High-velocity aerated flow is a common phenomenon in spillways. Its accurate modelling is challenging, mainly due to the lack of realistic physics in the conventional two-phase models. To this end, this study establishes a population balance model (PBM) approach to account for the evolutionary process of air bubbles. The air-water flow in a stepped chute is examined. The model performance is evaluated by statistical metrics: correlation coefficient (CC), root mean squared error (RMSE), and mean absolute error (MAE). Compared with conventional models, the PBM generates improved air-water predictions. However, the flow parameters are still underestimated, particularly in areas with intense air-water interactions. For further development, an error-corrected PBM (EPBM) is proposed by incorporating machine learning (ML) techniques into the PBM. Compared with the PBM, the EPBM leads to a mean augmentation in velocity prediction by 19.8% for the CC, 73.0% for the RMSE, and 77.1% for the MAE. The gains in air concentration estimation are 2.0%, 67.6% and 73.5%, respectively. The EPBM generates the most accurate results, with 99.6% and 89.6% of the velocity and air concentration predictions within a 20% relative error range. The main contributions are establishing a PBM for air-water flows and developing an error-corrected PBM using ML.

高速充气流是溢洪道中的常见现象。其精确建模具有挑战性，主要是因为传统的两相模型缺乏真实的物理特性。为此，本研究建立了种群平衡模型 (PBM) 方法来解释气泡的演化过程。检查阶梯式滑槽中的空气-水流。模型性能通过统计指标进行评估：相关系数 (CC)、均方根误差 (RMSE) 和平均绝对误差 (MAE)。与传统模型相比，PBM 生成改进的空气-水预测。然而，流动参数仍然被低估，特别是在气水相互作用强烈的地区。为了进一步发展，通过将机器学习 (ML) 技术结合到 PBM 中，提出了一种纠错 PBM (EPBM)。与 PBM 相比，EPBM 导致 CC 的速度预测平均增加 19.8%，RMSE 增加 73.0%，MAE 增加 77.1%。空气浓度估算的增益分别为 2.0%、67.6% 和 73.5%。EPBM 生成最准确的结果，99.6% 和 89.6% 的速度和空气浓度预测在 20% 的相对误差范围内。主要贡献是为空气-水流建立 PBM 并使用 ML 开发纠错 PBM。6% 的速度和空气浓度预测在 20% 的相对误差范围内。主要贡献是为空气-水流建立 PBM 并使用 ML 开发纠错 PBM。6% 的速度和空气浓度预测在 20% 的相对误差范围内。主要贡献是为空气-水流建立 PBM 并使用 ML 开发纠错 PBM。