River underwater topography inversion method

Abstract

The application discloses a river underwater topography inversion method based on a physical information neural network and a bias correction network, and proposes a two-stage inversion framework combining physical driving and data correction. A physical information neural network inversion model is constructed, water level and flow rate data at sparse monitoring points are used for training, a preliminary topography estimation field meeting the fluid mechanics law is obtained by minimizing a physical loss function containing a two-dimensional shallow water equation residual, a bias correction network is constructed, a prior data set containing rich non-Gaussian topography features is used for training, and systematic deviation patterns existing in the preliminary inversion result are learned, the preliminary topography estimation field is input into the trained bias correction network, a topography deviation field is predicted and superimposed and corrected, and finally, high-precision river underwater topography is output. The application realizes dynamic and high-precision reconstruction of complex topography features such as deep pits and sandbars, and provides a reliable dynamic boundary condition updating method for flood forecasting.

Description

Technical Field

[0001] This invention relates to the interdisciplinary fields of water conservancy engineering surveying, computational hydrodynamics and artificial intelligence, specifically to a method for underwater topography inversion of river channels based on physical information neural networks and bias correction networks. Background Technology

[0002] Underwater river topography is fundamental to river dynamics research, flood evolution simulation, and waterway planning. Accurate understanding of riverbed topography distribution is crucial for improving the forecasting accuracy of hydrodynamic models. Traditional sonar mapping is costly and lacks timeliness, making it difficult to capture rapid topographic changes caused by floods. Therefore, inversion methods based on hydrodynamic observation data (such as water level and flow velocity) have become a research hotspot.

[0003] To obtain information about unknown riverbed topography, inversion methods based on hydrodynamic observation data are typically used. Generally, the observation process for an open channel hydrodynamic system can be simply represented as follows:

[0004]

[0005] in, Represents the observation vector (such as water level and flow velocity at sparse monitoring points). This represents the model's input variables (such as upstream flow). This represents the model parameters to be inverted (i.e., the riverbed topographic field). This represents the observation error. (Function) This represents a numerical model operator for simulating the flow dynamics of open channels.

[0006] From a mathematical perspective, river channel topography inversion is a typical Bayesian statistical inference problem. Its goal is to leverage observational data... and numerical model operators Inferring unknown terrain parameters According to Bayes' theorem, the posterior probability distribution of terrain parameters can be expressed as:

[0007]

[0008] in, Let be the posterior probability distribution of the terrain parameters; It is a prior distribution. It is the likelihood function. This represents the marginal likelihood or evidence term of the observed data.

[0009] To solve this problem, an ensemble Kalman smoother ( This is one of the most widely used methods currently. In... In, a file containing is usually generated. The Monte Carlo set of members is used to represent the prior uncertainty of the model parameters. Its core update mechanism is shown in the following equation:

[0010]

[0011] in, and The first The terrain parameters of each set member after update (posterior) and before update (prior). Here is the Kalman gain matrix. For the first The observation perturbation vectors corresponding to each set member are used to characterize the randomness of measurement errors during parameter update. For numerical model operators The predicted output of the prior parameters represents the prediction of the first parameter using the open channel hydrodynamic model. The predicted water level or flow velocity values ​​are obtained by performing forward modeling on a sample of terrain parameters.

[0012] However, the above formula reveals the essential flaw of the traditional method: the Kalman gain matrix K is a linear operator calculated based on covariance. This linear update mechanism implicitly assumes a Gaussian distribution, that is, that the riverbed topography and observation errors both follow a normal distribution.

[0013] However, in actual natural river channels, the terrain is often extremely complex, containing features such as deep pits and sandbars that exhibit significant non-Gaussian characteristics. When faced with such non-Gaussian distribution scenarios, traditional methods based on linear assumptions can lead to the inversion results being "flattened," failing to reconstruct extreme terrain features and thus producing systematic biases.

[0014] Although deep learning methods attempt to replace linear matrices with neural networks However, in the absence of physical constraints, purely data-driven models often produce results that are not "realistic" enough, easily generating outliers that do not conform to actual laws, and are affected by the quality and quantity of data. Although the physically-informed neural networks that have emerged in recent years have introduced physical equation constraints, they are still limited by the nature of neural networks to learn low-frequency features. When dealing with high-frequency terrain changes, they tend to generate smooth solutions and find it difficult to accurately capture the details of steep terrain changes.

[0015] Therefore, there is an urgent need for a hybrid inversion method that can combine physical mechanism constraints with data-driven error correction, while also focusing on high-frequency feature matching, in order to solve the problem of high-precision reconstruction under complex non-Gaussian terrain. Summary of the Invention

[0016] This invention provides a method for underwater topography inversion in river channels based on a physical information neural network and a bias correction network. This method constructs a physical information neural network as the basic topography estimator, uses a two-dimensional shallow water equation set as physical constraints for preliminary inversion, and introduces a data-driven bias correction network to systematically compensate for errors in the preliminary estimation results. Thus, even with sparse observation data, it achieves high-precision reconstruction of riverbed topography containing complex non-Gaussian features. The method includes the following steps:

[0017] 1) Obtain sparse hydrodynamic observation data of the target river section, including data on water level and flow velocity changes over time at several discrete monitoring points;

[0018] 2) Construct a physical information neural network inversion model to establish the mapping relationship between spatiotemporal coordinates and flow field state variables and river topographic parameters;

[0019] 3) The physical information neural network inversion model is trained using the sparse hydrodynamic observation data, and a preliminary terrain estimation field is obtained by minimizing the loss function of physical constraints;

[0020] 4) Construct an additional bias correction network and train it using a pre-built prior dataset containing various known topographic estimation fields and flow field feature maps to learn the systematic bias field distribution characteristics of the river topography (including the learned topographic bias field features).

[0021] 5) Input the preliminary topographic estimation field and flow field characteristic data into the trained bias correction network to predict the topographic bias field; superimpose the topographic bias field with the preliminary topographic estimation field to output the final underwater topographic inversion result of the river channel.

[0022] In practical applications, step 1) is performed first: water level gauges and current meters are deployed at discrete monitoring points in the target river section to acquire water level and flow velocity data that change over time. This observation data serves as the real supervisory signal for training the physical information neural network model, guiding the network to learn the hydrodynamic response characteristics of that specific river section.

[0023] The physical information neural network inversion model in step 2) is constructed as follows:

[0024] The network architecture described uses a fully connected deep neural network as the basic inversion mechanism. The network input is spatiotemporal coordinates. The output includes time-varying hydrodynamic state variables and time-invariant topographic parameters; that is, the output is hydrodynamic state variables (water depth). , Directional flow velocity , Directional flow velocity and riverbed topographic parameters (i.e., riverbed elevation).

[0025] To reflect the time invariance of riverbed topography, the network design will... Set to depend only on spatial coordinates The parameters, or a separate subnetwork specifically for output. This subnetwork only receives As input.

[0026] The preliminary inversion of the physical information neural network inversion model in step 3) is as follows:

[0027] The model is iteratively optimized using the actual observation data obtained in step 1) to obtain a preliminary terrain estimation field that satisfies physical laws. First, a composite loss function is constructed, including a data fitting term and a physical residual term. :

[0028]

[0029] in, The residual loss of the two-dimensional shallow water equation system over the entire domain. This represents the fitting loss between the observed values ​​and the network predictions at sparse monitoring points. These are weighting coefficients used to balance the proportional relationship between the constraint strength of the physical equations and the fitting accuracy of the measured data. This is achieved by minimizing the composite loss function. To achieve the inversion of terrain parameters that satisfy physical laws.

[0030] The PDE residuals are calculated using neural network automatic differentiation techniques. In particular, the bottom slope source term in the momentum equation includes topographic parameters. Spatial derivative:

[0031]

[0032] in, For the bottom slope and friction source terms in the momentum equation in the x-direction; It is the acceleration due to gravity; For the riverbed elevation to be inverted Spatial derivative in the x-direction (i.e., bottom slope term); Let L be the bed shear stress in the x-direction. The inversion of topographic parameters that satisfy physical laws is achieved by minimizing the composite loss function L.

[0033] This step involves retrieving the terrain parameters to be inverted. It is directly coupled into physical constraints, enabling the network to automatically adjust terrain parameters based on the flow field dynamics during training.

[0034] A physical information neural network model is trained using sparse observation data acquired in practice. The Adam optimizer is used for iterative optimization until the loss function converges. At this point, the network output... This is a preliminary estimate of the riverbed elevation that satisfies the physical laws.

[0035] The loss function of the physical constraints consists of a data fitting term and a residual term of the governing equation;

[0036] The residual terms of the governing equations are constructed based on a two-dimensional shallow water equation system, including the continuity equation residuals and the momentum equation residuals. When calculating the residuals, the automatic differentiation technique inherent in the neural network is used to calculate the partial derivatives of the network output with respect to the input coordinates, and the riverbed elevation is then used as the basis for these calculations. The spatial derivative is substituted into the bottom slope source term in the momentum equation for calculation.

[0037] The bottom friction stress term in the two-dimensional shallow water equation set is calculated using the Manning formula, with the following specific form:

[0038]

[0039]

[0040] in, and for and Frictional stress on the bottom surface in the direction of the direction For fluid density, It is the acceleration due to gravity. The roughness coefficient is Manning's coefficient. , For flow rate, The water is deep.

[0041] The construction and training of the bias correction network in step 4) are as follows:

[0042] The deviation correction network employs a fully convolutional neural network and a U-Net architecture to establish an end-to-end mapping from the "preliminary terrain estimation field + flow field features" to the "terrain deviation field". The construction process of the prior dataset includes: generating a large number of virtual riverbed terrain samples with non-Gaussian distribution characteristics using a random field generation algorithm; performing forward modeling on the virtual samples using a numerical model to generate virtual observation data; using a physical information neural network to invert the virtual observation data to obtain the virtual preliminary terrain; and calculating the difference between the virtual preliminary terrain and the real virtual terrain as training label data.

[0043] Specifically, the bias correction network is trained using a pre-constructed prior dataset. The construction process of the prior dataset includes: first, generating a large number of virtual riverbed elevation field samples simulating different geomorphic features using a random field generation algorithm; second, obtaining corresponding virtual observation data through forward simulation using a numerical model and superimposing noise; and finally, performing preliminary inversion on the virtual data using a physical information neural network model, and using the difference between the inversion result and the real virtual terrain as bias label data for offline training of the bias correction network.

[0044] The offline training refers to the offline supervised learning of the deviation correction network using the "virtual preliminary terrain - terrain deviation label" dataset generated in step 1). The loss function uses pixel-level mean squared error. Through training, the network learns to identify common systematic error patterns in the physical information neural network inversion results.

[0045] For step 5), after completing the pre-training of the aforementioned model, online terrain correction and result output are performed.

[0046] Specifically, in practical applications, the optimized physical information neural network model is first run to obtain a preliminary topographic estimate of the target river segment that satisfies physical laws. Subsequently, the preliminary terrain estimate is input into the pre-trained bias correction network, which utilizes the forward inference characteristics of neural networks to quickly predict the corresponding terrain bias field. Finally, through calculation The results are synthesized and output high-precision underwater topographic inversion results of river channels that can accurately reproduce high-frequency geomorphic features such as scour pits and sandbar edges.

[0047] Furthermore, this invention also provides the application of the above-mentioned underwater topography inversion method based on physical information neural networks and bias correction networks for river topography monitoring, flood forecast boundary condition updates, and waterway maintenance monitoring. It is particularly suitable for complex topographic features with non-Gaussian distributions. This invention's method can be used to acquire the underwater topographic distribution of complex river channels in real time when large-scale direct mapping is not feasible.

[0048] The present invention also provides a computer-readable storage medium having a computer program stored thereon, which, when executed by a processor, implements the underwater topography inversion method for river channels based on a physical information neural network and a deviation correction network as described in the present invention.

[0049] Preferably, when the computer program runs the inversion method, it performs hot-start optimization using preset historical weight parameters to improve the convergence speed of online computation.

[0050] A river topography monitoring system is also provided, including:

[0051] 1) Data acquisition module, used to collect water level and flow velocity data of river cross-section in real time;

[0052] 2) A calculation module is used to run the underwater topography inversion method of the river channel based on the physical information neural network and the bias correction network of the present invention, and output the current underwater topography distribution map of the river channel; preferably, when running the inversion method, the calculation module performs hot start optimization through preset historical weight parameters to improve the convergence speed of online calculation.

[0053] 3) Update module, used to update the boundary condition parameters in the flood forecasting model based on the underwater topographic distribution map of the river channel obtained by inversion.

[0054] This invention can extract topographic feature information from sparse hydrodynamic observation data and achieve high-precision topographic inversion by combining physical laws and prior data. The advantages of this invention are: by introducing a physical information neural network and using hydrodynamic equations as soft constraints, it solves the inversion problem under sparse data; by introducing a bias correction network, it effectively compensates for the smoothing effect caused by spectral bias when the neural network processes drastic topographic changes, eliminating systematic errors; compared with the traditional Kalman filtering method, this invention can better adapt to complex topographic features with non-Gaussian distributions.

[0055] This invention provides a low-cost, high-frequency method for acquiring river topography. This method can effectively monitor topographic changes caused by flood erosion or siltation, thereby providing timely updated boundary conditions for flood forecasting models and solving the problem of decreased accuracy of forecasting models due to outdated topographic data.

[0056] The method of the present invention can be used in the following examples: deploying water level gauges and current meters at key sections of the river channel to transmit monitoring data in real time; running a physical information neural network on the server side for online inversion and calling a pre-trained bias correction network for correction, outputting the latest riverbed elevation map; and inputting the elevation map into the subsequent flood forecasting system.

[0057] In some cases, the method described in this invention can be applied to waterway maintenance monitoring. By analyzing the topographic changes obtained through inversion, potential siltation areas that obstruct navigation can be identified, guiding dredging operations.

[0058] This invention discloses a method for underwater topography inversion in river channels based on a bias-corrected physical information neural network, proposing a two-stage inversion framework combining physical driving and data correction. A physical information neural network inversion model is constructed and trained using water level and flow velocity data from sparse monitoring points. By minimizing a physical loss function containing the residuals of the two-dimensional shallow water equations, a preliminary topography estimation field satisfying the laws of hydrodynamics is obtained. A bias correction network is then constructed and trained using a pre-built prior dataset containing rich non-Gaussian topography features to learn the systematic bias patterns present in the preliminary inversion results. The preliminary topography estimation field is input into the trained bias correction network to predict the topography bias field and perform superposition correction, outputting the final high-precision underwater topography of the river channel. This invention achieves dynamic and high-precision reconstruction of complex topographic features such as deep pits and sandbars, providing a reliable method for updating dynamic boundary conditions for flood forecasting.

[0059] In other words, the beneficial effects of this invention compared to the prior art are as follows:

[0060] This invention constructs a two-stage inversion framework of "physical benchmark + data correction". The physical benchmark ensures that the inversion results conform to the laws of fluid motion on a large scale and will not produce non-physical singularities; the data correction focuses on restoring high-frequency details that have been smoothed out by the physical model, which significantly improves the inversion accuracy for extreme terrain features.

[0061] This invention presents a method for reconstructing underwater river topography using sparse hydrodynamic observation data, which is particularly suitable for in-situ and high-precision reconstruction of riverbed topography with complex non-Gaussian characteristics. This invention achieves in-situ, dynamic self-identification of topographic parameters, eliminating reliance on expensive sonar mapping and significantly reducing the cost of acquiring river topographic data. Attached Figure Description

[0062] Figure 1 This is a flowchart of the overall process for the underwater topography inversion method of the river channel based on the bias correction physical information neural network of the present invention; it shows the complete operation steps from sparse observation data acquisition, preliminary inversion of physical information neural network (PINN), input of bias correction network to final high-precision topography output.

[0063] Figure 2 This is a schematic diagram of the architecture principle of the two-stage inversion model in this invention; it shows in detail the data flow and coupling mechanism between the first-stage physical information neural network (which uses physical equations to constrain and solve the preliminary terrain) and the second-stage deviation correction network (which uses the U-Net architecture to predict the terrain deviation field). Detailed Implementation

[0064] The present invention will be further described below with reference to the accompanying drawings and specific embodiments. It should be understood that these embodiments are for illustrative purposes only and are not intended to limit the scope of the invention.

[0065] 1. Acquisition of hydrodynamic observation data for the target river section

[0066] Monitoring equipment such as water level gauges and current meters are deployed at key sections of the target river segment. This equipment is used to collect and transmit sparse observation data of the river channel in real time, specifically including water level and flow velocity information changing over time at several discrete monitoring points. This observation data serves as a supervision term in the subsequent training process of the physical information neural network, used to establish the correlation between physical spatial constraints and temporal evolution patterns.

[0067] 2. Construction of a Neural Network Inversion Model for Physical Information

[0068] This implementation example constructs a fully connected deep neural network as the basic inversion engine. The network input is spatiotemporal coordinates. The output is a hydrodynamic state variable (water depth). , Directional flow velocity , Directional flow velocity and riverbed topographic parameters (i.e., riverbed elevation). To reflect the time invariance of riverbed topography, the network design will incorporate... Set to depend only on spatial coordinates The parameters, or a separate subnetwork specifically for output. This subnetwork only receives As input.

[0069] The loss function of the physical constraints consists of the data fitting term. and physical residuals Composition, represented as follows:

[0070]

[0071]

[0072]

[0073] in, and These represent the number of observation data points and the number of physical distribution points, respectively. For sparse hydrodynamic observation data, This is the network prediction value. These are the weighting coefficients. , , These are the residuals of the continuity equations constructed based on the two-dimensional shallow water equation system, respectively. Directional momentum equation residuals and sum Residual of directional momentum equation. , and These are the penalty weighting coefficients for the residual terms of each physical equation.

[0074] The specific form of the residuals of the two-dimensional shallow water equation system is as follows:

[0075]

[0076]

[0077]

[0078] in, Because of the water depth, , They are respectively , directional flow velocity, It is the acceleration due to gravity. Water level elevation ( ), For fluid density, , The shear stress on the bed surface is often calculated using the Manning formula:

[0079]

[0080]

[0081] in, is the Manning roughness coefficient, which is a pre-defined known constant.

[0082] 3. Preliminary inversion training of river channel topography under physical constraints

[0083] The model is iteratively optimized using the actual observation data obtained in step 1) to obtain a preliminary terrain estimation field that satisfies physical laws.

[0084] 1) Construct a composite loss function that includes a data fitting term and a physical residual term. The residuals are calculated using automatic differentiation techniques; in particular, the bottom slope source term in the momentum equation includes topographic parameters. spatial derivative .

[0085] 2) Optimization is performed using the Adam optimizer. In this embodiment, a "warm start" strategy is preferred: if historical topographic data exists for the target river section, the weight parameters pre-trained using historical data can be used as initial weights for transfer learning. This method enables the model to converge quickly within minutes. The final output from the network... This is the preliminary topographic estimation field.

[0086] 4. Construction and training of the bias correction network

[0087] This phase improves the model's ability to capture high-frequency terrain features through offline methods. The process includes:

[0088] 1) Virtual Terrain Sample Generation: To train the bias correction network to recognize complex terrain features, a prior dataset containing rich terrain variations is first needed. Using radial basis functions or Gaussian random field generation algorithms, a large number of virtual riverbed elevation field samples with non-Gaussian distribution characteristics are generated.

[0089] The formula for generating the formula is as follows:

[0090]

[0091] in, and For two points in space, and The distance between two points For elevation standard deviation, and This refers to the relevant length. By adjusting these parameters, different terrain features such as sandbars and deep pits can be simulated. By adjusting the relevant length... , and elevation standard deviation By performing multi-scale parameter perturbations and combinations, the generated virtual terrain sample set can cover a variety of typical landforms from localized severe erosion to large-scale deposition in terms of statistical features, thereby ensuring that the trained bias correction network has the ability to generalize and recognize terrain at different feature scales.

[0092] 2) Virtual observation data generation: The generated virtual riverbed elevation field is used as boundary conditions and input into a high-precision hydrodynamic numerical model (such as HEC-RAS). Constant upstream flow and downstream water level boundaries are set, and forward modeling is performed until the flow field reaches steady state.

[0093] After the simulation is completed, water level and flow velocity data are extracted in the computational domain according to the principle of sparse distribution (e.g., 8×32 sampling points), and a certain level of Gaussian white noise (e.g., standard deviation of 0.01) is superimposed as virtual observation data.

[0094] 3) Bias Label Creation: For each virtual terrain sample, the aforementioned physical information neural network inversion model is used to perform a preliminary inversion based on the corresponding virtual observation data to obtain a "biased preliminary terrain estimate". The difference between this preliminary estimate and the real virtual terrain is calculated and used as the label data for training the bias correction network.

[0095] 5. Online terrain correction and result output

[0096] 1) Online Inversion: After obtaining real-time monitoring data, a pre-set physical information neural network basic model is first used for rapid iterative optimization. Benefiting from the constraints of physical equations, the physical information neural network can output a preliminary topographic estimation field that satisfies hydrodynamic laws in a short time. .

[0097] 2) Error compensation: The flow field map is input into a bias correction network that has already undergone offline supervised learning. This step involves feedforward neural network computation, which has instantaneous inference capabilities and can immediately predict the terrain bias field. .

[0098] 3) Result Synthesis: Calculate the final high-precision terrain:

[0099]

[0100] In the early stages of actual engineering deployment, if a small number of historically measured terrain slices are available, they can be used as additional monitoring samples to fine-tune the deviation correction network online.

[0101] Experimental results show that the terrain inversion results after bias correction have a root mean square error index that is reduced by about 20%-30% compared with the simple physical information neural network inversion. It can also accurately restore the deep pits and sandbar edges in the river channel, effectively solving the inversion distortion problem under non-Gaussian terrain.

[0102] Furthermore, it should be understood that after reading the above description of the present invention, those skilled in the art can make various modifications to the present invention, and these equivalent forms also fall within the scope defined by the appended claims.

Claims

1. A river underwater topography inversion method based on a physical information neural network and a bias correction network, characterized in that: The method includes the following steps: Step 1) Obtain sparse hydrodynamic observation data of the target river section, including data on water level and flow velocity changes over time at several discrete monitoring points; Step 2) Construct a physical information neural network inversion model to establish the mapping relationship between spatiotemporal coordinates and flow field state variables and river topographic parameters; Step 3) Use the sparse hydrodynamic observation data described in Step 1) to train the physical information neural network inversion model constructed in Step 2), and obtain the preliminary terrain estimation field by minimizing the loss function of physical constraints; Step 4) Construct an additional bias correction network. Train the bias correction network using a pre-built prior dataset containing various known topographic estimation fields and flow field feature maps to learn the systematic bias distribution characteristics of the river topography. Step 5) Input the preliminary topographic estimation field and corresponding flow field state features obtained in Step 3) into the bias correction network trained in Step 4) to predict the topographic bias field; superimpose the topographic bias field with the preliminary topographic estimation field to output the final underwater topographic inversion result of the river channel; Among them, step 4) the deviation correction network adopts a fully convolutional neural network and U-Net architecture to establish an end-to-end mapping from the preliminary terrain estimation field and flow field feature map to the terrain deviation field; The process of constructing the prior dataset includes: A large number of virtual riverbed topographic samples with non-Gaussian distribution characteristics are generated using random generation algorithms or image enhancement techniques; The virtual riverbed topography sample was subjected to forward modeling using a hydrodynamic numerical model to generate corresponding virtual hydrodynamic observation data. Based on virtual observation data, the corresponding virtual preliminary terrain estimation field is simulated using the physical information neural network inversion model. The difference between the virtual preliminary terrain estimation field and the reference virtual riverbed terrain sample is calculated and used as label data for training the bias correction network.

2. The method of claim 1, wherein, The network architecture of the physical information neural network inversion model is as follows: a fully connected deep neural network is constructed as the basic architecture of the physical information neural network inversion model; the input is spatiotemporal coordinates. The output includes time-varying hydrodynamic state variables and time-invariant topographic parameters; the hydrodynamic state variables include water depth. , Directional flow velocity and Directional flow velocity The terrain parameter is the riverbed elevation. ; During the training process, the riverbed elevations are set as outputs of an independent subnetwork that is only related to spatial coordinates and does not change over time. are set as outputs of an independent subnetwork that is only related to spatial coordinates 3. The method of claim 2, wherein, Step 3) The loss function of the physical constraints consists of a data fitting term and a residual term of the governing equation; The residual terms of the governing equations are constructed based on a two-dimensional shallow water equation system, including the residuals of the continuity equation and the momentum equation. When calculating the residuals, the automatic differentiation technique inherent in the neural network is used to calculate the partial derivatives of the network output with respect to the input coordinates, and the riverbed elevation is then considered. The spatial derivative is substituted into the bottom slope source term in the momentum equation for calculation.

4. The method of claim 1, wherein, Step 5) the terrain deviation field is used to compensate for the smoothing effect error caused by spectral deviation of the physical information neural network in the area with dramatic terrain changes or extreme values; and the final river channel underwater terrain inversion result The calculation formula is: ； wherein, is a preliminary terrain estimate field output by the physical information neural network inversion model, is a terrain bias field predicted by the bias correction network.

5. The method of claim 3, wherein, The bottom friction stress term in the two-dimensional shallow water equation set is calculated using the Manning formula, with the following specific form: ； ； in, and for and Frictional stress on the bottom surface in the direction of the direction. For fluid density, It is the acceleration due to gravity. The roughness coefficient is Manning's coefficient. , For flow rate, The water is deep.

6. The method described in any one of claims 1-5 is used for river topography monitoring, flood forecasting, and waterway maintenance monitoring.

7. Use according to claim 6, characterized in that: Applicable to complex terrain features with non-Gaussian distribution.

8. A computer-readable storage medium having stored thereon a computer program, characterized in that, When the program is executed by the processor, it implements the method described in any one of claims 1-5.

9. A river course topography monitoring system characterized by comprising: include: 1) Data acquisition module, used to collect water level and flow velocity data of river cross-section in real time; 2) A calculation module, used to run the inversion method according to any one of claims 1-5, and output the current underwater topographic distribution map of the river channel; 3) Update module, used to update the boundary condition parameters in the flood forecasting model based on the underwater topographic distribution map of the river channel obtained by inversion.

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