A flood rapid deduction method fusing terrain space intelligent reconstruction and physical enhanced fourier operator

Abstract

The application provides a flood rapid deduction method fusing terrain space intelligent reconstruction and physical enhanced Fourier operator, and comprises the following steps: S1, terrain calculation space reconstruction for flood rapid deduction; S2, constructing a flood evolution model architecture based on a Fourier neural operator; S3, adaptive balance training driven by physical information constraints; S4, fine reduction of a breach flood element. The application compresses physical evolution calculation of an hour level to a second level / minute level, can quickly respond to the dynamic deduction demand of a super large range flood, and provides strong technical support for quick early warning and multi-scenario scheme comparison and selection in flood control emergency decision-making. The application effectively solves the problems of low calculation efficiency of traditional numerical simulation and poor physical consistency of an existing deep learning model, and realizes second-level, conservation and fine rapid deduction under a super large flood scene.

Description

Technical Field

[0001] This invention belongs to the field of hydrology and hydrodynamics simulation in water conservancy engineering, and specifically relates to a method for rapid flood extrapolation that integrates intelligent topographic spatial reconstruction and physically enhanced Fourier operators. Background Technology

[0002] Levee-break floods are characterized by their suddenness, rapid evolution, destructive power, and significant influence from underlying topography, posing a serious threat to the flood control safety of river basins. In flood control emergency response and evacuation decision-making, rapidly and accurately obtaining key hydraulic elements such as the flood inundation area, water depth distribution, and flow velocity field is a prerequisite for formulating scientific evacuation plans and engineering scheduling measures.

[0003] Currently, calculations of levee breach flood evolution primarily rely on numerical simulation methods based on physical equations. These methods typically employ the finite volume method (FVM) or finite difference method (FDM) to discretize and solve shallow water equations (SWEs), possessing a clear physical mechanism and high computational accuracy. However, existing numerical simulation methods suffer from the following significant limitations: First, the numerical solution process is strictly constrained by the Cronbach's alpha (CFL) stability condition. Under large-scale, complex terrain conditions, to ensure computational convergence, high-resolution grids and extremely small time steps are often required, leading to an exponential increase in computational load. In catastrophic flood emergency scenarios, traditional numerical models consume excessive computation time, making it difficult to meet the real-time simulation requirements at the minute or even second level.

[0004] To address computational efficiency issues, some studies have attempted to reduce the dimensionality of the terrain computational space using mesh coarsening or unstructured mesh techniques. However, existing terrain spatial reconstruction methods have significant drawbacks: most mesh generation algorithms rely solely on geometric shapes or planar topological partitioning, failing to fully integrate hydrophysical features that control water flow, such as surface slope and runoff accumulation. In large-scale spatial dimensionality reduction, simple geometric resampling can easily lead to the smoothing or loss of key terrain features, resulting in a reconstructed computational space that cannot accurately represent the hydrodynamic response characteristics of floods on complex underlying surfaces, thus affecting simulation accuracy.

[0005] In recent years, data-driven models based on deep learning have attracted attention due to their fast inference speed. However, when applying artificial intelligence to flood evolution simulation, the following key technical challenges remain: First, the model architecture lacks generalization of physical mechanisms. Most existing models simplify flood evolution into a general time series prediction problem (such as using RNNs or LSTMs), without explicitly modeling the "first-order Markov property" inherent in the flood system itself. This approach ignores the physical logic of flow field state transitions, and when performing long-duration recursive predictions, it is prone to error accumulation and numerical drift, leading to unreliable prediction results. Second, physical consistency constraints are difficult to implement in discrete spaces. Although Physical Information Neural Networks (PINNs) attempt to introduce partial differential equation residuals as constraints, they are mostly based on continuous space assumptions. When facing discrete computational spaces with irregular terrain units or graph structures, it is difficult to construct applicable water mass conservation and energy conservation constraints. Existing models often lack effective physical constraints, resulting in predicted flow fields exhibiting water imbalances or violating physical common sense. Third, multi-objective training and optimization are difficult. In the joint training process that integrates data error and physical constraints, the data terms (usually scalars) and physical residual terms (usually gradient terms) have huge differences in dimensions and gradient magnitudes, which can easily lead to gradient competition, causing the model to fail to converge or to only fit the data while ignoring physical laws.

[0006] How to overcome the efficiency bottleneck of traditional numerical methods in the scenario of massive levee breach floods, while also overcoming the shortcomings of existing deep learning methods such as poor terrain adaptability, insufficient physical consistency and unstable training, and achieve high-precision and rapid extrapolation that takes into account both macroscopic computational efficiency, physical conservation laws and local flooding details, is a technical problem that urgently needs to be solved in this field. Summary of the Invention

[0007] The main objective of this invention is to provide a method for rapid flood extrapolation that integrates intelligent terrain spatial reconstruction and physically enhanced Fourier operators, addressing the aforementioned problems.

[0008] Therefore, the above-mentioned objective of the present invention is achieved through the following technical solution:

[0009] A rapid flood extrapolation method integrating intelligent terrain spatial reconstruction and physically enhanced Fourier operators includes the following steps:

[0010] S1. Reconstruction of the computational space for rapid flood simulation: Using a deep clustering algorithm that introduces spatial connectivity constraints, high-resolution terrain is adaptively aggregated into a low-dimensional topological unit graph with physical consistency, thereby achieving efficient dimensionality reduction of the computational space.

[0011] S2. Construct a flood evolution model architecture based on Fourier neural operators: Construct a graph network model based on Fourier neural operators, and utilize the Markov property of the flood system to achieve rapid recursive deduction of the state at the next moment directly from the current state.

[0012] S3. Adaptive Balance Training Driven by Physical Information Constraints: A composite loss function that integrates data fitting and mass conservation is designed, and an adaptive strategy based on neural tangent vector kernels is used to dynamically balance the training gradient to ensure that the model learns physical laws.

[0013] S4. Refined reconstruction of flood elements during levee breaches: Through local hydraulic gradient reconstruction, volume conservation correction, and hydraulic resistance weight allocation, the macroscopic unit prediction results are inverted into a high-resolution fine flow field, balancing efficiency and detail.

[0014] While adopting the above technical solutions, the present invention may also adopt or combine the following technical solutions:

[0015] As a preferred technical solution of the present invention, step S1 specifically includes the following steps:

[0016] S11. Construction of Topographic Feature Vectors: Based on the high-resolution digital elevation model (DEM) of the study area, a heterogeneous feature space is constructed to characterize the physical properties and hydrodynamic trends of the terrain. Five-dimensional feature vectors are then constructed for each grid cell within the study area. ;

[0017] S12. Deep manifold embedding clustering based on spatial-feature alignment: An unsupervised deep learning method, SFAD-MEC, which introduces hard constraints on spatial connectivity, is used to partition the high-resolution raster feature space into topological units.

[0018] S13. Topological Response Unit (TRU) Graph Structure Representation: Based on the clustering results, the discrete grid set is reconstructed into Topological Response Units (TRUs), and a graph space mapping is constructed.

[0019] As a preferred technical solution of the present invention: in step S11, the five-dimensional feature vector includes normalized elevation, normalized slope, logarithmically processed confluence accumulation, normalized spatial x-coordinate and normalized spatial y-coordinate.

[0020] As a preferred technical solution of the present invention, step S12 specifically includes:

[0021] Encoding network using deep autoencoder High-dimensional feature vectors Mapping to a low-dimensional latent manifold space to extract deep nonlinear features of the terrain Initialize in the embedded space Cluster centers to be optimized ( Using the student t-distribution kernel function to measure the first Embedding features of individual grid cells Belongs to the The probability of membership of each cluster center :

[0022]

[0023] In the formula, For the degrees of freedom of the t-distribution, Denotes the Euclidean norm;

[0024] Constructing a system that includes reconstruction loss Clustering loss and spatial continuity loss The joint objective function optimizes both the neural network weights and the cluster center distribution. The spatial continuity loss uses a Laplace regularization term to constrain the feature distance between adjacent grid cells in the embedding space, ensuring the connectivity of the partitioning results in the physical space.

[0025] As a preferred technical solution of the present invention, step S2 specifically includes the following steps:

[0026] S21. Construction of Fourier Neural Operator Network: To address the irregular grid characteristics of terrain topology response units, a network architecture coupling graph neural operators and Fourier neural operators is constructed.

[0027] S22. Construction of a shallow water equation surrogate model based on Markov properties: The evolution process of floodplain breach floods is generalized into a state transition process with Markov properties, that is, utilizing the current hydrodynamic state. Directly predicting the state at the next time step using boundary conditions Constructing a deep learning agent model It replaces the traditional difference solution process for shallow water equations.

[0028] As a preferred technical solution of the present invention: step S22 specifically involves: constructing a deep learning agent model. Instead of the traditional SWE difference solution process for shallow water equations, the state update equation is:

[0029]

[0030] In the formula, Let t be the water depth and velocity tensor of the entire TRU unit at time t; The boundary conditions for the breach flow at the corresponding time point; This includes various types of information for terrain response units, including unit nodes, adjacency relationships, and unit attribute data; For parameters The Fourier neural operator network model is used to continuously simulate the spatiotemporal evolution of floods through a recursive iteration mechanism.

[0031] As a preferred technical solution of the present invention, step S3 specifically includes the following steps:

[0032] S31. Multi-criteria composite loss function coupled with physical constraints: A comprehensive loss function considering both data fitting accuracy and physical conservation constraints is constructed to optimize the Fourier neural operator flood evolution model. On the one hand, a mean square error (MSE) term between the predicted results and high-precision numerical simulation samples is introduced; on the other hand, a mass conservation constraint term based on the water continuity equation is introduced to penalize non-conservative water behavior, forcing the model to follow the water balance law during training.

[0033]

[0034] In the formula, Represents a multi-criteria loss function with coupled physical constraints; This represents data consistency constraints; To represent the water mass conservation constraint term; Represents the dynamic weight of the water mass conservation constraint term;

[0035] S32. Water mass conservation constraint based on topological connectivity: For unstructured TRU cells, the continuity equation is discretized into a flux integral form based on a topological graph structure, forcing the model to follow the water balance law:

[0036]

[0037] In the formula, Indicates the first TRU units at time The water depth; The unit area; For unit The set of adjacent units; Indicates time unit Flowing unit Unit width flow rate; The length of the common boundary; For time step;

[0038] S33. Adaptive training strategy based on neural tangent vector kernel NTK: During the training process, due to... and The gradient magnitudes differ significantly, which can easily lead to optimization imbalance. Therefore, NTK adaptive weighting is introduced.

[0039] As a preferred technical solution of the present invention: step S33 specifically involves: at the beginning of each training epoch, calculating the loss terms with respect to the network parameters. Jacobian matrix ,in, And estimate the trace of its NTK matrix:

[0040]

[0041] In the formula, Represents the trace operator; For neural tangent vector kernels; Represents the Jacobian matrix;

[0042] Based on the convergence matching principle, the weight coefficients are dynamically updated. This makes it positively correlated with the ratio of the NTK traces of the data consistency term and the physical constraint term, thereby automatically balancing the gradient contributions of the data-driven term and the physical constraint term:

[0043]

[0044] In the formula, This represents the weight coefficients based on the convergence rate matching principle at the initial moment; This represents the weight coefficient based on the convergence rate matching principle at time t; Represents the trace operator; The neural tangent vector kernel for the data consistency constraint term; The neural tangent vector kernel for the water mass conservation constraint term; This indicates a positive correlation.

[0045] As a preferred technical solution of the present invention, step S4 specifically includes the following steps:

[0046] S41. Rapid and intelligent full-time calculation of levee breach floods: Input the breach flow sequence and initial state into the trained model to quickly predict the average water depth and flow velocity sequence of the entire field TRU unit, and realize the second-level extrapolation of large-scale floods.

[0047] S42. Water level redistribution based on local gradient reconstruction and volume correction: To meet the requirements of fine distribution within the TRU unit, a subgrid reconstruction technique based on local hydraulic gradient is adopted.

[0048] S43. Velocity field refinement based on hydraulic resistance weights: Based on the relative flow capacity weights defined by Manning's formula, the average velocity vector of the TRU unit is non-uniformly distributed to the high-resolution grid to obtain a refined velocity field reflecting the flood inundation area, thereby outputting a flood inundation map that meets the requirements of high-precision flood control decision-making.

[0049] As a preferred technical solution of the present invention: step S42 specifically involves: firstly, constructing a local hydraulic gradient vector based on the topological adjacency relationship between units. First, the water surface elevation is reconstructed by combining high-resolution DEM data within the unit; second, a volume conservation correction factor is introduced. The reconstructed water level field is compensated for by translation to ensure that the total water volume within the unit is strictly consistent with the model prediction.

[0050]

[0051] In the formula, Indicates the first Inside the first Terrain Topology Response Unit (TRU), the first Reconstructed water level of a high-resolution fine-grained raster (sub-grid); This indicates that the Fourier neural operator model directly predicts the output of the first... Average water level of each TRU unit; Indicates the first The center spatial coordinate vector of each fine grid ; No. Geometric centroid coordinate vector of each TRU unit .

[0052] Compared with the prior art, the present invention has the following beneficial effects:

[0053] 1) Overcoming the contradiction between computational efficiency and grid resolution in traditional hydrodynamic models, and significantly improving the timeliness of predictions in scenarios of extreme floods, this invention proposes an unsupervised deep manifold embedding clustering method based on SFAD-MEC. This method adaptively reconstructs the original massive high-resolution raster into a finite number of topographic response units (TRUs) with physical semantic consistency. While significantly reducing computational dimensionality, this method effectively preserves the dominant topographic features of key hydrodynamic areas such as river channels and floodplains, overcoming the shortcomings of traditional regular grid partitioning, which suffers from high computational cost or low accuracy of single-index partitioning. Based on this, and combining the global integral mapping advantage of the Fourier neural operator (FNO) in solving partial differential equations, a recursive prediction architecture based on Markov properties is constructed. Compared to traditional numerical models based on the finite volume method, this invention compresses hourly physical evolution calculations to second / minute levels, enabling rapid response to the dynamic prediction needs of large-scale floods and providing strong technical support for rapid early warning and multi-scenario scheme comparison in flood control emergency decision-making.

[0054] 2) This invention addresses the challenges of poor physical consistency and training non-convergence in purely data-driven models, ensuring the numerical stability of long-term predictions. To address the common problems of "water non-conservation," "abnormal energy dissipation," and "numerical drift" in existing deep learning flood models, this invention constructs a composite loss function system that integrates data fitting error and physical conservation constraints (water conservation). In particular, it introduces an adaptive training strategy based on Neural Transect Kernel (NTK). By monitoring the gradient convergence rate of different loss terms in real time, it dynamically balances the weight ratio of data-driven terms and physical constraint terms, effectively solving the problems of "gradient competition" and "optimization imbalance" caused by differences in gradient magnitudes in multi-task learning. This allows the model to learn evolution operators that conform to the physical laws of shallow water equations with only a small number of samples, significantly improving the physical reliability and generalization ability of the model in long-term recursive predictions.

[0055] 3) This invention achieves cross-scale simulation of "macroscopic calculation and microscopic reconstruction," balancing computational speed with the accuracy of local inundation details. The precision of the results is not sacrificed due to the dimensionality reduction of the computational space. By constructing a post-processing mechanism based on local hydraulic gradient reconstruction, volume conservation correction, and Manning resistance weight allocation, the macroscopic hydrodynamic results of low-dimensional TRU cells are successfully inverted to a high-resolution raster space. This mechanism utilizes micro-topographic data for super-resolution reconstruction of the flow field, accurately capturing changes in water level gradients and spatial differences in flow velocity caused by minute topographic undulations (such as dikes and ditches), overcoming the ambiguity in the characterization of inundation boundaries in traditional simplified models. Thus, while ensuring overall computational efficiency, it outputs high-precision flood element maps that meet the needs of refined flood control scheduling (such as the inundation depth of individual buildings and the flow velocity of specific roads). Attached Figure Description

[0056] Figure 1 The flowchart shows the rapid flood extrapolation method that integrates intelligent terrain spatial reconstruction and physically enhanced Fourier operators provided by this invention.

[0057] Figure 2 This is a schematic diagram of terrain computational spatial reconstruction based on SFAD-MEC.

[0058] Figure 3 This is a schematic diagram of the Fourier Neural Operator (FNO) network architecture and physical constraints.

[0059] Figure 4 This is a detailed schematic diagram illustrating the elements of a levee breach flood. Detailed Implementation

[0060] The present invention will now be described in further detail with reference to the accompanying drawings and specific embodiments.

[0061] like Figure 1As shown, a method for rapid flood extrapolation that integrates intelligent terrain spatial reconstruction and physically enhanced Fourier operators includes the following steps:

[0062] S1. Computational spatial reconstruction of terrain for rapid flood simulation:

[0063] S11. Construction of Topographic Feature Vectors: Based on the high-resolution digital elevation model (DEM) of the study area, a heterogeneous feature space is constructed to characterize the physical properties and hydrodynamic trends of the terrain. Five-dimensional feature vectors are then constructed for each grid cell within the study area. It includes normalized elevation, normalized slope, logarithmically processed confluence accumulation, normalized spatial x-coordinate, and normalized spatial y-coordinate;

[0064] S12. Deep manifold embedding clustering based on spatial-feature alignment: An unsupervised deep learning method (SFAD-MEC) that introduces hard constraints on spatial connectivity is used to partition the high-resolution raster feature space into topological units;

[0065] Encoding networks utilizing deep autoencoders High-dimensional feature vectors Mapping to a low-dimensional latent manifold space to extract deep nonlinear features of the terrain Initialize in the embedded space Cluster centers to be optimized ( Using the student t-distribution kernel function to measure the first Embedding features of individual grid cells Belongs to the The probability of membership of each cluster center :

[0066]

[0067] In the formula, For the degrees of freedom of the t-distribution, Denotes the Euclidean norm;

[0068] Constructing a system that includes reconstruction loss Clustering loss and spatial continuity loss The joint objective function optimizes both the neural network weights and the cluster center distribution. The spatial continuity loss uses a Laplace regularization term to constrain the feature distance between adjacent grid cells in the embedding space, ensuring the connectivity of the partitioning results in the physical space.

[0069] S13. Topological Response Unit (TRU) Graph Structure Representation: Based on clustering results, the discrete raster set is reconstructed into Topological Response Units (TRUs), and a graph space mapping is constructed. Using each TRU as a node, physical attributes such as elevation and roughness are aggregated using an area-weighted method based on confluence accumulation weights. Shared boundaries between adjacent TRUs are identified, and a topological graph is constructed with TRUs as nodes and adjacency relationships as edges. This transforms continuous terrain space into a low-dimensional structured representation that supports graph neural network computation.

[0070] S2. Construct a flood evolution model architecture based on Fourier neural operators:

[0071] S21. Construction of Fourier Neural Operator Network: To address the irregular grid characteristics of terrain topological response units, a network architecture coupling graph neural operators (Graph Neural Operator) and Fourier neural operators (FNO) is constructed. This network first maps the low-dimensional physical properties of TRU nodes to a high-dimensional latent representation space. Then, iterative updates are performed through multiple Fourier layers, each containing a spectral convolution branch and a residual linear branch. The spectral convolution branch performs a global integral transformation on the full-field hydrodynamic features in the frequency domain, capturing the long-range dependencies of flood evolution. Finally, the decoder projects the high-dimensional features back into the physical space, outputting the prediction results.

[0072] S22. Construction of a shallow water equation surrogate model based on Markov properties: The evolution process of floodplain breach floods is generalized into a state transition process with Markov properties, that is, utilizing the current hydrodynamic state. Directly predicting the state at the next time step using boundary conditions Constructing a deep learning agent model It replaces the traditional difference solution process for shallow water equations;

[0073] Building a deep learning agent model Instead of the traditional shallow water equation (SWE) difference solution process, its state update equation is:

[0074]

[0075] In the formula, Let t be the water depth and velocity tensor of the entire TRU unit at time t; The boundary conditions for the breach flow at the corresponding time point; This includes various types of information for terrain response units, including unit nodes, adjacency relationships, and unit attribute data; For parameters A Fourier neural operator network model is used to continuously simulate the spatiotemporal evolution of floods through a recursive iterative mechanism.

[0076] S3, Physical Information Constraint-Driven Adaptive Balance Training:

[0077] S31. Multi-criteria composite loss function coupled with physical constraints: Construct a comprehensive loss function that simultaneously considers data fitting accuracy and physical conservation constraints to optimize the Fourier neural operator flood evolution model. On the one hand, introduce the mean square error (MSE) term between the prediction results and high-precision numerical simulation samples; on the other hand, introduce a mass conservation constraint term based on the water continuity equation. By penalizing non-conservative water behavior, the model is forced to follow the water balance law during training.

[0078]

[0079] In the formula, Represents a multi-criteria loss function with coupled physical constraints; This represents data consistency constraints; To represent the water mass conservation constraint term; Represents the dynamic weight of the water mass conservation constraint term;

[0080] S32. Water mass conservation constraint based on topological connectivity: For unstructured TRU cells, the continuity equation is discretized into a flux integral form based on a topological graph structure, forcing the model to follow the water balance law:

[0081]

[0082] In the formula, Indicates the first TRU units at time The water depth; The unit area; For unit The set of adjacent units; Indicates time unit Flowing unit Unit width flow rate; The length of the common boundary; For time step;

[0083] S33. Adaptive training strategy based on neural tangent vector kernel NTK: During the training process, due to... and The gradient magnitudes differ significantly, which can easily lead to optimization imbalance. Therefore, NTK adaptive weighting is introduced.

[0084] At the beginning of each training epoch, calculate the loss terms with respect to the network parameters. Jacobian matrix ,in, And estimate the trace of its NTK matrix:

[0085]

[0086] In the formula, Represents the trace operator; For neural tangent vector kernels; Represents the Jacobian matrix;

[0087] Based on the convergence matching principle, the weight coefficients are dynamically updated. This makes it positively correlated with the ratio of the NTK traces of the data consistency term and the physical constraint term, thereby automatically balancing the gradient contributions of the data-driven term and the physical constraint term:

[0088]

[0089] In the formula, This represents the weight coefficients based on the convergence rate matching principle at the initial moment; This represents the weight coefficient based on the convergence rate matching principle at time t; Represents the trace operator; The neural tangent vector kernel for the data consistency constraint term; The neural tangent vector kernel for the water mass conservation constraint term; This indicates a positive correlation.

[0090] This strategy ensures that the physical constraints provide effective gradient guidance throughout the training cycle, preventing the model from simply fitting the data and ignoring physical laws.

[0091] S4. Refined reconstruction of elements of a levee breach flood:

[0092] S41. Rapid and intelligent full-time calculation of levee breach floods: Input the breach flow sequence and initial state into the trained model to quickly predict the average water depth and flow velocity sequence of the entire field TRU unit, and realize the second-level extrapolation of large-scale floods.

[0093] S42. Water level redistribution based on local gradient reconstruction and volume correction: To meet the requirements of fine distribution within the TRU unit, a subgrid reconstruction technique based on local hydraulic gradient is adopted.

[0094] First, a local hydraulic gradient vector is constructed based on the topological adjacency relationship between units. First, the water surface elevation is reconstructed by combining high-resolution DEM data within the unit; second, a volume conservation correction factor is introduced. The reconstructed water level field is compensated for by translation to ensure that the total water volume within the unit is strictly consistent with the model prediction.

[0095]

[0096] In the formula, Indicates the first Inside the first Terrain Topology Response Unit (TRU), the first Reconstructed water level of a high-resolution fine-grained raster (sub-grid); This indicates that the Fourier neural operator model directly predicts the output of the first... Average water level of each TRU unit; Indicates the first The center spatial coordinate vector of each fine grid ; No. Geometric centroid coordinate vector of each TRU unit ;

[0097] S43. Velocity field refinement based on hydraulic resistance weights: Based on the relative flow capacity weights defined by Manning's formula, the average velocity vector of the TRU unit is non-uniformly distributed to the high-resolution grid to obtain a refined velocity field reflecting the flood inundation area, thereby outputting a flood inundation map that meets the requirements of high-precision flood control decision-making.

[0098] Example

[0099] This embodiment takes a flood storage and detention area in a watershed as the research object and uses the method proposed in this invention to construct a rapid flood evolution model. This method mainly includes four steps: topographic computational spatial reconstruction, Fourier neural operator network construction, physically constrained training, and refined reconstruction of flood elements. Figure 1 As shown.

[0100] S1. Intelligent spatial reconstruction of terrain computation for rapid flood simulation:

[0101] S11. Terrain Feature Vector Construction: Obtain a high-resolution digital elevation model (DEM) of the study area and construct a five-dimensional feature space, enabling the model to perceive the physical properties of the terrain. Specifically, for the first feature vector within the region... For each grid cell, its feature vector is extracted as shown in the following formula:

[0102]

[0103] In the formula, This is a terrain feature vector; This is used to normalize elevations and eliminate differences in absolute elevation values. The normalized topographic slope reflects the gradient of gravitational potential energy of the water flow; This is the cumulative flow after logarithmic transformation, used to characterize potential confluence paths; and These are the normalized center space coordinates.

[0104] Through the above processing, an initial high-dimensional terrain feature matrix is ​​formed. ,in This represents the total number of grid cells.

[0105] S12. Spatial-Feature Alignment-Based Deep Manifold Embedding Clustering (SFAD-MEC):

[0106] To address the low computational efficiency of traditional regular grids, the SFAD-MEC algorithm is used to divide high-resolution rasters into Terrain Topology Response Units (TRUs) with physical semantic consistency.

[0107] 1. Feature Embedding: Construct a deep autoencoder consisting of three fully connected layers (dimensions 128-64-16). The feature vectors are then embedded... The input encoder is mapped to a low-dimensional latent manifold space to obtain the embedded features. .

[0108] 2. Cluster assignment: Initialization in the embedding space Cluster centers ( The student t-distribution kernel function is used to calculate the first... The grid belongs to the first The probability of soft assignment of each cluster center :

[0109]

[0110] In the formula, For degrees of freedom, this embodiment takes ; This represents the Euclidean norm.

[0111] 3. Auxiliary target distribution: To enhance cluster purity, a target distribution is constructed. .

[0112]

[0113] In the formula, This represents the soft clustering frequency.

[0114] 4. Joint Loss Optimization: Define the total loss function as shown in the following equation:

[0115]

[0116]

[0117] In the formula, To reconstruct the loss function; The clustering loss function; These are the clustering weight coefficients; These are the spatial constraint weighting coefficients; for and KL divergence; This is a Laplace regularization term used to penalize grids that are spatially adjacent but too far apart in feature space; This represents the set of spatial adjacency relationships of the original raster. By optimizing this loss function, clustering partitions with strong spatial connectivity can be achieved.

[0118] S13. Graph structure representation of topological response units: After clustering, a set of grid cells belonging to the same category is defined as a terrain topological response unit (TRU).

[0119] 1. Attribute Aggregation: Using TRU as a node, calculate its physical attributes. For the first... Each TRU unit has an average elevation Calculated using a weighted average based on the cumulative flow of the confluence:

[0120]

[0121] In the formula, For the first The confluence weights of each grid ensure that the topographic features of the main flood channels are preserved.

[0122] 2. Topology Graph Construction: Identify the common boundaries of adjacent TRU units and construct a topology graph. The node features include the cell center coordinates, area, average elevation, and Manning roughness; the edge features include the centroid distance between two cells. and shared boundary length A schematic diagram of terrain computational spatial reconstruction based on SFAD-MEC is shown below. Figure 2 As shown.

[0123] S2. Constructing a flood evolution model architecture based on Fourier neural operators.

[0124] S21. Construction of Fourier Neural Operator Network

[0125] Fourier Neural Operator (FNO) Network Design: The network designed in this embodiment includes a Lifting Layer, four Fourier Iterative Layers, and a Projection Layer.

[0126] 1. Input Tensor: Model Input It includes spatiotemporal feature tensors and graph structure data defined on terrain topology response units (graph nodes). The feature tensors contain hydrodynamic elements (water depth, flow velocity) and underlying surface static properties (elevation, roughness, etc.) at the current moment; the graph structure data is used to describe the adjacency topology relationships between units.

[0127] 2. Dimensional Upgrading Layer: Fully connected neural networks are used to map low-dimensional physical input signals to a high-dimensional latent feature space to enhance the expressive power of nonlinear features.

[0128] 3. Fourier Iteration Layer: In each Fourier layer, the feature update formula is as follows:

[0129]

[0130]

[0131] In the formula, For the first Layer input features; Use the GELU activation function; It is a linear spatial transformation matrix used to process local features; As a spectral convolution operator, its physical essence is to use the convolution theorem to transform global convolution operations in the spatial domain into multiplication operations in the frequency domain; This is the discrete Fourier transform on the graph; It is a learnable complex spectral weight matrix in the frequency domain, which processes global features and is used to filter out high-frequency noise and capture long-wave hydrodynamic features. This is the inverse Fourier transform.

[0132] 4. Decoding layer: Maps the high-dimensional abstract features after multiple Fourier transforms back to the low-dimensional physical space, and outputs the water depth and flow velocity components at the predicted time.

[0133] In this embodiment, to balance computational efficiency and the ability to capture complex flow fields, the network's specific hyperparameters are configured as follows: The Lifting Layer maps the input 5D terrain physical properties to the hidden layer channel dimensions. The core processing module consists of four stacked Fourier layers. In the spectral convolution operation of each layer, the number of low-frequency modes retained along both the horizontal and vertical directions is set to [value missing]. This means that only the first 12 low-frequency components are subjected to complex weight transformation to filter high-frequency noise and capture the dominant dynamic characteristics of flood waves; the nonlinear activation function is GELU; the final decoding layer (projection layer) contains two fully connected networks with 64 and 3 nodes respectively, which are used to map the evolved high-dimensional features back to the 3-dimensional output in physical space (water depth, horizontal flow velocity, and vertical flow velocity).

[0134] S22. Construction and Iterative Prediction of Shallow Water Equation Surrogate Model Based on Markov Properties

[0135] In this embodiment, a shallow water equation (SWE) surrogate model based on Markov properties is constructed. The core idea is to discretize the continuous flood dynamics evolution process into a series of state transition steps possessing Markov properties, and then learn from these properties by training a deep neural network. Time's up The state mapping operator at each time step replaces the difference iterative solution process in traditional numerical models. The specific construction and prediction process includes the following three sub-steps:

[0136] 1. Construction of multidimensional spatiotemporal feature tensors

[0137] To accommodate the input requirements of the Fourier neural operator network, hydrodynamic and topographic features need to be encapsulated as structured tensor data. The total number of Topographic Response Units (TRUs) within the study area is defined as follows: .

[0138] (1) Flood state tensor of the floodplain Used for characterization The hydrodynamic distribution across the entire field at any given moment. The tensor dimension is [missing value]. It includes three-dimensional feature channels for each cell: average water depth per cell. ; directional average flow velocity ; directional average flow velocity The data source is the calculation results of two-dimensional hydrodynamic models of levee breaches under different flood return periods or flood conditions.

[0139] (2) Boundary conditions for breach flow To characterize external inflow conditions, this tensor allows the model to identify the dynamic sources of floods and their intensity over time. The data source is the calculation results of riverbank breach models with different flood return periods or flood conditions.

[0140] (3) Nodes and adjacency tensors of terrain topology response units This is used to characterize the unit structure. Based on the terrain topology response units divided in step S1, the spatial coordinates (node ​​features) of the centroid of each unit and the adjacency relationship matrix (edge ​​features) between units are extracted.

[0141] (4) The physical properties tensor of the underlying surface is used to characterize the resistance and potential energy conditions. For each topographic response unit, this tensor integrates geographical environmental elements, mainly including the processed ground elevation, terrain slope and Manning roughness coefficient characterizing the surface friction characteristics.

[0142] 2. Construction of a flood evolution proxy model based on Markov properties

[0143] Based on the dynamic characteristics of shallow water equations, this invention abstracts the flood evolution process as a state transition process with first-order Markov properties. That is, it assumes that the system's next state is controlled only by the current state and real-time boundary constraints, and has no direct correlation with historical states. Based on this, a flood evolution proxy model is constructed, the mathematical logic of which is as follows:

[0144]

[0145] In the formula, Let t be the water depth and velocity tensor of the entire TRU unit at time t; The boundary conditions for the breach flow at the corresponding time point; This includes various types of information for terrain response units, including unit nodes, adjacency relationships, and unit attribute data; For parameters A Fourier neural operator network model is proposed. This model achieves continuous simulation of the spatiotemporal evolution of floods through a recursive iteration mechanism.

[0146] 3. Flood Prediction Process Based on Recursive Feedback

[0147] In the model inference stage, instead of relying on numerical models, a recursive feedback mechanism is established to achieve continuous simulation of the flooding process across the entire time domain.

[0148] (1) Initialization phase: definition The initial water depth and flow velocity data at each moment, as well as the terrain response unit information, are used as the initial inputs to the surrogate model;

[0149] (2) Single-step iterative calculation: The surrogate model calculates the current spatiotemporal tensor. Predict the output state value at the next time step. ;

[0150] (3) State loop feedback: As the input for the next stage, combined with the updated breach flow boundary conditions, it enters the subsequent calculation loop. The calculation results for the time point are shown in the following formula;

[0151]

[0152] (4) Sequence result output: Repeat the above recursive steps until the preset calculation time is reached, and finally obtain the complete data sequence of the submerged spatiotemporal evolution.

[0153] S3. Model Optimization and Training Driven by Physical Information Constraints

[0154] S31. Construction of a multi-criteria composite loss function coupled with physical constraints

[0155] In this embodiment, to ensure the accuracy of flood evolution prediction while constraining the model output to meet basic physical laws, a multi-criteria composite loss function that integrates data fitting error and physical information constraints is constructed for optimizing the Fourier neural operator flood evolution model. The Fourier neural operator (FNO) network architecture and physical constraints are illustrated in the diagram below. Figure 3 As shown. The composite loss function is denoted as... It includes data consistency constraints and mass conservation physical constraints.

[0156]

[0157] In the formula, Represents a multi-criteria loss function with coupled physical constraints; This represents data consistency constraints; To represent the water mass conservation constraint term; This represents the dynamic weight of the water mass conservation constraint term.

[0158] Data consistency constraints To measure the difference between the model's prediction results and the reference numerical simulation results, the mean squared error (MSE) is used to calculate the error between the Fourier neural operator model's predicted values ​​of water depth and flow velocity for terrain topology response units at each time step and the sample true values ​​generated by the two-dimensional hydrodynamic numerical simulation software.

[0159] S32. Construction of Water Mass Conservation Constraints: For irregular terrain topological response units, this invention discretizes the water continuity equation into an integral form based on topological connectivity, constructing water mass conservation constraints to force the model to follow the water balance law during training, as shown in the following equation:

[0160]

[0161] In the formula, Indicates the first TRU units at time The water depth; The unit area; For unit The set of adjacent units; Indicates time unit Flowing unit Unit width flow rate; The length of the common boundary; For time step.

[0162] S33. Adaptive training strategy based on Neural Transect Kernel (NTK):

[0163] When training deep learning models that incorporate physical constraints, the phenomenon of "gradient pathology" is prevalent. This is due to data consistency loss. (Typically based on scalar values ​​of water depth and flow velocity) and physical conservation losses The residuals (based on flux derivatives) differ significantly in physical dimensions and numerical magnitudes, leading to a severe imbalance in their gradient contributions during optimization. Typically, the convergence rate of physical constraint terms is much lower than that of data fitting terms, causing the model to tend to quickly fit data points while ignoring the constraints of physical laws. Therefore, this embodiment introduces an adaptive weighting strategy based on Neural Transect Kernel (NTK) to optimize the training process by dynamically balancing the convergence rates of different tasks.

[0164] The specific implementation steps are as follows:

[0165] 1. Jacobian matrix and NTK feature construction: In the training process of neural networks, the neural tangent vector kernel... The evolution dynamics of the network output as parameters change are described. For any loss term... (in (i.e., data consistency constraints or water quality conservation constraints), and its corresponding NTK matrix is ​​defined as the network output with respect to the network parameters. The inner product of the Jacobian matrices. At the beginning of each training epoch, using automatic differentiation, the gradients of the data loss term and the physical constraint loss term with respect to the shared parameters of the last layer of the network are calculated, and the Jacobian matrix is ​​constructed. :

[0166]

[0167] Because the computation of the complete NTK matrix is ​​too large, this embodiment uses the trace of the NTK matrix as a measure of convergence rate. A larger trace value indicates a faster gradient descent rate for that loss term in the current parameter space. Its calculation formula is approximately the sum of squares of the gradient norms:

[0168]

[0169] 2. Adaptive Calculation of Dynamic Weight Coefficients: Based on the principle of "convergence rate matching," it is desired that the convergence rate of the physical constraint term can catch up with the convergence rate of the data fitting term. Define the dynamic weight update ratio. The ratio of the NTK trace of the data item to the NTK trace of the physical item:

[0170]

[0171] In the formula, To prevent the use of tiny constants with a denominator of zero, this embodiment takes... This ratio intuitively reflects that when the gradient contribution (trace) of a physical term is too small, its weight needs to be increased to amplify its gradient signal.

[0172] 3. Smooth weight update mechanism: To avoid model oscillations caused by drastic fluctuations in weights during training, an exponential moving average (EMA) strategy is used to update the weight coefficients. Perform a smooth update. The final physical weight of the wheel is calculated as follows:

[0173]

[0174] In the formula, This is the initial physical weight, which defaults to 1.0; The smoothing coefficient is set to 0.9 in this embodiment.

[0175] Through the above strategy, the model can automatically assign larger weights to physical constraint terms in the early stages of training, forcing the network to quickly satisfy the law of conservation of mass while learning the data distribution. As training progresses and the physical residuals gradually decrease, the weights will automatically fall back, thus achieving a dynamic balance between data-driven and physics-driven approaches. This ensures that the final output has both high accuracy and meets physical interpretability requirements.

[0176] S4. Rapid intelligent calculation of levee breach flood evolution and refined reconstruction of flood elements

[0177] S41, Real-time Fast Intelligent Calculation of Dike Breach Floods

[0178] Boundary conditions (breach flow time series) ) and initial hydrodynamic state (TRU unit water depth) Horizontal flow velocity and vertical flow velocity This is constructed as the model input tensor, serving as the input to the already trained Fourier neural operator model. Utilizing its integral operator mapping capability, the model can complete full-time hydrodynamic predictions from input conditions to various topographic response units in a relatively short time. Specific outputs include the water depth of each TRU unit. Horizontal flow velocity and vertical flow velocity It covers the entire simulation period.

[0179] By employing closed-loop iterative mapping, the original second-order partial differential equation problem requiring global solution is transformed into a recursive calculation involving continuous state transitions. This enables the model to self-drive the sequential reasoning of hydrodynamic elements throughout the entire flood process, from the initial breach to the receding point. Compared to traditional two-dimensional hydrodynamic numerical models, the computation speed is improved by 2–3 orders of magnitude, compressed from hours to minutes, significantly enhancing the efficiency and stability of full-domain evolution simulation under extreme flood scenarios.

[0180] S42. Water level redistribution based on local gradient reconstruction and body volume correction

[0181] To obtain high-resolution, detailed results, subgrid reconstruction is performed while ensuring global water conservation. A detailed reconstruction diagram of levee breach flood elements is shown below. Figure 4 As shown.

[0182] 1. Calculation of local hydraulic gradient

[0183] For TRU units By utilizing the water level difference between the unit and its adjacent units, the instantaneous hydraulic gradient vector of the unit in the global coordinate system is calculated using the least squares method, as shown in the following formula. This gradient vector reflects the flow trend of the flood in the local area and the surface slope characteristics, providing a basis for the reconstruction of the water level slope.

[0184]

[0185] In the formula, Indicates the first Local water surface gradient vector at each TRU unit; The water level represents the terrain response unit; x and y represent the horizontal and vertical directions in the global coordinate system.

[0186] 2. Sloping plane reconstruction and body shape correction

[0187] For any high-resolution raster within a cell The initial water level is the water level at the center of the unit plus the gradient increment. To ensure water conservation, a volume correction factor is introduced. :

[0188]

[0189] In the formula, Indicates the first Inside the first Terrain Topology Response Unit (TRU), the first Reconstructed water level of a high-resolution fine-grained raster (sub-grid); This indicates that the Fourier neural operator model directly predicts the output of the first... Average water level of each TRU unit; Indicates the first The center spatial coordinate vector of each fine grid ; No. Geometric centroid coordinate vector of each TRU unit .

[0190] The correction factor is obtained by iteratively solving the equation using the Newton-Raps method. :

[0191]

[0192] In the formula, The model predicts the first Total water volume within each TRU unit; Indicates the first DEM surface elevation with a fine grid; This represents the area of ​​a single fine grid cell.

[0193] S43. Velocity field refinement based on hydraulic resistance weights

[0194] To avoid the problem of using a uniform value for flow velocity within a unit, which makes it difficult to reflect the actual hydrodynamic differences, this implementation method spatially refines the distribution of the average flow velocity within the unit based on the differences in flow capacity reflected by the Manning formula:

[0195] Based on the refined water depth distribution obtained in step S42, the relative flow capacity weight of each high-resolution grid within the calculation unit is calculated as follows:

[0196]

[0197] In the formula, This represents the relative flow capacity weight of the p-th grid cell within the unit. This weight is calculated based on the Manning formula, which states that flow rate is proportional to the 5 / 3 power of water depth, reflecting the physical characteristics of lower resistance and higher flow velocity in deep water regions. This represents the fine depth of the p-th fine grid cell; Manning roughness coefficient of the p-th fine grid.

[0198] 2. Flow velocity vector reconstruction

[0199] After obtaining the flow capacity weight, the average flow velocity of the unit is... Spatial allocation is performed according to the weight of each grid cell to obtain the flow velocity vector at the grid scale:

[0200]

[0201] In the formula, This represents the velocity vector of the p-th fine grid after reconstruction, reflecting the true velocity at that point after considering local micro-topography and resistance. The average velocity vector of the m-th TRU unit predicted by the model; This represents the total number of fine grids (subgrids) contained within the m-th TRU cell.

[0202] Using the velocity refinement method based on hydraulic resistance weights described above, the refined velocity field naturally exhibits a spatial stratification characteristic of "higher velocities in deep water regions and lower velocities in shallow water regions." Simultaneously, this method ensures that the total flow rate within each cell remains consistent before and after velocity downscaling, thus improving the spatial resolution of velocity while satisfying the requirements of hydrodynamic conservation.

[0203] The technical solution of the present invention has been described in conjunction with the specific experimental procedures shown in the accompanying drawings. However, the scope of protection of the present invention is not limited to these specific embodiments. Without departing from the principles of the present invention, those skilled in the art can make equivalent changes or substitutions to the relevant technical features, and the technical solutions resulting from such changes or substitutions will all fall within the scope of protection of the present invention.

Claims

1. A method for rapid flood extrapolation integrating intelligent terrain spatial reconstruction and physically enhanced Fourier operators, characterized in that, Includes the following steps: S1. Reconstruction of the computational space for rapid flood simulation: Using a deep clustering algorithm that introduces spatial connectivity constraints, high-resolution terrain is adaptively aggregated into a low-dimensional topological unit graph with physical consistency, thereby achieving efficient dimensionality reduction of the computational space. S2. Construct a flood evolution model architecture based on Fourier neural operators: Construct a graph network model based on Fourier neural operators, and utilize the Markov property of the flood system to achieve rapid recursive deduction of the state at the next moment directly from the current state. S3. Adaptive Balance Training Driven by Physical Information Constraints: A composite loss function that integrates data fitting and mass conservation is designed, and an adaptive strategy based on neural tangent vector kernels is used to dynamically balance the training gradient to ensure that the model learns physical laws. S4. Refined reconstruction of flood elements during levee breaches: Through local hydraulic gradient reconstruction, volume conservation correction, and hydraulic resistance weight allocation, the macroscopic unit prediction results are inverted into a high-resolution fine flow field, balancing efficiency and detail.

2. The method according to claim 1, characterized in that: Step S1 specifically includes the following steps: S11. Construction of Topographic Feature Vectors: Based on the high-resolution digital elevation model (DEM) of the study area, a heterogeneous feature space is constructed to characterize the physical properties and hydrodynamic trends of the terrain. Five-dimensional feature vectors are then constructed for each grid cell within the study area. ; S12. Deep manifold embedding clustering based on spatial-feature alignment: An unsupervised deep learning method, SFAD-MEC, which introduces hard constraints on spatial connectivity, is used to partition the high-resolution raster feature space into topological units. S13. Topological Response Unit (TRU) Graph Structure Representation: Based on the clustering results, the discrete grid set is reconstructed into Topological Response Units (TRUs), and a graph space mapping is constructed.

3. The method according to claim 1, characterized in that: In step S11, the five-dimensional feature vector includes normalized elevation, normalized slope, logarithmically processed confluence accumulation, normalized x-coordinate, and normalized y-coordinate.

4. The method according to claim 1, characterized in that: Step S12 is as follows: Encoding network using deep autoencoder High-dimensional feature vectors Mapping to a low-dimensional latent manifold space to extract deep nonlinear features of the terrain ; Initialize in the embedded space Cluster centers to be optimized ( Using the student t-distribution kernel function to measure the first Embedding features of individual grid cells Belongs to the The probability of membership of each cluster center : In the formula, For the degrees of freedom of the t-distribution, Denotes the Euclidean norm; Constructing a system that includes reconstruction loss Clustering loss and spatial continuity loss The joint objective function optimizes both the neural network weights and the cluster center distribution. The spatial continuity loss uses a Laplace regularization term to constrain the feature distance between adjacent grid cells in the embedding space, ensuring the connectivity of the partitioning results in the physical space.

5. The method according to claim 1, characterized in that: Step S2 specifically includes the following steps: S21. Construction of Fourier Neural Operator Network: To address the irregular grid characteristics of terrain topology response units, a network architecture coupling graph neural operators and Fourier neural operators is constructed. S22. Construction of a shallow water equation surrogate model based on Markov properties: The evolution process of floodplain breach floods is generalized into a state transition process with Markov properties, that is, utilizing the current hydrodynamic state. Directly predicting the state at the next time step using boundary conditions Constructing a deep learning agent model It replaces the traditional difference solution process for shallow water equations.

6. The method according to claim 1, characterized in that: Step S22 specifically involves: constructing a deep learning agent model. Instead of the traditional SWE difference solution process for shallow water equations, the state update equation is: In the formula, Let t be the water depth and velocity tensor of the entire TRU unit at time t; The boundary conditions for the breach flow at the corresponding time point; This includes various types of information for terrain response units, including unit nodes, adjacency relationships, and unit attribute data; For parameters The Fourier neural operator network model is used to continuously simulate the spatiotemporal evolution of floods through a recursive iteration mechanism.

7. The method according to claim 1, characterized in that: Step S3 specifically includes the following steps: S31. Multi-criteria composite loss function coupled with physical constraints: A comprehensive loss function considering both data fitting accuracy and physical conservation constraints is constructed to optimize the Fourier neural operator flood evolution model. On the one hand, a mean square error (MSE) term between the predicted results and high-precision numerical simulation samples is introduced; on the other hand, a mass conservation constraint term based on the water continuity equation is introduced to penalize non-conservative water behavior, forcing the model to follow the water balance law during training. In the formula, Represents a multi-criteria loss function with coupled physical constraints; This represents data consistency constraints; To represent the water mass conservation constraint term; Represents the dynamic weight of the water mass conservation constraint term; S32. Water mass conservation constraint based on topological connectivity: For unstructured TRU cells, the continuity equation is discretized into a flux integral form based on a topological graph structure, forcing the model to follow the water balance law: In the formula, Indicates the first TRU units at time The water depth; The unit area; For unit The set of adjacent units; Indicates time unit Flowing unit Unit width flow rate; The length of the common boundary; For time step; S33. Adaptive training strategy based on neural tangent vector kernel NTK: During the training process, due to... and The gradient magnitudes differ significantly, which can easily lead to optimization imbalance. Therefore, NTK adaptive weighting is introduced.

8. The method according to claim 1, characterized in that: Step S33 specifically involves: at the beginning of each training epoch, calculating the loss terms with respect to the network parameters. Jacobian matrix ,in, And estimate the trace of its NTK matrix: In the formula, Represents the trace operator; For neural tangent vector kernels; Represents the Jacobian matrix; Based on the convergence matching principle, the weight coefficients are dynamically updated. This makes it positively correlated with the ratio of the NTK traces of the data consistency term and the physical constraint term, thereby automatically balancing the gradient contributions of the data-driven term and the physical constraint term: In the formula, This represents the weight coefficients based on the convergence rate matching principle at the initial moment; This represents the weight coefficient based on the convergence rate matching principle at time t; Represents the trace operator; The neural tangent vector kernel for the data consistency constraint term; The neural tangent vector kernel for the water mass conservation constraint term; This indicates a positive correlation.

9. The method according to claim 1, characterized in that: Step S4 specifically includes the following steps: S41. Rapid and intelligent full-time calculation of levee breach floods: Input the breach flow sequence and initial state into the trained model to quickly predict the average water depth and flow velocity sequence of the entire field TRU unit, and realize the second-level extrapolation of large-scale floods. S42. Water level redistribution based on local gradient reconstruction and volume correction: To meet the requirements of fine distribution within the TRU unit, a subgrid reconstruction technique based on local hydraulic gradient is adopted. S43. Velocity field refinement based on hydraulic resistance weights: Based on the relative flow capacity weights defined by Manning's formula, the average velocity vector of the TRU unit is non-uniformly distributed to the high-resolution grid to obtain a refined velocity field reflecting the flood inundation area, thereby outputting a flood inundation map that meets the requirements of high-precision flood control decision-making.

10. The method according to claim 1, characterized in that: Step S42 specifically involves: First, constructing a local hydraulic gradient vector based on the topological adjacency relationship between units. First, the water surface elevation is reconstructed by combining high-resolution DEM data within the unit; second, a volume conservation correction factor is introduced. The reconstructed water level field is compensated for by translation to ensure that the total water volume within the unit is strictly consistent with the model prediction. In the formula, Indicates the first Inside the first Terrain Topology Response Unit (TRU), the first Reconstructed water level of a high-resolution fine-grained raster (sub-grid); This indicates that the Fourier neural operator model directly predicts the output of the first... Average water level of each TRU unit; Indicates the first The center spatial coordinate vector of each fine grid ; No. Geometric centroid coordinate vector of each TRU unit .

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