We consider non-spherical rigid body particles in an incompressible fluid in the regime where the particles are too large to assume that they are simply transported with the fluid without back-coupling and where the particles are also too small to make fully resolved direct numerical simulations feasible. Unfitted finite element methods with ghost-penalty stabilisation are well suited to fluid-structure-interaction problems as posed by this setting, due to the flexible and accurate geometry handling and for allowing topology changes in the geometry. In the computationally under resolved setting posed here, accurate computations of the forces by their boundary integral formulation are not viable. Furthermore, analytical laws are not available due to the shape of the particles. However, accurate values of the forces are essential for realistic motion of the particles. To obtain these forces accurately, we train an artificial deep neural network using data from prototypical resolved simulations. This network is then able to predict the force values based on information which can be obtained accurately in an under-resolved setting. As a result, we obtain forces which are on average an order of magnitude more accurate compared to the direct boundary-integral computation from the Navier-Stokes solution.

中文翻译：

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使用深层神经网络预测不可压缩流动中欠解析的三角刚体的运动

我们考虑不可压缩流体中的非球形刚体粒子，在这种情况下，粒子太大以至于无法假定它们只是随流体一起运输而没有反向耦合，并且粒子也太小而无法进行完全解析的直接数值模拟可行的。由于具有灵活而准确的几何处理能力，并且允许拓扑发生几何变化，因此，具有重罚稳定性的不适合的有限元方法非常适合此设置引起的流体-结构相互作用问题。在此处提出的计算不足的解决方案中，无法通过力的边界积分公式来精确计算力。此外，由于颗粒的形状，分析定律不可用。然而，力的精确值对于粒子的真实运动至关重要。为了准确地获得这些力，我们使用来自原型解析模拟的数据来训练人工深度神经网络。然后，该网络能够基于在欠解析设置中可以准确获取的信息来预测力值。结果，与从Navier-Stokes解中直接进行边界积分计算相比，我们平均获得的力平均要高一个数量级。