A Deep Learning-Based Method and System for Predicting River Cross-Sectional Flow

Abstract

This invention relates to the field of river flow prediction technology, and more particularly to a method and system for predicting river cross-section flow based on deep learning. The method includes the following steps: acquiring upstream rainfall data, downstream water level data, and meteorological forecast data for a target watershed; aligning the upstream rainfall data, downstream water level data, and meteorological forecast data according to a unified time reference to construct a time-series aligned dataset; constructing a flow prediction model based on the time-series aligned dataset; wherein, the flow prediction model extracts the time-series correlation feature vector between upstream rainfall and downstream water level, identifies the spatial dependency vector between the confluence points of multiple tributaries and the target cross-section, and fuses the time-series correlation feature vector and the spatial dependency vector to output a feature fusion vector. This invention fundamentally overcomes the defect of pure data-driven model prediction results violating basic physical laws, significantly improving the prediction reliability under extreme rainfall events and data-missing scenarios.

Description

Technical Field

[0001] This invention relates to the field of river flow prediction technology, and in particular to a method and system for predicting river cross-section flow based on deep learning. Background Technology

[0002] During torrential rains and floods in small and medium-sized river basins, monitoring personnel need to quickly estimate downstream cross-sectional flows to support flood control scheduling. Traditional hydrological forecasting is mainly based on conceptual hydrological models and physical equations (such as the Saint-Venant equations), relying on precise topographic parameters and boundary conditions. This approach is difficult to implement in complex watersheds and computationally expensive. In recent years, deep learning methods have made significant progress in flow prediction due to their powerful nonlinear fitting capabilities. However, existing purely data-driven models lack physical constraints, and their predictions often violate fundamental physical laws such as mass and momentum conservation, leading to insufficient reliability in rare events or scenarios with missing data. Furthermore, existing technologies fail to fully integrate the temporal correlation between upstream rainfall and downstream water levels with the spatial dependence of multiple tributaries, resulting in limited spatiotemporal feature extraction capabilities. Therefore, there is an urgent need for a flow prediction method that organically integrates deep learning with physical mechanisms to improve prediction accuracy while ensuring consistency with hydrophysical principles, providing more reliable decision support for hydrological monitoring and management. Summary of the Invention

[0003] Therefore, it is necessary for the present invention to provide a method and system for predicting river cross-sectional flow based on deep learning, in order to solve at least one of the above-mentioned technical problems.

[0004] To achieve the above objectives, a deep learning-based method for predicting river cross-sectional flow includes the following steps: Step S1: Obtain upstream rainfall data, downstream water level data, and meteorological forecast data for the target watershed; Step S2: Align the upstream rainfall data, downstream water level data, and meteorological forecast data according to a unified time base to construct a time-series aligned dataset; Step S3: Construct a flow prediction model based on the time-series aligned dataset; wherein, the flow prediction model extracts the time-series correlation feature vector between upstream rainfall and downstream water level, and identifies the spatial dependency vector between the confluence points of multiple tributaries and the target section, and performs feature fusion of the time-series correlation feature vector and the spatial dependency vector to output the feature fusion vector. Step S4: In the training process of the flow prediction model, introduce mass conservation constraints and momentum conservation constraints; Step S5: Using the trained traffic prediction model, generate a second traffic prediction value for the target section in the future for a specified period, and perform physical consistency verification on the second traffic prediction value, outputting prediction data containing the predicted traffic value and the verification result. Step S6: Transmit the predicted data to the hydrological monitoring and management platform via the data interface.

[0005] Preferably, the present invention also provides a deep learning-based river cross-sectional flow prediction system for performing the deep learning-based river cross-sectional flow prediction method described above, the deep learning-based river cross-sectional flow prediction system comprising: The data acquisition module is used to acquire upstream rainfall data, downstream water level data, and meteorological forecast data for the target watershed. The alignment module is used to align upstream rainfall data, downstream water level data, and weather forecast data according to a unified time base to build a time-series aligned dataset. The fusion module is used to build a flow prediction model based on a time-series aligned dataset. The flow prediction model extracts the time-series correlation feature vector between upstream rainfall and downstream water level, and identifies the spatial dependency vector between the confluence points of multiple tributaries and the target section. It then fuses the time-series correlation feature vector and the spatial dependency vector to output a feature fusion vector. The constraint module is used to introduce mass conservation constraints and momentum conservation constraints during the training process of the flow prediction model. The verification module is used to generate a second traffic prediction value for a target section in a specified future time period using the trained traffic prediction model, and to perform physical consistency verification on the second traffic prediction value, outputting prediction data containing the predicted traffic value and the verification result. The push module is used to transmit forecast data to the hydrological monitoring and management platform through a data interface.

[0006] The beneficial effects of this invention are as follows: On the one hand, by introducing mass conservation constraints and momentum conservation constraints during model training, and embedding hydrophysical mechanisms such as the Saint-Venant equations into the neural network loss function, the model is forced to satisfy the theoretical relationship between the continuity equation and the momentum equation while the model is data-driven fitting. This fundamentally overcomes the defect that the prediction results of the pure data-driven model violate the basic physical laws, and significantly improves the prediction reliability in extreme rainfall events and data-missing scenarios.

[0007] On the other hand, by constructing a dual-channel feature extraction architecture of temporal correlation feature vector and spatial dependency relationship vector, it deeply integrates the lag correlation and cumulative effect between upstream rainfall and downstream water level, as well as the multi-dimensional spatial dependencies such as distance, catchment area, and elevation of multiple tributary confluence points, and achieves accurate characterization of the spatiotemporal heterogeneity of rainfall-runoff response in complex watersheds, breaking through the limitations of insufficient spatiotemporal feature extraction capabilities of existing technologies.

[0008] On the other hand, by verifying the physical consistency of the prediction results based on the continuity equation and momentum equation, and by combining historical flow quantile screening and Dropout uncertainty quantification, abnormal prediction values ​​are automatically identified and eliminated, and reliable prediction data with a 95% confidence interval are output. This provides the hydrological monitoring and management platform with decision support that combines high accuracy and physical consistency, effectively meeting the actual needs of rapid flood control and dispatching during rainstorms and floods in small and medium-sized river basins. Attached Figure Description

[0009] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description taken in conjunction with the accompanying drawings: Figure 1 A flowchart illustrating the steps of a deep learning-based method for predicting river cross-section flow is shown in this embodiment.

[0010] Figure 2 A schematic diagram illustrating the trend of river cross-section flow prediction is shown in one embodiment.

[0011] Figure 3 A schematic diagram of a digital elevation model of a target watershed is shown in one embodiment. Detailed Implementation

[0012] The technical method of the present invention will now be clearly and completely described with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0013] Furthermore, the accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. The same reference numerals in the drawings denote the same or similar parts, and therefore repeated descriptions of them will be omitted. Some block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor methods and / or microcontroller methods.

[0014] It should be understood that although the terms "first," "second," etc., may be used herein to describe various units, these units should not be limited by these terms. These terms are used merely to distinguish one unit from another. For example, without departing from the scope of the exemplary embodiments, a first unit may be referred to as a second unit, and similarly, a second unit may be referred to as a first unit. The term "and / or" as used herein includes any and all combinations of one or more of the associated listed items.

[0015] To achieve the above objectives, please refer to Figures 1 to 3 This invention provides a deep learning-based method for predicting river cross-sectional flow, comprising the following steps: Step S1: Obtain upstream rainfall data, downstream water level data, and meteorological forecast data for the target watershed; Step S2: Align the upstream rainfall data, downstream water level data, and meteorological forecast data according to a unified time base to construct a time-series aligned dataset; Step S3: Construct a flow prediction model based on the time-series aligned dataset; wherein, the flow prediction model extracts the time-series correlation feature vector between upstream rainfall and downstream water level, and identifies the spatial dependency vector between the confluence points of multiple tributaries and the target section, and performs feature fusion of the time-series correlation feature vector and the spatial dependency vector to output the feature fusion vector. Step S4: In the training process of the flow prediction model, introduce mass conservation constraints and momentum conservation constraints; Step S5: Using the trained traffic prediction model, generate a second traffic prediction value for the target section in the future for a specified period, and perform physical consistency verification on the second traffic prediction value, outputting prediction data containing the predicted traffic value and the verification result. Step S6: Transmit the predicted data to the hydrological monitoring and management platform via the data interface.

[0016] Preferably, the construction of the traffic prediction model in step S3 includes: Step S31: Based on the time-series aligned dataset, extract the time-series correlation feature vector between upstream rainfall data and downstream water level data. The time-series correlation feature vector includes the cumulative rainfall feature of upstream rainfall, the rate of change feature of downstream water level, and the lag correlation feature between upstream rainfall and downstream water level. In this embodiment, upstream rainfall data and downstream water level data are read from a time-series aligned dataset to construct a bivariate time series analysis framework. A sliding window cross-correlation analysis method is used to calculate cross-correlation function values ​​at multiple lag time points within a 0-48 hour range with a 1-hour step size. A peak detection algorithm automatically identifies the dominant lag time corresponding to the maximum cross-correlation value. After determining the dominant lag time, the 1-hour, 3-hour, 6-hour, 12-hour, and 24-hour sliding cumulative rainfall corresponding to that lag time is calculated to form a multidimensional cumulative rainfall feature vector. Piecewise linear fitting is performed on the downstream water level data to identify rising and falling water level segments. The average slope of each segment is calculated as the water level change rate feature, and auxiliary features such as water level amplitude and average water level within the dominant lag time window are statistically analyzed. All time-series features are standardized and combined to form a time-series correlation feature vector.

[0017] Step S32: Identify the spatial dependency vector between the confluence points of multiple tributaries and the target cross section, wherein the spatial dependency vector includes the distance characteristics between each confluence point of the tributaries and the target cross section, the catchment area characteristics of each confluence point of the tributaries, and the elevation characteristics of each confluence point of the tributaries. In this embodiment, the river centerline is identified from the digital elevation model (DEM), and topological connectivity is verified using water system network data. All tributary inflow points flowing into the target cross-section are automatically identified, and each inflow point is assigned a unique number and its geographical coordinates are recorded. Furthermore, the spatial distance characteristics from each inflow point to the target cross-section are calculated, including the Euclidean straight-line distance and the actual water flow path distance along the river. The path distance calculation considers river curvature and flow direction. Using a watershed watershed analysis algorithm, the area of ​​the sub-basins above each inflow point is calculated and normalized to a percentage weight relative to the total catchment area of ​​the target cross-section. The elevation values ​​between each inflow point and the target cross-section are obtained from the DEM, the elevation difference is calculated, and an average slope index is generated by combining the distance along the river. The spatial characteristics of all tributaries are stored in sub-vector form.

[0018] Step S33: Perform feature fusion between the temporal correlation feature vector and the spatial dependency vector, and output the feature fusion vector through vector concatenation and fully connected layer processing.

[0019] In this embodiment, the temporal correlation feature vector and the spatial dependency vector are directly concatenated along the feature dimension to form a high-dimensional combined feature vector. The concatenation process maintains the order of temporal features first, followed by spatial features. The concatenated high-dimensional vector is input into a fully connected network containing two hidden layers. The first layer has 128 neurons and uses the ReLU activation function to introduce non-linear transformation capability. The second layer has 64 neurons and continues to use the ReLU activation function for feature abstraction. Finally, the output layer generates a fixed-dimensional feature fusion vector, with the dimension set to 32.

[0020] Preferably, extracting the temporal correlation feature vector between upstream rainfall data and downstream water level data includes: Calculate the cross-correlation values ​​of upstream rainfall data and downstream water level data at multiple time lag points, and select the time lag with the largest cross-correlation value as the dominant lag time. In this embodiment, upstream rainfall time series and downstream water level time series are received as inputs. The cross-correlation function values ​​of the two series are calculated with a fixed step size within a preset lag time search range. The search range covers 0 to 48 hours, and the step size is set to 1 hour. The calculation process uses a sliding window mode. For each lag time point, the upstream rainfall series is shifted backward by the corresponding number of hours, aligned with the downstream water level series, and then the correlation coefficient is calculated. The system maintains a cross-correlation value array, recording the correlation coefficient value corresponding to each lag point. The peak detection algorithm traverses this array, locating the global maximum value point by comparing adjacent values; the lag time corresponding to this point is the dominant lag time.

[0021] In one implementation of this invention, it is assumed that the system has acquired hourly rainfall data upstream and hourly water level data downstream for a certain rainstorm event. After the cross-correlation calculation engine is started, starting from lag 0 hours, the rainfall sequence and water level sequence are mismatched and aligned hourly, and the correlation coefficient is calculated, resulting in a cross-correlation value of 0.35 at lag 0 hours. Cross-correlation values ​​are calculated for lags of 1 hour, 2 hours, up to 48 hours, forming a cross-correlation function curve. Analysis shows that when the lag time is 11 hours, the cross-correlation value reaches a peak of 0.82, significantly higher than the correlation coefficients at other lag points. The peak prominence meets the preset minimum threshold requirement, therefore, the dominant lag time is determined to be 11 hours.

[0022] Based on the dominant lag time, the upstream rainfall data is time-shifted, and the cumulative amount of upstream rainfall after shifting within a preset time window is calculated as the rainfall accumulation feature. In this embodiment, multiple preset time window lengths are set, including 1 hour, 3 hours, 6 hours, 12 hours, and 24 hours, each window corresponding to the cumulative rainfall effect at different time scales. The offset rainfall sequence is truncated forward from the end of the dominant lag time as a reference, extracting data segments of the corresponding duration. The hourly rainfall values ​​within each window are summed to obtain the cumulative rainfall feature value for that window. The cumulative values ​​of all windows are arranged in ascending order of time scale, forming a cumulative rainfall feature sub-vector.

[0023] The rate of change of downstream water level data during the dominant lag time is extracted. The rate of change of water level is calculated by the average slope of the rising and falling water levels and is used as a water level response feature. In this embodiment, the inflection points of the water level time series are identified, separating the continuous rising and falling segments. For each rising segment, the linear regression fitting module calculates the slope between the starting and ending points of the segment as the rising rate feature; similarly, each falling segment is processed to obtain the falling rate feature. If there are multiple rising and falling segments within the dominant lag time, the average rate of each segment is calculated separately, and then the overall average is taken as the final water level change rate feature. In addition to the basic change rate, the system also extracts auxiliary features such as water level amplitude, peak time, and rising duration. The rising duration is defined as the time taken from the start of the water level rise to the peak value, and the peak time refers to the offset of the peak value relative to the starting point of the dominant lag time window. After standardization, all water level features are combined in the logical order of change rate, amplitude, duration, and peak time. If the dominant lag time window contains multiple independent flood waves, the features of each flood wave are extracted and their primary and secondary relationships are marked.

[0024] The cumulative rainfall characteristics and water level response characteristics are combined to form a time-series correlated feature vector.

[0025] In this embodiment, the cumulative rainfall feature vector and the water level response feature vector are integrated into a unified temporal correlation feature vector. The combination process adopts a sequential concatenation strategy, prioritizing rainfall-related features, followed by water level-related features.

[0026] Preferably, identifying the spatial dependency vector between the confluence points of multiple tributaries and the target cross-section includes: Acquire digital elevation models and river network data for the target watershed; In this embodiment, please refer to Figure 3 The digital elevation model (DEM) and river network data for the target watershed are retrieved from a geographic information database. The DEM uses raster data format with a spatial resolution of 30 meters, covering the entire target watershed. The river network data uses vector line feature format and includes topological information such as river centerlines, river segment codes, and flow direction attributes.

[0027] Based on the digital elevation model and water system network data of the target watershed, identify the inflow points of all tributaries flowing into the target section; For each tributary confluence point, calculate its straight-line distance and river-side distance from the target cross section, as distance features; In this embodiment, the D8 flow direction algorithm is used to calculate the flow direction of the digital elevation model, determining the water flow direction of each grid cell and generating a flow direction grid. Based on the flow direction grid, the cumulative runoff is calculated to identify confluence points in the river network. Simultaneously, the vector topology of the river network data is parsed to find the endpoints and intersections of all line elements. The confluence points obtained from the grid analysis are spatially matched with the intersection points obtained from the vector analysis; points within a 100-meter distance are considered the same physical confluence point. False confluence points near the watershed boundary are automatically filtered out, retaining only points where actual water flow enters the main channel. Each identified confluence point is assigned a unique identifier, recording its latitude and longitude coordinates, the name of its tributary, and the order of flow, generating a confluence point element layer.

[0028] In another embodiment of the invention, two distance indices are calculated for each tributary confluence point. The straight-line distance is calculated using the spherical distance formula in the geodetic coordinate system, taking into account the Earth's curvature, and output in meters. The river-side distance is based on river network vector data, tracing upstream along the river centerline from the tributary confluence point to the target cross-section, accumulating the lengths of each river segment along the route. The tracing process strictly follows the water flow direction to avoid reverse calculation. For meandering rivers, a line segment approximation method is used, discretizing the river centerline into multiple small segments, calculating the length of each segment, and then summing them. After both distances are calculated, a logarithmic transformation is performed to compress the dimensional differences. The distance features are stored in binary form, with the first element being the logarithmically transformed straight-line distance and the second element being the logarithmically transformed river-side distance. The ratio of the river-side distance to the straight-line distance is calculated and included in the distance features as an indicator of river meandering.

[0029] Calculate the catchment area of ​​each tributary confluence point and normalize it to a percentage of the total catchment area relative to the target cross section, as the catchment area feature; In this embodiment, each tributary's confluence point is considered as its outlet. All grid cells flowing towards that point are traced in reverse to form the tributary's catchment area. The tracing process employs a recursive algorithm, starting from the outlet grid and searching for all cells within an 8-neighborhood flowing towards it, continuously expanding outwards until the watershed boundary. The number of all grid cells within the catchment area is counted and multiplied by the area of ​​each grid cell to obtain the tributary's catchment area. This process is repeated for each tributary to obtain the catchment area values ​​for all tributaries. The catchment areas of all tributaries are summed to obtain the total catchment area of ​​the target cross-section. Normalization is performed by dividing the catchment area of ​​each tributary by the total area and then multiplying by 100 to convert it into a percentage. This percentage directly reflects the contribution weight of each tributary to the target cross-section's area.

[0030] Calculate the elevation difference between each tributary confluence point and the target cross section, and calculate the average slope based on the elevation difference and distance as an elevation feature; In this embodiment, the elevation values ​​of each tributary confluence point and the target cross-section are read from the digital elevation model. The elevation difference is calculated by subtracting the target cross-section elevation from the confluence point elevation to obtain the relative elevation difference; a positive value indicates the confluence point is higher than the target cross-section, and a negative value indicates it is lower. The average slope is calculated by dividing the elevation difference by the distance along the river, rather than the straight-line distance, because the slope along the actual flow path better reflects the hydraulic driving characteristics. The slope calculation results are expressed as a percentage (‰). Additionally, the elevation coefficient of variation is calculated as a supplementary feature by selecting a 3×3 grid window near the confluence point and calculating the ratio of the standard deviation to the mean elevation within the window. All elevation features undergo outlier detection; if the slope value exceeds a reasonable range, a data quality check is triggered. Elevation features are stored in triplets, including elevation difference, average slope, and elevation coefficient of variation.

[0031] The distance characteristics, catchment area characteristics, and elevation characteristics of each tributary confluence point are combined into a spatial feature sub-vector; In this embodiment, the three types of features at each tributary confluence point are integrated into a unified vector representation. A standardized vector structure is defined, with the first two elements representing distance features, the third element representing the percentage of catchment area, and the fourth to sixth elements representing elevation features.

[0032] The spatial feature subvectors of all tributary confluence points are weighted and averaged to output a spatial dependency vector, where the weights are based on the historical flow contribution ratio of each tributary.

[0033] In this embodiment, the daily average flow sequence of each tributary over the past ten years is extracted from the hydrological historical database, and the multi-year average flow value of each tributary is calculated. The average flows of all tributaries are summed to obtain the total average flow, and the average flow of a single tributary is divided by the total average flow to obtain its contribution ratio. The weighting coefficients are updated periodically and recalculated after the flood season each year. During the weighted average calculation, the spatial feature sub-vector of each tributary is multiplied by its weighting coefficient, and then all weighted sub-vectors are summed element-wise to obtain the final spatial dependency vector. The calculation process uses double-precision floating-point numbers to ensure accuracy. After weighted averaging, the system performs L2 norm normalization on the output vector.

[0034] Preferably, the introduction of mass conservation constraints in step S4 includes: The feature fusion vector is predicted using a traffic prediction model, and the first traffic prediction value is output. In this embodiment, the traffic prediction model receives a feature fusion vector as input. The model's forward propagation process includes multiple fully connected layers and non-linear activation functions, ultimately mapping the features to traffic prediction values. During the training phase, each batch of data, after inference by the model, outputs the first traffic prediction value.

[0035] Obtain the first observed water level and the corresponding observed flow rate value corresponding to the first predicted flow rate; In this embodiment, observational data matching the predicted flow rate is retrieved from the hydrological monitoring database. Based on the timestamp corresponding to the predicted value, the measured water level and measured flow rate data for that specific moment are precisely retrieved.

[0036] Based on the preset continuity equation formula, calculate the first theoretical relationship deviation between the first predicted flow rate and the observed water level, and calculate the sum of squares of the first theoretical relationship deviation to output the continuity equation constraint terms. In this embodiment, a theoretical relationship model is established based on hydraulic principles. According to the continuity equation for unsteady flow in an open channel, a theoretical relationship expression between flow rate and water level change is established. During calculation, the first predicted flow rate value and the observed water level value are read and substituted into the theoretical relationship expression to calculate the deviation between them. This deviation reflects whether the law of conservation of mass is satisfied between the predicted flow rate and the actual water level. The deviation calculation adopts an hourly difference form to discretize the continuity equation. The calculated first theoretical relationship deviation is a scalar value; a positive value indicates that the predicted flow rate is too high, and a negative value indicates that it is too low. The deviation value is squared to eliminate the influence of the sign and amplify larger deviations, resulting in the constraint terms of the continuity equation.

[0037] The prediction error term of the model is calculated based on the first predicted flow value and the observed flow value; In this embodiment, the first predicted flow rate and the observed flow rate at the same timestamp are read, and the absolute error or squared error between them is calculated. The absolute error calculation is simple and intuitive, directly reflecting the magnitude of the prediction deviation; the squared error imposes a greater penalty on large deviations. The system defaults to using the squared error form, consistent with the constraint terms of the continuity equation.

[0038] The total loss function is formed by combining the constraint terms of the continuous equation with the prediction error terms of the model in a weighted manner.

[0039] In this embodiment, the constraint terms of the continuity equation and the model prediction error terms are weighted and summed. An adjustable weight coefficient is assigned to each constraint term, and the weight values ​​are set in the training configuration file. The combined calculation uses a linear weighting form, and the sum of the two weighted terms forms the total loss function value.

[0040] Preferably, the momentum conservation constraint introduced in step S4 includes: The predicted flow rate is obtained by performing time difference calculation on the first flow forecast value; In this embodiment, the predicted flow rates for multiple consecutive time periods are arranged in chronological order, and the flow rate change between adjacent time periods is calculated using a first-order backward difference method. The calculated flow rate change rate is expressed in cubic meters per second per hour.

[0041] Calculate the rate of change of the downstream water level at the target section during the preset first time period to obtain the downstream water level gradient; In this embodiment, the downstream water level time series corresponding to the flow prediction period is read, and a difference operation is performed using the same time step as the flow change rate calculation. The water level gradient is measured in meters per hour, with positive values ​​indicating rising water levels and negative values ​​indicating falling water levels. The central difference method is used in the calculation, meaning that the water level gradient at the current moment is determined by the water level values ​​at the two preceding and following moments, reducing the lag caused by unilateral difference. If the first time period is preset to 3 hours, the average water level change rate within this time period is calculated as a representative value.

[0042] Based on the preset momentum equation formula, the second theoretical relationship deviation between the predicted flow rate change rate and the downstream water level gradient is calculated, and the second theoretical relationship deviation is squared to calculate the momentum equation constraint term. In this embodiment, a theoretical relationship model is established based on the equations of motion in the Saint-Venant equations. The predicted flow rate change and downstream water level gradient are read and substituted into a preset momentum equation formula to calculate the theoretical deviation between them. This momentum equation considers the balance between gravity, pressure gradient, and inertial force, and in a simplified form, expresses the flow rate change as proportional to the water level gradient. The calculated second theoretical relationship deviation characterizes the degree to which the prediction result violates momentum conservation. The deviation is calculated as an hourly difference, and the result is a scalar value. The deviation is squared to generate a momentum equation constraint term, which is numerically of the same order as the continuity equation constraint term. The squaring operation amplifies larger deviations, imposing a stronger penalty on predictions that severely violate momentum conservation. The module records the momentum constraint term values ​​for each training sample and calculates the average value within the batch to monitor the satisfaction of momentum conservation. If the momentum constraint term remains consistently high, the system triggers a model structure adjustment or parameter reset mechanism.

[0043] The momentum equation constraint terms are combined with the continuity equation constraint terms and data fitting error terms in the total loss function in a weighted manner to form a multi-constraint joint loss function.

[0044] In this embodiment, the momentum equation constraint terms calculated in the previous step are read, and the continuity equation constraint terms and data fitting error terms are extracted from the total loss function. The weight allocation strategy combines manual setting with adaptive adjustment. The initial weights are defined in the configuration file; the momentum constraint term weight is typically set to 0.4, the continuity equation constraint term weight to 0.6, and the data fitting error term weight to 1.0. The weighted calculation uses a linear superposition method, and the three weighted terms are added together to form a multi-constraint joint loss function.

[0045] Of particular importance, the introduction of mass conservation constraints and momentum conservation constraints in step S4 also includes: If the deviation value of the theoretical relationship of the continuous equation in the current batch of data exceeds the preset threshold, the weight coefficient of the constraint term of the continuous equation will be increased. In this embodiment, the average deviation of the continuity equation for all samples in the current batch is calculated. This deviation reflects the degree to which the predicted flow rate violates the mass conservation law between the observed water level and the predicted flow rate. A preset threshold is set in the training configuration file, and is set to an upper limit within a reasonable range based on the watershed characteristics. The monitor compares the batch average deviation with the preset threshold. If the deviation exceeds the threshold, it indicates that the current model output deviates significantly from physical laws, and the mass conservation constraint needs to be strengthened. At this time, a weight adjustment mechanism is triggered, increasing the weight coefficient of the continuity equation constraint term by a fixed step size of 0.1, with an upper limit of 2.0 for the weight coefficient.

[0046] If the deviation value of the momentum equation theoretical relationship of the current batch of data exceeds the preset threshold, the weight coefficient of the momentum equation constraint term will be increased. In this embodiment, the adaptive weighting mechanism for the momentum equation constraint terms is similar to that of the continuity equation, but the deviation value of the theoretical relationship of the momentum equation is evaluated independently. After each batch, the average deviation of the momentum equation for all samples is calculated. This deviation characterizes the degree to which the predicted rate of change of flow and the downstream water level gradient violate momentum conservation.

[0047] Crucially, a preset threshold is set separately, typically lower than the threshold for the continuous equation, because momentum deviation is more sensitive to model parameters. The monitor continuously tracks the batch-average momentum deviation, and if it exceeds the limit, it immediately initiates a weighting process with a step size of 0.1 and a weight cap of 1.5.

[0048] If the deviation values ​​of the theoretical relationship between the continuity equation and the momentum equation for the current batch of data do not exceed the preset threshold, the weighting coefficients remain unchanged. In this embodiment, the continuity equation deviation and momentum equation deviation are evaluated simultaneously after each batch. Only when both deviations do not exceed their respective preset thresholds is the current batch determined to meet the physical consistency requirements. At this time, the weight adjuster does not perform any increase or decrease operations, keeping the existing weight coefficients unchanged.

[0049] The weighting coefficient can be adjusted between the preset minimum and maximum values.

[0050] In this embodiment, the weights of the continuity equation constraint terms are set to a minimum of 0.2 and a maximum of 2.0, while the weights of the momentum equation constraint terms are set to a minimum of 0.1 and a maximum of 1.5. Before each weight adjustment, the boundary checker reads the current weight value and determines whether increasing the step size will exceed the maximum value or decreasing it will fall below the minimum value. If increasing the step size may cause an out-of-bounds movement, the adjustment is truncated to the maximum value, and a boundary warning is recorded. If decreasing the step size may cause an out-of-bounds movement, the adjustment is truncated to the minimum value.

[0051] Preferably, the physical consistency verification of the second flow prediction value in step S5 includes: Obtain the second observed water level corresponding to the second predicted flow rate; In this embodiment, the system connects to the hydrological monitoring database in real time during the prediction phase and accurately retrieves the synchronously observed water level based on the timestamp corresponding to the second flow prediction value.

[0052] Based on the preset continuity equation formula, the third theoretical relationship deviation of the second observed water level corresponding to the second flow prediction value is calculated; In this embodiment, the second predicted flow rate and the second observed water level are read and substituted into the discrete form of a preset continuity equation. The calculation process considers factors such as cross-sectional shape and water flow compressibility to generate a theoretical flow rate value. This theoretical value represents the flow rate that should occur under the observed water level conditions if mass conservation is strictly satisfied. The absolute difference between the second predicted flow rate value and the theoretical flow rate value is then calculated to obtain the third theoretical relationship deviation. This deviation is expressed in cubic meters per second; a larger value indicates a more severe deviation of the prediction result from physical laws.

[0053] If the deviation of the third theoretical relationship exceeds the preset threshold of the continuous equation, the second flow prediction value will be marked as the first outlier. In this embodiment, the threshold setting is based on the watershed hydraulic characteristics and historical error analysis, with a default value of 10 cubic meters per second. Different thresholds are supported for peak flood periods and calm water periods. The comparator calculates the deviation value at each prediction time. If the deviation exceeds the threshold, an anomaly marking process is immediately triggered. The marking mechanism sets an anomaly flag in the prediction result data structure, setting the flag to 1 to indicate the first anomaly, and simultaneously recording the degree and time of exceeding the threshold.

[0054] The second predicted flow rate is obtained by performing time difference calculation on the second flow rate prediction value; In this embodiment, multiple consecutive predicted flow rates are generated within the prediction period, forming a prediction time series. The rate of change is calculated using the forward differencing method, which involves subtracting the current predicted flow rate from the next predicted flow rate and then dividing by the time interval. The time interval is consistent with the prediction time step and is set to 1 hour. The calculated rate of change is expressed in cubic meters per second per hour, with positive values ​​indicating an increase in predicted flow and negative values ​​indicating a decrease.

[0055] Calculate the rate of change of the downstream water level of the target section in the preset second time period to obtain the second downstream water level gradient; In this embodiment, the downstream water level observation sequence synchronized with the prediction period is read, with a time resolution of hourly. The water level gradient calculation uses the central difference method to improve accuracy, i.e., subtracting the water level of the previous moment from the water level of the next moment and dividing by twice the time interval. A second time period is preset to 3 hours, and the average water level gradient within this period is calculated as a representative value. Before calculation, outlier filtering is performed on the water level data, removing jump points with differences exceeding 0.5 meters from adjacent points. If missing observation data exists, linear interpolation is used to fill in the gaps, but the reliability of the marked filler segments is reduced. The unit of water level gradient is meters per hour.

[0056] Historical flow data of the target section were collected, and the 99th and 1st percentiles of the flow were calculated based on the historical flow data. In this embodiment, historical flow data for the target section is extracted from a long-term hydrological observation database. The data time span is set to the past 10 years to ensure complete coverage of the variation range of wet, normal, and dry years. The raw daily average flow data is cleaned to remove outliers caused by equipment malfunctions and data records marked as abnormal. The cleaned data is sorted in ascending order, and the 99th and 1st quantiles are calculated using linear interpolation. The 99th quantile represents the upper limit of historical flow that is almost impossible to exceed, and the 1st quantile represents the lower limit of historical flow that is almost impossible to fall below. The calculation process uses double-precision floating-point numbers to ensure accuracy, and the results are retained to two decimal places. The system updates the quantile values ​​annually to incorporate the latest observation data.

[0057] If the second flow prediction value exceeds the 99th percentile or falls below the 1st percentile of the historical observed flow, the second flow prediction value will be marked as the second outlier and removed. In this embodiment, after each generation of the second flow prediction value, it is immediately compared with the 99th and 1st quantiles. If the predicted value is greater than the 99th quantile, it indicates an abnormal flood exceeding historical extremes, which is highly unlikely; if the predicted value is less than the 1st quantile, it indicates an unreasonable low flow, which is also unreasonable. Once the comparator detects an outlier, it immediately marks the corresponding predicted value as the second outlier, setting the outlier flag to 2. Unlike the first outlier, the second outlier is directly removed from the prediction result set after being marked. The removal operation is performed in memory, and the result set after removal is reindexed. The first and second outliers are removed from the prediction results.

[0058] Preferably, the predicted data output in step S5 further includes: By enabling the randomness of the Dropout layer in the traffic prediction model, the feature fusion vector is predicted independently multiple times, generating multiple sets of predicted traffic results. In this embodiment, the Dropout layer, which is only enabled during training, is activated during the model inference phase, causing it to randomly deactivate some neurons probabilistically. The number of predictions is set to 100, with the random seed reset before each prediction. The feature fusion vector serves as a fixed input, undergoing different neuron deactivation modes during the 100 forward propagations, generating 100 slightly different traffic prediction values. These prediction values ​​form a prediction result matrix, with each row corresponding to an independent prediction and each column corresponding to the traffic value at different times within the prediction period.

[0059] Statistically analyze the dispersion of multiple sets of predicted flow results and calculate the variance of the predicted flow. In this embodiment, 100 sets of prediction result matrices are read, and the variance is calculated separately for each prediction time. The calculation process uses the sample variance formula: first, the average of the 100 predicted values ​​at that time is calculated; then, the squared deviation of each predicted value from the average is calculated; finally, the sums are obtained and divided by 99 to get the unbiased estimated variance. The variance time series is output, with one variance value corresponding to each time point.

[0060] The mean of multiple predicted flow results is calculated as the central predicted value; In this embodiment, the arithmetic mean of 100 predicted values ​​at each prediction time is calculated to obtain the center predicted value at that time.

[0061] The distribution range of the predicted flow rate is determined based on the mean and variance; In this embodiment, a statistical distribution model for the predicted flow is constructed based on the mean and variance. The system assumes by default that the predicted values ​​follow a normal distribution, with the central predicted value as the distribution mean and the calculated variance as the distribution variance. Based on this assumption, the system determines the distribution range of the predicted flow, taking the mean plus or minus three standard deviations as the theoretical minimum and maximum boundaries. To verify the rationality of the normality assumption, a Shapiro-Wilk normality test is performed on 100 predicted values. If the test result rejects the normality assumption, a non-parametric method is switched, directly using the actual minimum and maximum values ​​of the predicted values ​​as the distribution range. After the distribution range is calculated, discrete sampling points for the probability density function are generated.

[0062] Based on the distribution range, calculate the confidence interval range covering a 95% probability, and output the upper and lower limits of the confidence interval.

[0063] In this embodiment, the two-sided quantile method of the normal distribution is used, with 1.96 times the standard deviation as the half-width. The upper and lower limits of the confidence interval are obtained by adding or subtracting this half-width from the center predicted value. The lower limit is calculated as the mean minus 1.96 times the standard deviation, and the upper limit is the mean plus 1.96 times the standard deviation. The confidence interval time series is calculated independently for each prediction time. The interval width is proportional to the standard deviation; the interval is wider for periods with greater uncertainty. The confidence interval output includes a triplet of the lower limit, upper limit, and center predicted value.

[0064] Preferably, the concatenation operation between the temporal correlation feature vector and the spatial dependency vector includes: Calculate the association strength between each dimension of the spatial dependency vector and the target section; In this embodiment, the spatial dependency vector includes multiple dimensions such as distance characteristics, catchment area characteristics, and elevation characteristics of each tributary, each with varying degrees of influence on the target cross-section flow. A correlation analysis method is used to calculate the Pearson correlation coefficient between each dimension and historical flow data, serving as the initial correlation strength. A sliding window mechanism is employed, with a window length of 30 days, updating the correlation strength value daily. For distance characteristics, the correlation with flow lag is calculated; for catchment area characteristics, the correlation with flow contribution is calculated; and for elevation characteristics, the correlation with flood propagation velocity is calculated. The correlation strength values ​​of all dimensions form the correlation strength vector, with each element ranging from -1 to 1.

[0065] The association strength is transformed into normalized attention weights by using the fully connected layer and the Softmax function in the traffic prediction model, forming an attention weight matrix. In this embodiment, the association strength vector is input into the fully connected layer of the traffic prediction model for transformation. The fully connected layer has 64 hidden neurons and uses the ReLU activation function to perform non-linear mapping on the association strength, extracting deeper feature association patterns. The output of the fully connected layer is fed into a Softmax function, which transforms the association strength of each dimension into a normalized probability distribution, with the sum of all weights being 1. The generated attention weight matrix is ​​in diagonal form, with the main diagonal elements being the attention weights corresponding to each dimension, and the off-diagonal elements being 0. The dimension of the weight matrix is ​​consistent with the dimension of the spatial dependency vector.

[0066] The spatial dependency vector is weighted using an attention weight matrix, and a weighted spatial dependency vector is output. In this embodiment, the attention weight matrix is ​​multiplied by the spatial dependency vector. Element-wise multiplication is used, meaning each dimension of the spatial dependency vector is multiplied by its corresponding attention weight. The weighted vector is then L2-norm normalized to a magnitude of 1.

[0067] The weighted spatial dependency vector is concatenated with the temporal correlation feature vector to form a high-dimensional fused feature vector; In this embodiment, the weighted spatial dependency vector and the temporal correlation feature vector are concatenated along the feature dimension. The concatenation order is defined as temporal features first, followed by spatial features.

[0068] The high-dimensional fused feature vector is reduced in dimensionality by a fully connected layer, and the fused feature vector is output.

[0069] In this embodiment, a fully connected layer is used to compress the high-dimensional fused feature vector. The fully connected layer has 32 output neurons, with a weight matrix of dimension 16×32 and a bias vector of dimension 32. The input 16-dimensional vector is multiplied by the weight matrix and the bias is added, then passed through the ReLU activation function to output a 32-dimensional fused feature vector.

[0070] In this case, a flow prediction model is used to predict the trend of cross-sectional flow in the target watershed over the next year. Please refer to [link to relevant documentation]. Figure 2 The diagram illustrates the changing trend of predicted river cross-section flow over an annual cycle. The horizontal axis represents the time series from January to December, and the vertical axis represents the flow value (unit: cubic meters per second). The diagram shows the predicted flow values ​​for some months, and the overall pattern exhibits typical seasonal fluctuations.

[0071] Preferably, the present invention also provides a deep learning-based river cross-sectional flow prediction system for performing the deep learning-based river cross-sectional flow prediction method described above, the deep learning-based river cross-sectional flow prediction system comprising: The data acquisition module is used to acquire upstream rainfall data, downstream water level data, and meteorological forecast data for the target watershed. The alignment module is used to align upstream rainfall data, downstream water level data, and weather forecast data according to a unified time base to build a time-series aligned dataset. The fusion module is used to build a flow prediction model based on a time-series aligned dataset. The flow prediction model extracts the time-series correlation feature vector between upstream rainfall and downstream water level, and identifies the spatial dependency vector between the confluence points of multiple tributaries and the target section. It then fuses the time-series correlation feature vector and the spatial dependency vector to output a feature fusion vector. The constraint module is used to introduce mass conservation constraints and momentum conservation constraints during the training process of the flow prediction model. The verification module is used to generate a second traffic prediction value for a target section in a specified future time period using the trained traffic prediction model, and to perform physical consistency verification on the second traffic prediction value, outputting prediction data containing the predicted traffic value and the verification result. The push module is used to transmit forecast data to the hydrological monitoring and management platform through a data interface.

[0072] Therefore, the embodiments should be considered as exemplary and non-limiting in all respects, and the scope of the invention is defined by the appended claims rather than the foregoing description. Thus, all variations falling within the meaning and scope of the equivalents of the application are intended to be included within the invention.

[0073] The above description is merely a specific embodiment of the present invention, enabling those skilled in the art to understand or implement the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features of the invention herein.

Claims

1. A method for predicting river cross-sectional flow based on deep learning, characterized in that, Includes the following steps: Step S1: Obtain upstream rainfall data, downstream water level data, and meteorological forecast data for the target watershed; Step S2: Align the upstream rainfall data, downstream water level data, and meteorological forecast data according to a unified time base to construct a time-series aligned dataset; Step S3: Construct a flow prediction model based on the time-series aligned dataset; wherein, the flow prediction model extracts the time-series correlation feature vector between upstream rainfall and downstream water level, and identifies the spatial dependency vector between the confluence points of multiple tributaries and the target section, and performs feature fusion of the time-series correlation feature vector and the spatial dependency vector to output the feature fusion vector. Step S4: In the training process of the flow prediction model, introduce mass conservation constraints and momentum conservation constraints; Among them, the mass conservation constraints include: The feature fusion vector is predicted using a traffic prediction model, and the first traffic prediction value is output. Obtain the first observed water level and the corresponding observed flow rate value corresponding to the first predicted flow rate; Based on the preset continuity equation formula, calculate the first theoretical relationship deviation between the first predicted flow rate and the observed water level, and calculate the sum of squares of the first theoretical relationship deviation to output the continuity equation constraint terms. The prediction error term of the model is calculated based on the first predicted flow value and the observed flow value; The constraint terms of the continuity equation are combined with the model prediction error terms in a weighted manner to form the total loss function; Among them, the momentum conservation constraint includes: The predicted flow rate is obtained by performing time difference calculation on the first flow forecast value; Calculate the rate of change of the downstream water level at the target section during the preset first time period to obtain the downstream water level gradient; Based on the preset momentum equation formula, the second theoretical relationship deviation between the predicted flow rate change rate and the downstream water level gradient is calculated, and the second theoretical relationship deviation is squared to calculate the momentum equation constraint term. The momentum equation constraint terms are combined with the continuity equation constraint terms and data fitting error terms in the total loss function in a weighted manner to form a multi-constraint joint loss function. Step S5: Using the trained traffic prediction model, generate a second traffic prediction value for the target section in the future for a specified period, and perform physical consistency verification on the second traffic prediction value, outputting prediction data containing the predicted traffic value and the verification result. Step S6: Transmit the predicted data to the hydrological monitoring and management platform via the data interface.

2. The deep learning-based river cross-sectional flow prediction method according to claim 1, characterized in that, Step S3, which involves building the traffic prediction model, includes: Step S31: Based on the time-series aligned dataset, extract the time-series correlation feature vector between upstream rainfall data and downstream water level data. The time-series correlation feature vector includes the cumulative rainfall feature of upstream rainfall, the rate of change feature of downstream water level, and the lag correlation feature between upstream rainfall and downstream water level. Step S32: Identify the spatial dependency vector between the confluence points of multiple tributaries and the target cross section, wherein the spatial dependency vector includes the distance characteristics between each confluence point of the tributaries and the target cross section, the catchment area characteristics of each confluence point of the tributaries, and the elevation characteristics of each confluence point of the tributaries. Step S33: Perform feature fusion between the temporal correlation feature vector and the spatial dependency vector, and output the feature fusion vector through vector concatenation and fully connected layer processing.

3. The deep learning-based river cross-sectional flow prediction method according to claim 2, characterized in that, The temporal correlation feature vector between upstream rainfall data and downstream water level data includes: Calculate the cross-correlation values ​​of upstream rainfall data and downstream water level data at multiple time lag points, and select the time lag with the largest cross-correlation value as the dominant lag time. Based on the dominant lag time, the upstream rainfall data is time-shifted, and the cumulative amount of upstream rainfall after shifting within a preset time window is calculated as the rainfall accumulation feature. The rate of change of downstream water level data during the dominant lag time is extracted. The rate of change of water level is calculated by the average slope of the rising and falling water levels and is used as a water level response feature. The cumulative rainfall characteristics and water level response characteristics are combined to form a time-series correlated feature vector.

4. The deep learning-based river cross-sectional flow prediction method according to claim 2, characterized in that, The spatial dependency vectors between the confluence points of multiple tributaries and the target section include: Acquire digital elevation models and river network data for the target watershed; Based on the digital elevation model and water system network data of the target watershed, identify the inflow points of all tributaries flowing into the target section; For each tributary confluence point, calculate its straight-line distance and river-side distance from the target cross section, as distance features; Calculate the catchment area of ​​each tributary confluence point and normalize it to a percentage of the total catchment area relative to the target cross section, as the catchment area feature; Calculate the elevation difference between each tributary confluence point and the target cross section, and calculate the average slope based on the elevation difference and distance as an elevation feature; The distance characteristics, catchment area characteristics, and elevation characteristics of each tributary confluence point are combined into a spatial feature sub-vector; The spatial feature subvectors of all tributary confluence points are weighted and averaged to output a spatial dependency vector, where the weights are based on the historical flow contribution ratio of each tributary.

5. The deep learning-based river cross-sectional flow prediction method according to claim 1, characterized in that, Step S5, which involves verifying the physical consistency of the second flow prediction value, includes: Obtain the second observed water level corresponding to the second predicted flow rate; Based on the preset continuity equation formula, the third theoretical relationship deviation of the second observed water level corresponding to the second flow prediction value is calculated; If the deviation of the third theoretical relationship exceeds the preset threshold of the continuous equation, the second flow prediction value will be marked as the first outlier. The second predicted flow rate is obtained by performing time difference calculation on the second flow rate prediction value; Calculate the rate of change of the downstream water level of the target section in the preset second time period to obtain the second downstream water level gradient; Historical flow data of the target section were collected, and the 99th and 1st percentiles of the flow were calculated based on the historical flow data. If the second flow prediction value exceeds the 99th percentile or falls below the 1st percentile of the historical observed flow, the second flow prediction value will be marked as the second outlier and removed. The first and second outliers are removed from the prediction results.

6. The deep learning-based river cross-sectional flow prediction method according to claim 1, characterized in that, The predicted data output in step S5 also includes: By enabling the randomness of the Dropout layer in the traffic prediction model, the feature fusion vector is predicted independently multiple times, generating multiple sets of predicted traffic results. Statistically analyze the dispersion of multiple sets of predicted flow results and calculate the variance of the predicted flow. The mean of multiple predicted flow results is calculated as the central predicted value; The distribution range of the predicted flow rate is determined based on the mean and variance; Based on the distribution range, calculate the confidence interval range covering a 95% probability, and output the upper and lower limits of the confidence interval.

7. The deep learning-based river cross-sectional flow prediction method according to claim 2, characterized in that, The concatenation operation between temporal correlation feature vectors and spatial dependency vectors includes: Calculate the association strength between each dimension of the spatial dependency vector and the target section; The association strength is transformed into normalized attention weights by using the fully connected layer and the Softmax function in the traffic prediction model, forming an attention weight matrix. The spatial dependency vector is weighted using an attention weight matrix, and a weighted spatial dependency vector is output. The weighted spatial dependency vector is concatenated with the temporal correlation feature vector to form a high-dimensional fused feature vector; The high-dimensional fused feature vector is reduced in dimensionality by a fully connected layer, and the fused feature vector is output.

8. A deep learning-based river cross-sectional flow prediction system, characterized in that, For executing the deep learning-based river cross-sectional flow prediction method as described in claim 1, the deep learning-based river cross-sectional flow prediction system comprises: The data acquisition module is used to acquire upstream rainfall data, downstream water level data, and meteorological forecast data for the target watershed. The alignment module is used to align upstream rainfall data, downstream water level data, and weather forecast data according to a unified time base to build a time-series aligned dataset. The fusion module is used to build a flow prediction model based on a time-series aligned dataset. The flow prediction model extracts the time-series correlation feature vector between upstream rainfall and downstream water level, and identifies the spatial dependency vector between the confluence points of multiple tributaries and the target section. It then fuses the time-series correlation feature vector and the spatial dependency vector to output a feature fusion vector. The constraint module is used to introduce mass conservation constraints and momentum conservation constraints during the training process of the flow prediction model. The verification module is used to generate a second traffic prediction value for a target section in a specified future time period using the trained traffic prediction model, and to perform physical consistency verification on the second traffic prediction value, outputting prediction data containing the predicted traffic value and the verification result. The push module is used to transmit forecast data to the hydrological monitoring and management platform through a data interface.

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