Predicting the dynamic behaviors of particles in suspension subject to hydrodynamic interaction (HI) and external drive can be critical for many applications. By harvesting advanced deep learning techniques, the present work introduces a new framework, hydrodynamic interaction graph neural network (HIGNN), for inferring and predicting the particles’ dynamics in Stokes suspensions. It overcomes the limitations of traditional approaches in computational efficiency, accuracy, and/or transferability. In particular, by uniting the data structure represented by a graph and the neural networks with learnable parameters, the HIGNN constructs surrogate modeling for the mobility tensor of particles which is the key to predicting the dynamics of particles subject to HI and external forces. To account for the many-body nature of HI, we generalize the state-of-the-art GNN by introducing higher-order connectivity into the graph and the corresponding convolutional operation. For training the HIGNN, we only need the data for a small number of particles in the domain of interest, and hence the training cost can be maintained low. Once constructed, the HIGNN permits fast predictions of the particles’ velocities and is transferable to suspensions of different numbers/concentrations of particles in the same domain and to any external forcing. It has the ability to accurately capture both the long-range HI and short-range lubrication effects. We demonstrate the accuracy, efficiency, and transferability of the proposed HIGNN framework in a variety of systems. The requirement on computing resource is minimum: most simulations only require a desktop with one GPU; the simulations for a large suspension of 100,000 particles call for up to 6 GPUs.

预测悬浮液中颗粒在流体动力学相互作用 (HI) 和外部驱动下的动态行为对于许多应用来说都是至关重要的。通过收获先进的深度学习技术，目前的工作引入了一个新的框架，即流体动力学交互图神经网络。(HIGNN)，用于推断和预测斯托克斯悬浮液中的粒子动力学。它克服了传统方法在计算效率、准确性和/或可迁移性方面的局限性。特别是，通过将由图表示的数据结构和具有可学习参数的神经网络结合起来，HIGNN 构建了粒子迁移张量的代理建模，这是预测受 HI 和外力影响的粒子动力学的关键。为了解释 HI 的多体特性，我们通过在图中引入高阶连接性和相应的卷积运算来推广最先进的 GNN。对于 HIGNN 的训练，我们只需要感兴趣域中少量粒子的数据，因此可以保持较低的训练成本。建成后，HIGNN 允许快速预测粒子的速度，并且可以转移到同一域中不同数量/浓度的粒子的悬浮液以及任何外力。它具有准确捕获远程 HI 和短程润滑的能力效果。我们展示了所提出的 HIGNN 框架在各种系统中的准确性、效率和可迁移性。对计算资源的要求最低：大多数模拟只需要一个带有一个 GPU 的桌面；对 100,000 个粒子的大型悬浮液的模拟需要多达 6 个 GPU。