基于物理约束GRU神经网络的河流水质预测模型

A Physics-Constrained GRU Neural Network for River Water Quality Prediction

河流水质预测对于水环境管理与水污染防治具有重要意义。近年来,以神经网络为代表的非机理性水质预测模型已被广泛应用于河流水质预测领域。然而,此类模型不考虑水质因子变化的物理机理,导致预测结果难以解释、稳定性差。为此,本文将水质因子变化的物理规律视为一种先验知识约束,建模于门控循环单元神经网络(Gated Recurrent Unit,GRU)之中,以河流水质预测的重要参数溶解氧为例,提出了一种物理约束的门控循环单元网络(Physics-constrained Gated Recurrent Unit,PHY_GRU)。以美国亚特兰大市2021年河流溶解氧预测为例进行实例验证,结果表明:(1)PHY_GRU与差分自回归移动平均模型、多层感知机和门控循环单元模型相比,预测精度和稳定性明显提升,其中预测均方根误差分别降低了94.8%,62.9%和37.2%;(2)综合考虑多种物理规律约束可以提升PHY_GRU的预测精度和稳定性;(3)PHY_GRU采用门控循环单元模型训练样本的30%,其预测精度和稳定性即可超过门控循环单元模型。本文提供了一种在神经网络模型中融入水质先验知识的研究思路,有助于提升水质预测模型辅助决策的水平。

River water quality prediction plays a key role in water environment management and water pollution prevention.In recent years,artificial neural networks have been widely used in river water quality prediction.However,the lack of physical mechanism becomes a major limitation of artificial neural networks.As a result,the prediction results obtained by artificial neural networks are usually difficult to interpret and are unstable.To overcome this limitation,this study proposed a physics-constrained Gated Recurrent Unit model(PHY_GRU)for predicting dissolved oxygen in rivers.Specifically,two kinds of physical rules were identified,i.e.,the rule of monotonicity and the rule of gradation.These physical rules were modeled as the loss functions of Gated Recurrent Unit(GRU).The water quality dataset in Atlanta,USA was used to evaluate the performance of the PHY_GRU.The experimental results show that:(1)Compared with autoregressive integrated moving average,multilayer perceptron,and GRU model,the prediction accuracy and stability of PHY_GRU were the highest(the root mean square error of prediction was reduced by 94.8%,62.9%and 37.2%,respectively);(2)the PHY_GRU performed best when different physical rules were considered simultaneously;(3)When PHY_GRU used 30%of the training samples of GRU,it could outperform GRU in terms of prediction accuracy and stability.The proposed PHY_GRU effectively incorporates physical mechanism into artificial neural networks and may be helpful for water management.