Graph neural differential equation-based rainstorm torrential flood physical constraint prediction method and system

Abstract

The invention discloses a rainstorm torrential flood physical constraint prediction method and system based on a graph neural differential equation, and belongs to the technical field of rainstorm torrential flood prediction. Carrying out space-time attention fusion based on a graph; carrying out modeling and dynamic deduction based on a graph neural differential equation of physical constraints; predicting and outputting a multi-task flood hydrograph; and carrying out joint loss function design and end-to-end training. The system comprises a multi-modal hydrological feature obtaining and coding module used for multi-source heterogeneous data feature extraction, a graph-based space-time attention fusion module used for deep fusion of multi-source heterogeneous features, and a physical constraint-based graph neural differential equation dynamic core module used for continuous dynamic process modeling. And the prediction output module is used for outputting the spatial distributed flood hydrograph. According to the method, the problems of low reliability, poor timeliness and poor extrapolation capability during rainstorm torrential flood prediction in the prior art are solved.

Description

Technical Field

[0001] This invention belongs to the field of rainstorm and flash flood prediction technology, specifically relating to a physical constraint prediction method and system for rainstorm and flash flood based on graph neural differential equations. Background Technology

[0002] Flash floods are natural disasters with extremely short response times and immense destructive power, making accurate prediction a major challenge in disaster prevention and mitigation. Their complexity manifests itself in the following aspects: 1. High nonlinearity and spatiotemporal heterogeneity: The formation of flash floods is a highly coupled and complex dynamic interaction process among meteorological drivers (such as short-term heavy rainfall), underlying surface conditions (topography, soil, vegetation), and river hydraulic characteristics.

[0003] 2. Uncertainty of driving factors: The spatial distribution, movement path and intensity evolution of heavy rainfall, which is the main triggering factor, are inherently highly uncertain.

[0004] 3. Extreme suddenness of response: The short confluence path and steep slope of mountainous watersheds result in a very short time from rainfall to flood peak formation, which places extremely stringent requirements on the timeliness of prediction models.

[0005] Accurately predicting flash floods essentially requires models to precisely characterize the dynamic interactions between the aforementioned multiple physical processes, which is an extremely challenging scientific task.

[0006] Current mainstream flash flood prediction technologies, whether traditional or modern, all have significant limitations and are unable to systematically address the aforementioned challenges. These include: 1. Empirical statistical model These methods (such as the ID threshold curve method) establish a statistical relationship between rainfall and disasters using historical data. Their main drawback is: (1) The fundamental flaw of the “lumped” model is that it treats the entire watershed as a homogeneous unit and completely ignores the spatial unevenness of rainfall and underlying surface conditions, which is seriously inconsistent with the characteristics of flash floods being triggered by local heavy rainfall.

[0007] (2) Lack of dynamic physical state considerations: The failure to explicitly consider key dynamic factors such as soil moisture content in the early stage may lead to inaccurate prediction results under the same rainfall conditions.

[0008] (3) Poor extrapolation ability: It relies heavily on historical data and has almost no reliable predictive ability for extreme events that are beyond the scope of experience.

[0009] 2. Hydrological Models Based on Physical Processes These models attempt to simulate the flow generation and merging process by solving mathematical physics equations. The main obstacle to their practical application is: (1) High computational cost: In order to capture the rapid response of flash floods, the model needs extremely high spatiotemporal resolution, resulting in huge computational load, which makes it difficult to meet the timeliness requirements of real-time early warning.

[0010] (2) Difficulty in parameter calibration: The model contains a large number of physical parameters that are difficult to measure directly (such as soil hydraulic conductivity and Manning roughness). The calibration process requires a large amount of high-quality observation data. However, in mountainous areas, hydrological monitoring stations are often very sparse, resulting in extremely high parameter uncertainty.

[0011] 3. Data-driven and machine learning models Deep learning models, such as LSTM and CNN, have been introduced into this field, but their inherent structural flaws have brought new problems, including: (1) Lack of physical mechanism and unreliability: Pure data-driven models are not constrained by physical laws, and their prediction results may violate basic physical laws (such as mass conservation). Their reliability cannot be guaranteed when facing extreme events.

[0012] (2) Neglect of hydrological topology: Standard CNN models are designed to process regular grid data (such as images) and cannot understand the tree-like, non-Euclidean topology of watershed networks. They cannot distinguish between geographically adjacent but hydrologically unrelated points (such as the sides of a ridge), and therefore cannot intrinsically simulate the physical process of water flow converging along the river network.

[0013] (3) Limitations of discrete-time modeling: Standard RNNs and their variants model at discrete time steps, which cannot accurately reflect continuous dynamic hydrological processes such as flood wave propagation. Summary of the Invention

[0014] This invention provides a method and system for predicting flash floods and rainstorms based on graph neural differential equations with physical constraints, aiming to solve the following technical problems: 1. How to effectively integrate the hydrological and hydraulic physical mechanisms of flash floods into deep learning models to solve the problem that pure data-driven models, lacking physical law constraints, may lead to prediction results that violate basic laws such as mass conservation, and their reliability cannot be guaranteed under extreme events.

[0015] 2. How to design an advanced architecture that can understand the hydrological topology of a watershed to solve the problem that standard deep learning models (such as CNN) cannot handle the tree-like, non-Euclidean topology of river networks, cannot distinguish between geographically proximate but hydrologically unrelated points (such as both sides of a ridge), and thus cannot intrinsically simulate the core physical process of water flow converging along the river network.

[0016] 3. How to construct a prediction method that can accurately capture the continuous dynamic evolution of floods to solve the limitations of traditional time series models (such as RNNs) in modeling at discrete time steps, so that they can more realistically reflect the continuously changing dynamic hydrological processes such as flood wave propagation.

[0017] 4. How to design an advanced multimodal data fusion mechanism to achieve deep fusion of multi-source heterogeneous data such as topography, land use, spatially distributed rainfall, and historical flow, and dynamically identify and focus on the "key runoff generating areas" that contribute the most through mechanisms such as graph spatial attention.

[0018] A method for predicting flash floods under physical constraints based on graph neural differential equations includes the following steps: (1) Multimodal hydrological feature acquisition and parallel coding: Construct a multimodal hydrological feature acquisition and coding module, and rely on a parallel encoder cluster to extract deep and multidimensional feature representations from multi-source heterogeneous data; (2) Graph-based spatiotemporal attention fusion: Construct a graph-based spatiotemporal attention fusion module, use graph attention network to dynamically weigh the influence of different spatial locations in the watershed, and deeply fuse the multi-source heterogeneous features encoded in step (1) to identify and focus on key spatiotemporal nodes and generate a unified spatiotemporal feature vector. (3) Modeling and dynamic derivation based on physical constraints of graph neural differential equations: The unified spatiotemporal feature vector generated in step (2) is used as the external driving force. A dynamic core module for graph neural differential equations based on physical constraints is constructed. Under the strong constraints of classical hydraulic laws, the future hydrological state of the entire river network system is continuously extrapolated over time. The specific steps are as follows: (3.1) Formalization of continuous-time system: The hydrological state of the entire river network is represented as a comprehensive state matrix. Its evolution over time is described by an ordinary differential equation: ;in, It is the river network state matrix Over time The rate of change; It is implemented using a graph neural network with parameters of The function; The adjacency matrix representing the river network topology; It is the external driving force at that moment; thus forming a graph neural differential equation; (3.2) Solving for future states: Using an efficient numerical ordinary differential equation solver, the graph neural differential equation defined in step (3.1) is solved from the current state. Begin integration to predict any future moment. System status ; (3.3) Differentiable physical constraints: The classical hydraulic control equations are transformed into differentiable loss function terms, which forces the learning process of the graph neural differential equations to follow physical laws and prevents the model from producing prediction results that violate physical laws. (4) Multi-task flood hydrograph prediction and output: Construct a prediction output module to decode the system state matrix of a series of future moments output by the dynamic core module of graph neural differential equation based on physical constraints, and output flood warning products. The specific steps are as follows: (4.1) State Decoding and Target Generation: The system state matrix for a series of future moments is generated from the dynamic core module of the graph neural differential equation based on physical constraints. , Decode the data to extract the time series of key physical quantities such as flow rate and water level for each warning section; (4.2) Generate spatially distributed flood hydrographs: output spatially distributed flood hydrographs, which simultaneously predict the complete flow time series for one or more key nodes in the basin over a period of time in the future, and output the peak arrival time, peak magnitude, and flood duration; (5) Joint loss function design and end-to-end training: The complete prediction architecture consisting of the multimodal hydrological feature acquisition and encoding module in step (1), the graph-based spatiotemporal attention fusion module in step (2), the physical constraint-based graph neural differential equation dynamic core module in step (3), and the prediction output module in step (4) is treated as a unified whole model. The joint loss function is minimized and the model is uniformly optimized and trained in an end-to-end manner.

[0019] Further, step (1) specifically includes: (1.1) Data acquisition and preprocessing: (1.1.1) Static data: Collect and process data describing the static underlying surface conditions of the watershed, including digital elevation model data, slope and aspect calculated based on the digital elevation model, and lithological distribution maps; (1.1.2) Dynamic data: Collect and process data on key dynamic triggering factors that cause disasters, including rainfall, soil moisture, normalized vegetation index representing vegetation cover, and river water level and flow in time series form; (1.1.3) River network topology construction: The river network system of the study area is abstracted into a directed graph structure, where each computing node represents a section of river or a sub-basin, and the edges represent the upstream and downstream connection relationships of the water flow; (1.2) Parallel Encoding of Multimodal Features: A parallel encoder cluster is constructed to process and extract features from multi-source heterogeneous input data. Corresponding encoders are designed for different data modalities, including a static watershed attribute encoder, a river network topology encoder, and a dynamic driving force encoder, wherein: The static watershed attribute encoder uses a multi-scale convolutional neural network to encode the raster data of the digital elevation model. It extracts and fuses multiple levels of topographic spatial features, including mountain range orientation and valley morphology, in parallel through convolutional kernels of different sizes. The river network topology encoder uses a graph convolutional network to encode the abstracted river network graph structure. The graph convolutional network aggregates neighbor node information through a message passing mechanism, so that the node features it ultimately learns not only include its own physical attributes, but also recursively encode its topological location information in the entire river network. The dynamic driving force encoder targets three-dimensional data of radar rainfall with spatiotemporal two-dimensional variations. It uses a three-dimensional convolutional neural network to directly extract the dynamic evolution pattern of the rainstorm system from the data cube. It uses a hybrid architecture that combines one-dimensional convolution and long short-term memory networks to process the one-dimensional time series data of the stations. One-dimensional convolution is used to capture local mutation patterns within a local window, and long short-term memory network is used to capture long-term dependencies that need to be accumulated over a long period of time.

[0020] Furthermore, step (2) specifically includes: Temporal attention module: Employs a multi-head self-attention mechanism, which is applied to the encoded temporal features to ensure that the model can autonomously identify the key time nodes that play a decisive role in causing disasters; Graph Space Attention Module: A graph attention network is built on top of the river network graph structure. The graph attention network ensures that when the model is aggregating information, downstream nodes can dynamically and specifically focus on their numerous upstream tributaries, ensuring that the model automatically concentrates computing resources and attention on the key runoff generating areas that contribute the most to the flood peak. Cross-modal attention and gating fusion: Through the cross-attention mechanism, deep interaction and semantic alignment between information from different modalities are achieved. Then, the aligned features are dynamically weighted and fused through the gating fusion unit to generate a unified spatiotemporal feature vector.

[0021] Further, step (3.3) specifically includes: Quality Balance: Construct a quality balance loss term Mass balance loss item It accurately calculates the changes in inflow, outflow, and storage volume at each node at every moment, and penalizes any predictions that violate the basic principle of "inflow - outflow = storage volume change"; Momentum equation: For mountain rivers with steep slopes, the water flow is simplified using a kinematic wave model, and the energy gradient... Approximately equal to the riverbed slope The Manning formula is transformed into a fully differentiable form, enabling the calculation of energy gradient based on the flow rate and water depth derived from the hidden state of the graph neural differential equation. Therefore, a motion wave loss term is constructed. motion wave loss term The penalty model is calculated Compared to the actual riverbed slope The deviation between them, the loss term of the moving wave The flow-depth relationship learned by the forced graph neural differential equations must conform to the basic laws of open channel hydraulics.

[0022] Furthermore, step (5) specifically includes: Joint loss function: Total loss function It consists of three weighted parts: ;

[0023] Predicting losses The mean squared error index is used to measure the difference between the flood hydrograph predicted by the model and the actual observed hydrograph. Physical loss It is the weighted sum of all physical constraint loss terms, i.e. = ; Regularization term L1 or L2 regularization is used to penalize model complexity, prevent overfitting, and enhance the model's generalization ability. End-to-end training: Total loss during training. The gradient will propagate back through the entire network, thereby simultaneously optimizing the parameters of all modules. .

[0024] A physical constraint prediction system for rainstorms and flash floods based on graph neural differential equations includes a multimodal hydrological feature acquisition and encoding module for feature extraction from multi-source heterogeneous data, a graph-based spatiotemporal attention fusion module for deep fusion of multi-source heterogeneous features, a physical constraint-based graph neural differential equation dynamic core module for continuous dynamic process modeling, and a prediction output module for outputting spatially distributed flood process lines.

[0025] In summary, due to the adoption of the above technical solution, the beneficial effects of the present invention are: 1. Dual improvement in prediction accuracy and physical rationality: Through the dual drive of physics and data, the model ensures the physical rationality and consistency of the prediction results while fitting historical data, which greatly enhances the model's extrapolation ability and reliability under extreme events.

[0026] 2. A graph-centric watershed hydrological system representation paradigm: For the first time, mountainous watersheds are completely abstracted into topologically accurate graph structures. Through GNN, a fundamental shift in model cognition is achieved from "geospatial proximity" to "hydrological process connectivity", enabling the model to explicitly learn and utilize the key physical concept of hydrological connectivity.

[0027] 3. Continuous spatiotemporal dynamic simulation based on graph neural differential equations: It innovatively combines GNN with neural ODE to construct a GDE dynamic core specifically for hydrology, which improves the discrete time step recursion to the integral solution in the continuous time domain, which is closer to the physical nature of hydrological processes and gives the model flexibility.

[0028] 4. Differentiable hydraulic constraints for open channel flow: Classical hydraulic laws (motion wave approximation) are transformed into a loss function term that can be directly used for gradient backpropagation using the differentiable Manning formula. This forces the data-driven model to adhere to physical boundaries during learning, fundamentally solving the problem of potentially physically unreasonable predictions from "black box" models.

[0029] 5. Fundamental enhancement of spatial cognitive ability and potential for generalization to data-free areas: The graph-based architecture and learning of universal physical laws enable the model to have stronger spatial generalization ability, making it possible to make reliable predictions in "data-free watersheds" where historical observation data is lacking.

[0030] 6. High-resolution output information and effective decision support: The output "process-oriented" flood hydrograph forecast product provides emergency managers with high spatiotemporal resolution decision information, including when the flood peak will arrive and its height, making it possible to formulate refined emergency response plans. 7. Enhanced Model Interpretability and Credibility: The hybrid-driven nature breaks the "black box" dilemma. Some hidden states within the model have clear physical meaning, and the magnitude of the physical constraint loss term can serve as a built-in "physical consistency checker," providing a quantitative indicator for evaluating the credibility of the prediction results. Detailed Implementation

[0031] To make the objectives, technical solutions, and advantages of this invention clearer, the technical solutions in the embodiments of this invention are described clearly and completely below. Obviously, the described embodiments are only some, not all, of the embodiments of this invention. Furthermore, the specific embodiments described herein are only used to explain this invention and are not intended to limit this invention.

[0032] A method for predicting flash floods based on graph neural differential equations with physical constraints is described in detail below: Step 1: Multimodal Hydrological Feature Acquisition and Parallel Encoding This step aims to build a multimodal hydrological feature acquisition and encoding module, which relies on a parallel encoder cluster to extract deep, multi-dimensional feature representations from multi-source heterogeneous data as the basis for subsequent model-driven approaches.

[0033] Data acquisition and preprocessing, including: 1. Static Data: Collect and process data describing the static underlying surface conditions of the watershed, mainly including: digital elevation model (DEM), slope and aspect calculated from the DEM, lithological distribution maps, etc. This data provides static background information for the formation of disasters.

[0034] 2. Dynamic data: Collect and process key dynamic triggering factors that cause disasters, mainly including: rainfall, soil moisture, normalized vegetation index (NDVI) representing vegetation cover, and river water level and flow, which exist in time series.

[0035] 3. River network topology construction: The river network system of the study area is abstracted into a directed graph structure, where each computing node represents a section of river or a sub-basin, and the edges represent the upstream and downstream connections of the water flow.

[0036] Multimodal feature parallel encoding is employed, constructing a parallel encoder cluster to process and extract features from multi-source heterogeneous input data. Corresponding encoders are designed for different data modalities, including static watershed attribute encoders, river network topology encoders, and dynamic driving force encoders. 1. Static watershed attribute encoder: For regular raster data such as DEM, a multi-scale convolutional neural network (CNN) is used for encoding. By using convolutional kernels of different sizes, multiple levels of topographic spatial features are extracted and fused in parallel, such as macroscopic mountain range orientation and microscopic valley morphology.

[0037] 2. River Network Topology Encoder: A Graph Convolutional Network (GCN) is used to encode the abstracted river network structure. GCN aggregates neighbor node information through a "message passing" mechanism, ensuring that the node features it ultimately learns not only include their own physical attributes but also recursively encode their topological location information within the entire river network. This achieves a fundamental shift in the model's spatial cognition from "pixel-based geographical proximity" to "physical connectivity based on hydrological processes."

[0038] 3. Dynamic Driving Force Encoder: For three-dimensional data with spatiotemporal two-dimensional variations, such as radar rainfall, a three-dimensional convolutional neural network (3D-CNN) is used to directly extract the dynamic evolution patterns of the rainstorm system, including its movement and development, from the data cube. For one-dimensional time series data such as station rainfall and flow, a hybrid architecture combining one-dimensional convolutional (1D-CNN) and long short-term memory (LSTM) networks is adopted. The 1D-CNN is used to capture local abrupt change patterns within local windows, such as short-duration heavy rainfall, while the LSTM is used to capture long-term dependencies, such as previous effective rainfall that requires long-term accumulation.

[0039] Step 2: Graph-based spatiotemporal attention fusion This step, serving as the "information fusion hub" of the model, constructs a graph-based spatiotemporal attention fusion module. Utilizing a graph attention network, it dynamically weighs the influence of different spatial locations within the watershed, dynamically and selectively performing deep fusion of the multi-source heterogeneous features encoded in the first step. This identifies and focuses on key spatiotemporal nodes, generating a unified spatiotemporal feature vector, including: 1. Temporal Attention Module: A multi-head self-attention mechanism is applied to the encoded temporal features. This mechanism can automatically learn the importance weights of different time points, allowing the model to autonomously identify key time nodes that play a decisive role in causing disasters. For example, different weights are assigned to short-term heavy rainfall in the hours before a disaster and cumulative rainfall in the days before the disaster.

[0040] 2. Graph Attention Module: This is one of the innovations of this invention. A Graph Attention Network (GAT) is constructed on top of the river network graph structure. This network allows downstream nodes to dynamically and selectively "pay attention" to their numerous upstream tributaries when the model is aggregating information. This means that the model can automatically focus computational resources and attention on the "critical runoff-generating areas" that contribute the most to the flood peak, rather than treating all upstream information equally.

[0041] 3. Cross-modal gated fusion: Through a cross-attention mechanism, deep interaction and semantic alignment between different modal information (such as meteorological driving features and topographic features) are achieved. Subsequently, a gated fusion unit dynamically weights and fuses the aligned features to generate an information-rich and unified spatiotemporal feature vector, which drives the next dynamic core module.

[0042] Step 3: Modeling and Dynamic Derivation of Physically Constrained Graph Neural Differential Equations (GDEs) This step is the model's "dynamic evolution engine" and the most core innovative module. It uses the unified spatiotemporal feature vector generated in step (2) as an external driving force. A dynamic core module for graph neural differential equations based on physical constraints is constructed. Under the strong constraints of classical hydraulic laws, the future hydrological state of the entire river network system is continuously extrapolated over time. The specific steps are as follows: 1. Formalization of continuous-time systems: The hydrological state of the entire river network (e.g., the discharge Q and water depth h at each node) is represented as a comprehensive state matrix. Its evolution over time is described by an ordinary differential equation (ODE): .in, It is the river network state matrix Over time The rate of change; It is implemented using a graph neural network (GNN) with parameters of The function that the model needs to learn; It is the adjacency matrix representing the river network topology; This represents the external driving force at that moment (such as spatially distributed rainfall). The above equations together constitute a Graph Neural Differential Equation (GDE).

[0043] 2. Future State Solution: Using an efficient numerical ODE solver, the GDE above is solved from the current state. By starting the integration process, one can predict any future moment. System status This simulation in the continuous time domain approximates the essence of continuous physical processes such as flood wave propagation more closely than the discrete step size modeling of traditional RNNs.

[0044] 3. Differentiable physical constraints: To fundamentally solve the problem that pure data-driven models may produce physically unreasonable results, the classical hydraulic control equations are transformed into differentiable loss function terms, forcing the learning process of GDE to follow physical laws.

[0045] Constraint 1: Mass Balance: Construct a mass balance loss term. The loss term accurately calculates the changes in inflow, outflow and storage at each node at each moment, and penalizes any prediction that violates the basic principle of "inflow - outflow = storage change", ensuring that the model does not "create" or "destroy" water out of thin air.

[0046] Constraint 2: Momentum Equation: For mountain rivers with steep slopes, the flow motion can be simplified using a kinematic wave model, the core assumption of which is energy gradient. Approximately equal to the riverbed slope The classic Manning formula establishes the relationship between flow rate, water depth, roughness, and energy gradient. This invention transforms the Manning formula into a fully differentiable form, enabling the calculation of the energy gradient based on the flow rate and water depth derived from the hidden state of the GDE. Therefore, a motion wave loss term is constructed. This loss term is used to penalize the model's calculated loss. Compared to the actual riverbed slope The deviation between the two. This loss term forces the flow-depth relationship learned by the GDE to conform to the basic laws of open channel hydraulics.

[0047] Step 4: Multi-task flood process curve prediction and output: Construct a prediction output module to transform the future state trajectory with physical meaning output in the previous step into a flood early warning product for practical applications.

[0048] State Decoding and Target Generation: This involves generating the system state matrix for a series of future moments from the output of the GDE dynamic core module. , Decode the data to extract the time series of key physical quantities such as flow rate and water level for each warning section.

[0049] Generate a spatially distributed flood hydrograph: The core output is a spatially distributed flood hydrograph, representing one or more key nodes within the basin, while also predicting the complete flow time series over a future period (e.g., the next 1-6 hours). This forecast product contains all the critical information needed for emergency decision-making, such as peak arrival time, peak magnitude, and flood duration.

[0050] Step 5: Design of Joint Loss Function and End-to-End Training The complete prediction architecture, consisting of a multimodal hydrological feature acquisition and encoding module, a graph-based spatiotemporal attention fusion module, a physically constrained graph neural differential equation dynamic core module, and a step prediction output module, is treated as a unified whole model. The entire model is uniformly optimized and trained in an end-to-end manner by minimizing a carefully designed joint loss function.

[0051] Joint loss function: Total loss function It consists of three weighted parts: ;

[0052] Predicting losses The mean square error (MSE) and other indicators are used to measure the difference between the flood hydrograph predicted by the model and the actual observed hydrograph.

[0053] Physical loss It is the weighted sum of all the aforementioned physical constraint loss terms, i.e. = .

[0054] Regularization term L1 or L2 regularization is used to penalize model complexity, prevent overfitting, and enhance the model's generalization ability.

[0055] End-to-end training: Total loss during training. The gradient will propagate back through the entire network (including the numerical ODE solver), thereby simultaneously optimizing the parameters of all modules. This training method ensures that both the model's prediction accuracy and physical consistency can be improved simultaneously.

[0056] A physical constraint prediction system for rainstorms and flash floods based on graph neural differential equations includes a multimodal hydrological feature acquisition and encoding module for feature extraction from multi-source heterogeneous data, a graph-based spatiotemporal attention fusion module for deep fusion of multi-source heterogeneous features, a physical constraint-based graph neural differential equation dynamic core module for continuous dynamic process modeling, and a prediction output module for outputting spatially distributed flood process lines.

[0057] The above description constitutes an embodiment of the present invention. The foregoing descriptions are preferred embodiments of the present invention. Unless there is a clear contradiction or a prerequisite for a particular preferred embodiment, the preferred embodiments can be arbitrarily combined and used. The embodiments and specific parameters described are merely for clearly illustrating the verification process of the invention and are not intended to limit the scope of patent protection of the present invention. The scope of patent protection of the present invention is still determined by its claims. Similarly, any equivalent structural changes made based on the content of the present invention's specification should also be included within the scope of protection of the present invention.

Claims

1. A storm flood physical constraint prediction method based on graph neural differential equation, characterized in that, The method comprises the following steps: (1) Multi-modal hydrological feature acquisition and parallel coding: a multi-modal hydrological feature acquisition and coding module is constructed, and deep and multi-dimensional feature representations are extracted from multi-source heterogeneous data by relying on a parallel encoder cluster; (2) Graph-based spatio-temporal attention fusion: a graph-based spatio-temporal attention fusion module is constructed, the influences of different spatial positions in a basin are dynamically weighted by using a graph attention network, and the multi-source heterogeneous features coded in step (1) are deeply fused to identify and focus on key spatio-temporal nodes, so that a unified spatio-temporal feature vector is generated; (3) Modeling and dynamic deduction based on physical constraint graph neural differential equation: taking the unified spatio-temporal feature vector generated in step (2) as an external driving force , a dynamic core module based on a physical constraint graph neural differential equation is constructed, and under the strong constraint of classical hydrology laws, the future hydrological state of the entire river network system is deduced in continuous time, and the specific steps are as follows: (3.1) Formalization of continuous-time system: The hydrological state of the entire river network is represented as a comprehensive state matrix. Its evolution over time is described by an ordinary differential equation: ;in, It is the river network state matrix Over time The rate of change; It is implemented using a graph neural network with parameters of The function; The adjacency matrix representing the river network topology; It is the external driving force at that moment; thus forming a graph neural differential equation; (3.2) Future state solving: by an efficient numerical ordinary differential equation solver, solve the graph neural differential equation defined in step (3.1) from the current state to predict the system state at any future time ;​ (3.3) Differentiable physical constraints: the classical hydraulic control equation is converted into a differentiable loss function item, the learning process of the graph neural differential equation is forced to follow the physical law, and the model is prevented from generating prediction results that violate the physical law; (4) Multi-task flood hydrograph prediction and output: a prediction output module is constructed, a series of system state matrices at future time points output by the graph neural differential equation dynamic core module based on physical constraints are decoded, and flood warning products are output, and the specific steps are as follows: (4.1) State decoding and target generation: decode the system state matrix at a series of future time instants output by the dynamic core module of the physics-constrained graph neural differential equation , ,... to extract the time series of key physical quantities such as flow and water level at each warning section; (4.2) Generation of spatially distributed flood hydrograph: a spatially distributed flood hydrograph is output, the complete flow time series in a future period of time is predicted for one or more key nodes in the basin at the same time, and the flood peak arrival time, flood peak magnitude and flood duration are output; (5) Joint loss function design and end-to-end training: the complete prediction architecture composed of the multi-modal hydrological feature acquisition and coding module in step (1), the graph-based spatio-temporal attention fusion module in step (2), the graph neural differential equation dynamic core module based on physical constraints in step (3) and the prediction output module in step (4) is taken as a unified whole model, and the unified optimization training is carried out in an end-to-end manner by minimizing the joint loss function.

2. The storm flood physical constraint prediction method based on graph neural differential equations according to claim 1, characterized in that, The step (1) is specifically: (1.1) Data acquisition and preprocessing: (1.1.1) Static data: collecting and processing data describing the static underlying surface conditions of the basin, including digital elevation model data, slope and slope direction calculated from the digital elevation model, and lithology distribution map; (1.1.2) Dynamic data: collecting and processing key dynamic trigger factor data that cause disasters, including rainfall, soil moisture, normalized vegetation index representing vegetation coverage, and river water level and flow in the form of time series; (1.1.3) River network topology construction: the river network system of the study area is abstracted into a directed graph structure, each calculation node represents a river or a sub-basin, and the edge represents the upstream and downstream connection relationship of water flow; (1.2) Multi-modal feature parallel coding: a parallel encoder cluster is constructed to process and extract features of multi-source heterogeneous input data, corresponding encoders are designed for different data modalities, including a static basin attribute encoder, a river network topology encoder and a dynamic driving force encoder, wherein: The static basin attribute encoder adopts a multi-scale convolutional neural network to encode the raster data of the digital elevation model, and extracts and fuses multiple levels of terrain spatial features, including mountain trend and valley morphology, in parallel through different sizes of convolution kernels; The river network topology encoder adopts a graph convolution network to encode the abstracted river network graph structure, and the graph convolution network aggregates neighbor node information through a message passing mechanism, so that the node features learned finally not only contain their own physical properties, but also recursively encode the topological position information in the entire river network; The dynamic driving force encoder adopts a three-dimensional convolutional neural network to directly extract the dynamic evolution pattern of the rainstorm system from the three-dimensional data of the radar rainfall with spatial and temporal two-dimensional changes, and adopts a hybrid architecture combining one-dimensional convolution and long short-term memory network to process one-dimensional time series data at the station, one-dimensional convolution is used to capture local mutation patterns within a local window, and long short-term memory network is used to capture long-term dependencies that need to be accumulated over a long period of time.

3. The storm flood physical constraint prediction method based on graph neural differential equations according to claim 1, characterized in that, The step (2) is specifically: The time attention module adopts a multi-head self-attention mechanism and acts on the encoded time sequence features to ensure that the model can automatically identify key time nodes that play a decisive role in disaster; The graph space attention module constructs a graph attention network on the river network graph structure, and the graph attention network ensures that the downstream nodes can dynamically and specifically focus on the numerous tributaries upstream when aggregating information, and ensures that the model automatically concentrates computing resources and attention on the key runoff areas that contribute most to the flood peak; Cross-modal attention and gating fusion: through cross-attention mechanism, realize the deep interaction and semantic alignment between different modal information, and then through the gating fusion unit, dynamically weight and fuse the aligned features to generate a unified spatio-temporal feature vector.

4. The storm flood physical constraint prediction method based on graph neural differential equations according to claim 1, wherein, The step (3.3) is specifically: Mass balance: construct a mass balance loss term , mass balance loss term Precisely compute inflow, outflow, and change in storage for each node at each time step, and penalize any predictions that violate the basic principle that "inflow - outflow = change in storage"; Momentum equation: for steep mountainous rivers, the water flow is simplified by the kinematic wave model, and the energy slope is approximately equal to the river bed slope , the Manning formula is converted into a fully differentiable form, which can calculate the energy slope according to the flow and water depth derived from the graph neural differential equation hidden state , thus constructing a kinematic wave loss term , the kinematic wave loss term is used to punish the deviation between the calculated and the real river bed slope , the kinematic wave loss term forces the flow-water depth relationship learned by the graph neural differential equation to comply with the basic open channel hydraulics.

5. The storm flood physical constraint prediction method based on graph neural differential equations according to claim 1, wherein, The step (5) is specifically: Joint loss function: total loss function weighted by three parts Composition: ； Prediction loss : The difference between the predicted flood hydrograph and the observed hydrograph is measured by the mean square error index. Physical loss : is the weighted sum of all physical constraint loss terms, i.e. ;​ regularization term : L1 or L2 regularization is used to penalize model complexity, prevent overfitting, and enhance the generalization ability of the model; End-to-end training: During training, the gradient of the total loss is backpropagated through the entire network, thus synchronously optimizing the parameters of all modules .​ 6. A storm flood physical constraint prediction system based on graph neural differential equations, characterized in that, It includes a multi-modal hydrological feature acquisition and encoding module for multi-source heterogeneous data feature extraction, a graph-based spatio-temporal attention fusion module for deep fusion of multi-source heterogeneous features, a physically constrained graph neural differential equation dynamic core module for continuous dynamic process modeling, and a prediction output module for outputting spatially distributed flood hydrograph.

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