Coupling Machine Learning Into Hydrodynamic Models to Improve River Modeling With Complex Boundary Conditions

Abstract

However, rivers, especially those with complex hydrological boundary conditions, are prone to flood disasters (J. Xia & Chen, 2021). Modeling the river hydrodynamic variation helps to quickly grasp or even forecast the hydrological regime of rivers under changing environment. It is an effective technical means to strengthen water security assessment and water resources management, and convenient for decision makers to develop response plans in time.There are many methods for numerical modeling of rivers with complex boundaries like typical lake-connected rivers (

A Deep Learning Approach Based on Physical Constraints for Predicting Soil Moisture in Unsaturated Zones

“…Physics‐informed deep learning methods exhibit higher accuracy than PM and LSTM in several test scenarios (Sections 3.1‐3.4), and the reasons for this performance improvement may include the following: The loss function points the way to the training and optimization process of deep learning; the ordinary deep learning method (LSTM) establishes a fit to the mapping relationship between input and output (Huang et al., 2022; Xiang et al., 2020), where the loss function only considers the numerical deviation of the data itself. The loss function of PIDL however, compared to the ordinary deep learning, is modified and updated.…”

“…Examples are Gate Recurrent Unit (GRU) (Huang et al., 2022), Restricted Boltzmann Machine (RBM) (Xing et al., 2022), Convolutional Neural Network (CNN) (Mo et al., 2017, 2019), Multilayer Perceptron (MLP) (Vincent De Paul Adombi et al., 2022), and Random Forests (RF) (Zahura et al., 2020). In addition, the physical constraints used in combining the two different driving methods can be replaced according to the specific context of the different research problems and applied to other areas of hydrological research, such as replacing the core physical process from the water balance principle and Richard's equation in this study with similar elements in other problems, such as the Navier‐Stokes equation，the heat transport equation, the basic differential equation for groundwater seepage, and the Saint‐Venant equation for river flow, to solve other problems accordingly (Huang et al., 2022; Kamrava et al., 2021; Ma et al., 2022; Read et al., 2019; Vincent De Paul Adombi et al., 2022; Xie et al., 2022). All of these hybrid modeling implementations use a framework similar to the PIDL in this study to achieve the combination of physical constraints and deep learning and obtain good results, confirming the generalizability of this combined framework in the field of hydrological research.…”

“…The underlying theory‐driven model for deep learning does not only need to be LSTM (Cho & Kim, 2022; Read et al., 2019; Xie et al., 2022; Xing et al., 2022) but can also be replaced with other machine learning or deep learning methods validated and applied in the field of hydrology under different demand scenarios. Examples are Gate Recurrent Unit (GRU) (Huang et al., 2022), Restricted Boltzmann Machine (RBM) (Xing et al., 2022), Convolutional Neural Network (CNN) (Mo et al., 2017, 2019), Multilayer Perceptron (MLP) (Vincent De Paul Adombi et al., 2022), and Random Forests (RF) (Zahura et al., 2020). In addition, the physical constraints used in combining the two different driving methods can be replaced according to the specific context of the different research problems and applied to other areas of hydrological research, such as replacing the core physical process from the water balance principle and Richard's equation in this study with similar elements in other problems, such as the Navier‐Stokes equation，the heat transport equation, the basic differential equation for groundwater seepage, and the Saint‐Venant equation for river flow, to solve other problems accordingly (Huang et al., 2022; Kamrava et al., 2021; Ma et al., 2022; Read et al., 2019; Vincent De Paul Adombi et al., 2022; Xie et al., 2022).…”

“…The uncertainty brought by the physical mechanisms is the parameter uncertainty, and for the three physical mechanisms of PIDL, the Richard equation involves some parameters of soil-and water-related properties, which are fitted by the VG formulation, and this fitting method can reduce the parameter uncertainty as low as possible when using a large amount of in situ monitoring data (Gao et al, 2019;Li et al, 2023;Ma et al, 2019Ma et al, , 2023Zhang et al, 2016;Zhao et al, 2020). Uncertainty from raw data, on the other hand, is due to the unavoidable noise in the data collection process and objective errors (truncation error, rounding error) during processing, which belong to chance uncertainty, and this part of uncertainty can usually be reduced by maximizing the accuracy of observations and quantity of data (Huang et al, 2022;Hüllermeier & Waegeman, 2021). The data in this study are derived from high-frequency, high-precision in situ monitoring, which can largely reduce this part of uncertainty.…”

“…The data in this study are derived from high-frequency, high-precision in situ monitoring, which can largely reduce this part of uncertainty. The uncertainty caused by the model structure is cognitive uncertainty, which comes from the limitations of the model itself, mainly contributed by the number of layers and hyperparameters of the neural network, and this type of uncertainty can be reduced by having more training data and more strategic hyperparameter optimization (Huang et al, 2022;Hüllermeier & Waegeman, 2021;Yang et al al., 2021). The physical constraints added in this study reduce this part of uncertainty.…”