcomes the limitations of conventional methods. By building on the hierarchical model of Siddani and Balachandar (Siddani and Balachandar, 2023), our framework incorporates global and local heterogeneities and integrates higher-order interactions. We leverage machine learning, to first sequentially train neural networks to predict isolated $n$-order interactions for $(N=n)$-body systems. We then feed the information obtained from binary $n=2$, ternary $n=3$ and quaternary $n=4$ interactions to a suspension neural network, with an architecture featuring distinct, shared blocks for each $n$ interaction order and linear activation to integrate interactions of varying orders. Our findings demonstrate significant promise in capturing the hydrodynamic disturbances within suspensions of homogeneous and stepwise heterogeneous test cases. Specifically, our study indicates that the reformulated Quaternary Hierarchical Model (QHM), which incorporates four hierarchical structures (based on unary, binary, ternary, and quaternary interactions), provides promising results in predicting the forces and torques experienced by a reference particle. By varying the number of neighboring particles and interaction orders, the QHM consistently outperforms the Binary and Ternary Hierarchical Models, achieving testing $〈R^2〉$ values of 0.738, 0.752, and 0.829 for streamwise drag force $F_x^i$, transverse lift force $F_y^i$ and transverse torque $T_{\perp }^i$, respectively. Optimizing both the number of neighbors and interaction order is crucial for maximizing the model performance, especially for predicting $F_x^i$. To predict $F_y^i$ and $T_{\perp }^i$, the interaction order with neighboring particles significantly affects performance, with higher-order interactions proving more critical than the number of neighbors. Our results support the generalizability and universality of all proposed model architectures with minimal variation in performance between training and testing across all datasets, as well as for each individual subset.