$\mathcal{H}$-HIGNN: A Scalable Graph Neural Network Framework with Hierarchical Matrix Acceleration for Simulation of Large-Scale Particulate Suspensions

Abstract

We present a fast and scalable framework, leveraging graph neural networks (GNNs) and hierarchical matrix ($\mathcal{H}$-matrix) techniques, for simulating large-scale particulate suspensions, which have broader impacts across science and engineering. The framework draws on the Hydrodynamic Interaction Graph Neural Network (HIGNN) that employs GNNs to model the mobility tensor governing particle motion under hydrodynamic interactions (HIs) and external forces. HIGNN offers several advantages: it effectively captures both short- and long-range HIs and their many-body nature; it realizes a substantial speedup over traditional methodologies, by requiring only a forward pass through its neural networks at each time step; it provides explainability beyond black-box neural network models, through direct correspondence between graph connectivity and physical interactions; and it demonstrates transferability across different systems, irrespective of particles' number, concentration, configuration, or external forces. While HIGNN provides significant speedup, the quadratic scaling of its overall prediction cost (with respect to the total number of particles), due to intrinsically slow-decaying two-body HIs, limits its scalability. To achieve superior efficiency across all scales, in the present work we integrate $\mathcal{H}$-matrix techniques into HIGNN, reducing the prediction cost scaling to quasi-linear. Through comprehensive evaluations, we validate $\mathcal{H}$-HIGNN's accuracy, and demonstrate its quasi-linear scalability and superior computational efficiency. It requires only minimal computing resources; for example, a single mid-range GPU is sufficient for a system containing 10 million particles. Finally, we demonstrate $\mathcal{H}$-HIGNN's ability to efficiently simulate practically relevant large-scale suspensions of both particles and flexible filaments.

References in corpus (12)

• Learning to Simulate Complex Physics with Graph Networks
• Self-propelled Worm-like Filaments: Spontaneous Spiral Formation, Structure, and Dynamics
• Spectral Ewald Acceleration of Stokesian Dynamics for polydisperse suspensions
• Fast crystallization of rotating membrane proteins
• A scalable computational platform for particulate Stokes suspensions
• Methods for suspensions of passive and active filaments
• Point-particle drag, lift, and torque closure models using machine learning: hierarchical approach and interpretability
• A spatially adaptive high-order meshless method for fluid-structure interactions
• Colloidal transport by active filaments
• Fast Simulation of Particulate Suspensions Enabled by Graph Neural Network
• Dynamics of flexible filaments in oscillatory shear flows
• A Multigrid Preconditioner for Spatially Adaptive High-order Meshless Method on Fluid-solid Interaction Problems