We harness the physics-informed neural network (PINN) approach to extend the utility of phenomenological models for particle migration in shear flow. Specifically, we propose to constrain the neural network training via a model for the physics of shear-induced particle migration in suspensions. Then, we train the PINN against experimental data from the literature, showing that this approach provides both better fidelity to the experiments, and a novel understanding of the relative roles of the hypothesized migration fluxes. We first verify the PINN approach for solving the inverse problem of radial particle migration in a non-Brownian suspension in an annular Couette flow. In this classical case, the PINN yields the same value (as reported in the literature) for the ratio of the two parameters of the empirical model. Next, we apply the PINN approach to analyze experiments on particle migration in both non-Brownian and Brownian suspensions in Poiseuille slot flow, for which a definitive calibration of the phenomenological migration model has been lacking. Using the PINN approach, we identify the unknown/empirical parameters in the physical model through the inverse solver capability of PINNs. Specifically, the values are significantly different from those for the Couette cell, highlighting an inconsistency in the literature that uses the latter value for Poiseuille flow. Importantly, the PINN results also show that the inferred values of the empirical model's parameters vary with the shear P\'eclet number and the particle bulk volume fraction of the suspension, instead of being constant as assumed in some previous literature.

翻译：我们利用基于物理信息的神经网络（PINN）方法，拓展了剪切流中颗粒迁移唯象模型的适用范围。具体而言，我们通过描述悬浮液中剪切诱导颗粒迁移的物理模型来约束神经网络的训练过程。随后，将PINN与文献中的实验数据对比验证，结果表明该方法不仅能更准确地拟合实验数据，还能揭示假设的迁移通量之间相对作用的新认识。我们首先验证了PINN在环形库埃特流中非布朗悬浮液径向颗粒迁移反问题求解中的有效性。在这一经典案例中，PINN得到的经验模型两个参数比值与文献报道值一致。接着，我们应用PINN方法分析了泊肃叶狭槽流中非布朗和布朗悬浮液的颗粒迁移实验——此类系统的唯象迁移模型此前缺乏明确标定。通过PINN的逆问题求解能力，我们识别出物理模型中的未知/经验参数：具体而言，其数值与库埃特流情形存在显著差异，这揭示了文献中直接将库埃特流参数用于泊肃叶流的不一致性。更重要的是，PINN结果表明，经验模型参数的推断值会随剪切佩克莱数和悬浮液颗粒体积分数变化，而非如部分前人文献假设的恒为常数。