This study presents two different machine learning approaches for the modeling of hydrodynamic force on particles in a particle-laden multiphase flow. Results from particle-resolved direct numerical simulations (PR-DNS) of flow over a random array of stationary particles for eight combinations of particle Reynolds number ($Re$) and volume fraction ($\phi$) are used in the development of the models. The first approach follows a two step process. In the first flow prediction step, the perturbation flow due to a particle is obtained as an axisymmetric superposable wake using linear regression. In the second force prediction step, the force on a particle is evaluated in terms of the perturbation flow induced by all its neighbors using the generalized Faxen form of the force expression. In the second approach, the force data on all the particles from the PR-DNS simulations is used to develop an artificial neural network (ANN) model for direct prediction of force on a particle. Due to the unavoidable limitation on the number of fully resolved particles in the PR-DNS simulations, direct force prediction with the ANN model tends to over-fit the data and performs poorly in the prediction of test data. In contrast, due to the millions of grid points used in the PR-DNS simulations, accurate flow prediction is possible, which then allows accurate prediction of particle force. This hybridization of multiphase physics and machine learning is particularly important, since it blends the strength of each, and the resulting pairwise interaction extended point-particle (PIEP) model cannot be developed by either physics or machine learning alone.

中文翻译：

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使用机器学习和成对相互作用扩展点粒子 (PIEP) 近似在多相流的欧拉-拉格朗日模拟中实现粒子分辨精度

这项研究提出了两种不同的机器学习方法，用于模拟载有颗粒的多相流中颗粒的流体动力。对于粒子雷诺数 ($Re$) 和体积分数 ($\phi$) 的八种组合，在静止粒子的随机阵列上流动的粒子分辨直接数值模拟 (PR-DNS) 的结果用于开发楷模。第一种方法遵循两步过程。在第一个流动预测步骤中，使用线性回归将粒子引起的扰动流作为轴对称叠加尾流获得。在第二个力预测步骤中，使用力表达式的广义 Faxen 形式，根据所有相邻粒子引起的扰动流评估粒子上的力。在第二种方法中，来自 PR-DNS 模拟的所有粒子的力数据用于开发人工神经网络 (ANN) 模型，用于直接预测粒子上的力。由于 PR-DNS 模拟中完全解析粒子数量的不可避免的限制，使用 ANN 模型的直接力预测往往会过度拟合数据并且在测试数据的预测中表现不佳。相比之下，由于 PR-DNS 模拟中使用了数百万个网格点，因此可以进行准确的流动预测，从而可以准确预测粒子力。这种多相物理学和机器学习的混合尤其重要，因为它融合了各自的力量，并且由此产生的成对相互作用扩展点粒子 (PIEP) 模型不能单独通过物理学或机器学习来开发。