A physically coded explainable urban rainfall runoff inundation rapid inference method and system

Abstract

The application discloses a kind of physical encoding explainable urban rainfall runoff inundation quick deduction method and system, solve the technical problem that existing urban rainfall runoff inundation quick deduction method is difficult to consider deduction efficiency, physical credibility and result explainability.The method includes building uniform state space according to the obtained urban target area basic input data, completing surface-pipe network-river system collaborative hydrodynamic coupling solution in uniform state space, combining absolute water level difference set, system net exchange flux and external boundary state quantity to complete state collaborative update and output structured state set, complete physical relationship to space-time diagram structure explicit coding, generate space-time directed graph with physical properties, carry out constraint space-time recursive prediction with absolute water level difference driving and system exchange flux linkage as core to obtain global flood candidate situation, complete residual error checking and local resolvent with the aid of physical consistency closed loop, output the final global flood situation after correction.

Description

Technical Field

[0001] This invention relates to the field of urban flood control technology, and in particular to a method and system for rapid extrapolation of urban rainfall runoff inundation that can be interpreted by physical coding. Background Technology

[0002] Under the combined influence of global climate change and rapid urbanization, urban flooding disasters induced by extreme heavy rainfall are characterized by their suddenness, complex evolution process, and significant spatial differentiation. Frequent and recurring rainstorm-induced urban flooding has become a prominent problem restricting the safe operation and sustainable development of cities, and seriously threatens the stable operation of urban infrastructure and regional public safety.

[0003] With the iterative upgrading of urban disaster prevention and mitigation concepts, urban flood control research and engineering practice are gradually shifting from traditional post-disaster emergency response to rapid simulation, dynamic risk assessment and proactive defense covering the entire chain of rainfall generation, runoff, transmission and inundation evolution. The core technical support for achieving the above goals is to build a unified modeling technology system that can cover the entire process of urban rainfall-runoff-inundation, while taking into account the authenticity of physical mechanisms, computational simulation efficiency and interpretability of results.

[0004] To meet the practical needs of rapid prediction and proactive defense of the entire urban flood process, existing rapid simulation technologies for urban rainfall runoff inundation generally rely on static digital elevation models to set fixed water flow directions for basic simulation calculations. This fixed flow direction setting cannot keep up with real-time changes in the hydraulic environment. Once extreme rainfall occurs, and conditions such as local water accumulation and uplift, overloaded underground pipe networks causing water accumulation, high water levels in rivers causing backflow, and changes in the boundary state of external receiving water bodies occur, the technology cannot adaptively adjust the flow path, nor can it accurately reproduce complex hydraulic behaviors such as backflow and reverse overflow. Consequently, the hydraulic processes between the three major hydrological systems—surface, river, and underground pipe networks—are not tightly coupled, and the technology cannot fully reproduce the true hydrodynamic evolution of the entire region. Based on this, if we want to improve the accuracy of the simulation results, we must use high-fidelity physical models to carry out the calculations. However, such models require solving a large number of complex equations, which greatly increases the amount of computation and makes it difficult to meet the timeliness requirements of rapid flood emergency simulation. If we simplify the calculation logic to adapt to the needs of rapid simulation, we will abandon core physical constraints such as mass conservation, water level gradient flow direction, and continuity of cross-system water exchange. This makes the rapidly output prediction results prone to deviations that violate the hydraulic operation mechanism, making it difficult to balance simulation efficiency, physical reliability, and interpretability of results. Summary of the Invention

[0005] This invention provides a physical coding-interpretable method and system for rapid prediction of urban rainfall runoff inundation. It solves the technical problems of insufficient coupling between surface, pipeline and river processes, the flow direction relying on static presets, the lack of mass conservation, water level gradient direction and cross-system exchange continuity constraints in the rapid prediction results, and the difficulty in balancing prediction efficiency, physical reliability and interpretability.

[0006] The first aspect of this invention provides a method for rapid extrapolation of urban rainfall-runoff inundation using physically coded interpretable methods, comprising:

[0007] Acquire basic input data for the target urban area, and construct a unified state space based on the basic input data for the target urban area;

[0008] The unified state space is used to perform a coordinated hydrodynamic coupling solution for the surface-pipeline-river system. Within the unified state space, the system state is updated collaboratively based on the set of absolute water level differences, the net exchange flux between systems, and the external boundary state quantities, and a structured state set is output.

[0009] The structured state set is explicitly encoded into a spatiotemporal graph structure based on physical relationships, and a spatiotemporal directed graph with physical attributes is output.

[0010] The spatiotemporal directed graph with physical attributes is subjected to spatiotemporal recursive prediction based on physical constraints driven by absolute water level difference and inter-system exchange flux linkage, and the candidate flood situation of the whole region is output.

[0011] The physical residual verification and local re-solution are performed on the candidate flood situation and the unified state space through a physical consistency closed-loop method, and the final flood situation after physical consistency correction is output.

[0012] Optionally, the unified state space is specifically composed of external boundary state quantities, dynamic hydraulic state data, net exchange flux between systems, absolute water level difference set, and basic static data in the basic input data of the urban target area.

[0013] Optionally, the net exchange flux between systems includes river depth, surface-to-river net exchange flux, and surface-to-pipeline net exchange flux; the unified state space is used to perform a surface-pipeline-river system coordinated hydrodynamic coupling solution, and the system state is coordinatedly updated within the unified state space based on the absolute water level difference set, the net exchange flux between systems, and the external boundary state quantities, outputting a structured state set, including:

[0014] The surface water flow motion and soil infiltration loss within the unified state space are solved to obtain surface water depth and infiltration loss data.

[0015] The one-dimensional evolution process of the river channel within the unified state space is solved based on the surface water depth and the infiltration loss data to obtain the river channel depth and the net surface-to-channel exchange flux.

[0016] Based on the surface water depth, the infiltration loss data, the river water depth and the surface-to-river net exchange flux, the underground pipeline transportation and discharge process in the unified state space is solved to obtain the pipeline node head and the surface-to-pipeline net exchange flux.

[0017] Based on the surface water depth, the river water depth, and the water head at the pipeline nodes, calculate the set of absolute water level differences;

[0018] The water level at the boundary of the external receiving water body is taken as the external boundary state quantity.

[0019] By integrating the surface water depth, the river water depth, the water head of the pipeline node, the net exchange flux between the surface and the pipeline, the net exchange flux between the surface and the river, the absolute water level difference set, and the external boundary state quantity, a structured state set is obtained;

[0020] The two-dimensional surface water flow movement, the one-dimensional river flow evolution process, and the underground pipeline transportation and discharge process are all updated collaboratively within the unified state space based on the absolute water level difference set, the net exchange flux between systems, and the external boundary state quantity. The solution is achieved through coupled solutions via water exchange feedback between the surface and the pipeline, the surface and the river, and the pipeline and the receiving water body.

[0021] Optionally, the set of absolute water level differences includes water level differences between adjacent surface units, between the surface and the pipe network, between the surface and the river, and between the pipe network and the external receiving water body;

[0022] Absolute water level includes one or more of the following: the sum of surface elevation and dynamic water depth, water head at pipeline nodes, river water level, or boundary water level of external receiving water bodies.

[0023] The absolute water level difference set is used to determine the direction, intensity and spatiotemporal directional graph edge direction of water exchange between surface units, pipeline nodes, river units and external receiving water bodies, so that the flow path can be dynamically updated with the real-time water level status.

[0024] Optionally, the step of explicitly encoding the physical relationships into a spatiotemporal graph structure of the structured state set, and outputting a spatiotemporal directed graph with physical attributes, includes:

[0025] The structured state set is subjected to node feature extraction processing to generate node feature vectors;

[0026] Edge features are extracted from the structured state set to generate edge feature vectors;

[0027] Based on the node feature vectors and the edge feature vectors, a spatiotemporal directed graph with physical attributes is constructed.

[0028] The node feature vector includes one or more of the following: surface water depth, river water depth, pipeline node head, external boundary water level, local storage and discharge status, and absolute water level.

[0029] The edge feature vector includes one or more of the following: absolute water level difference, net surface-to-pipeline exchange flux, net surface-to-river exchange flux, internal connectivity of the pipeline network, boundary type, flow direction identifier, and exchange continuity identifier.

[0030] The edge directions in the spatiotemporal directed graph with physical attributes are jointly determined by the real-time absolute water level difference, physical connectivity, and inter-system exchange flux, and are used to characterize the dynamic flow direction and cross-system exchange relationships in the flood hydrodynamic process.

[0031] Optionally, the step of performing spatiotemporal recursive prediction on the spatiotemporally directed graph with physical attributes, driven by absolute water level difference and with inter-system exchange flux linkage as the core, to output candidate flood situations for the entire region, includes:

[0032] Along the physical connectivity path of the spatiotemporal directed graph with physical attributes, using the absolute water level difference of nodes as the basis for spatial transmission and the exchange flux between systems as the hydraulic linkage benchmark, spatial aggregation of node feature vectors is performed to obtain spatial aggregation features.

[0033] Based on the spatial aggregation features, the node feature vectors are recursively updated in the time dimension to obtain the spatiotemporal recursive intermediate results.

[0034] Mass conservation constraints, water level gradient direction constraints, exchange continuity constraints, and spatiotemporal smoothing constraints are applied as propagation constraints to the intermediate spatiotemporal recursion results. These constraints are simultaneously applied to the entire process of node spatial aggregation, time recursion update, and candidate situation generation to optimize the physical constraints of mass conservation, water level gradient direction, and spatiotemporal smoothing, resulting in optimized spatiotemporal recursion results.

[0035] Based on the optimized spatiotemporal recursive results, candidate flood situations for the entire region are determined;

[0036] The constraint on the water level gradient direction is used to restrict the predicted water flow direction from being consistent with or not conflicting with the hydrodynamic driving direction determined by the real-time absolute water level difference.

[0037] Optionally, the step of performing physical residual verification and local re-solution on the candidate global flood situation and the unified state space through a physical consistency closed-loop method, and outputting the final global flood situation after physical consistency correction, includes:

[0038] Based on the physical constraint rules of the unified state space, the following residuals are calculated: macroscopic conservation residuals representing the deviation of water balance between the whole region and the local area in the candidate flood situation; directional conflict residuals representing the conflict between the predicted water flow direction and the driving direction of the absolute water level difference; and exchange continuity residuals representing the jump in flux at the interaction boundary between the surface and the pipe network and the surface and the river channel.

[0039] Determine whether the macroscopic conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the entire region trigger the limit-breaking condition;

[0040] If the aforementioned over-limit condition is not triggered, the candidate global flood situation will be taken as the final global flood situation after the physical consistency correction.

[0041] Optionally, it also includes:

[0042] If the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the whole region trigger the limit-breaking condition, then based on the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the whole region, an abnormal spatial sub-region is locked in the target urban area.

[0043] Perform a local re-solution on the aforementioned abnormal spatial sub-region to obtain the corrected local calculation results;

[0044] The corrected local calculation results are fed back into the unified state space to complete the update, resulting in a new unified state space.

[0045] Jump to execute the step of performing a coordinated hydrodynamic coupling solution of the surface-pipeline-river system in the unified state space and outputting a structured state set until the macroscopic conservation residual, directional conflict residual and exchange continuity residual of the candidate flood situation in the whole region do not trigger the over-limit condition;

[0046] The candidate state of the global flood situation determined when the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate state of the global flood situation do not trigger the above-mentioned over-limit conditions is taken as the final global flood situation after the physical consistency correction.

[0047] The abnormal spatial sub-region is determined based on the spatial distribution of the macroscopic conservation residual, the directional conflict residual, and the exchange continuity residual, and includes the surface grid, pipeline nodes, river units, and their adjacent hydraulic connectivity regions where the residuals trigger the limit-breaking conditions;

[0048] The corrected local calculation results include one or more of the following: corrected surface water depth, pipeline node head, river water depth, inter-system exchange flux, and absolute water level difference set, which are used for the next round of structured state set generation, spatiotemporal map encoding, and recursive prediction.

[0049] A second aspect of the present invention provides a physical coding-interpretable urban rainfall-runoff inundation rapid projection system, comprising:

[0050] The acquisition module is used to acquire basic input data of the target urban area and construct a unified state space based on the basic input data of the target urban area.

[0051] The solution module is used to perform a coordinated hydrodynamic coupling solution of the surface-pipeline-river system in the unified state space. Within the unified state space, it completes the coordinated update of the system state based on the set of absolute water level differences, the net exchange flux between systems, and the external boundary state quantities, and outputs a structured state set.

[0052] The encoding module is used to explicitly encode the physical relationships of the structured state set into a spatiotemporal graph structure, and output a spatiotemporal directed graph with physical attributes.

[0053] The prediction module is used to perform spatiotemporal recursive prediction on the spatiotemporal directed graph with physical attributes, with physical constraints embedded as the core of absolute water level difference driving and inter-system exchange flux linkage, and output the candidate situation of flood in the whole region.

[0054] The closed-loop verification module is used to perform physical residual verification and local re-solution on the candidate flood situation of the whole domain and the unified state space through a physical consistency closed-loop method, and output the final flood situation of the whole domain after physical consistency correction.

[0055] A third aspect of the present invention provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and when the computer program is executed by the processor, the processor performs the steps of the physical coding interpretable rapid extrapolation method for urban rainfall runoff inundation as described above.

[0056] As can be seen from the above technical solutions, the present invention has the following advantages:

[0057] The above-mentioned technical solution of the present invention provides a method for rapid extrapolation of urban rainfall-runoff inundation with physical coding interpretability. It acquires basic input data of the target urban area and constructs a unified state space based on this data. The unified state space is then used for coordinated hydrodynamic coupling solution of the surface-pipeline-river system. Within the unified state space, the system state is collaboratively updated based on the absolute water level difference set, the net exchange flux between systems, and the external boundary state quantities, outputting a structured state set. The structured state set is then explicitly encoded into a spatiotemporal graph structure based on physical relationships, outputting a spatiotemporal directed graph with physical attributes. Finally, the spatiotemporal graph with physical attributes is further encoded. Directed graphs are used for spatiotemporal recursive prediction based on physical constraints driven by absolute water level differences and inter-system exchange flux linkages, outputting candidate flood situations for the entire region. A physical consistency closed-loop approach is used to verify physical residuals and perform local re-solution on the candidate flood situations and the unified state space, outputting the final, physically consistent flood situation for the entire region. Based on this scheme, a unified state space is built as the unified carrier for hydraulic computation across the entire region. This is combined with multi-system state collaborative update operations based on the absolute water level difference set, net inter-system exchange flux, and external boundary state quantities, completely changing the previous situation where surface, pipeline, and river hydrological processes were independent. The implementation mode of the operation uses the absolute water level difference obtained in real time as the core driving condition for the overall inference. It abandons the traditional method of relying on static presets to determine the direction of water flow, allowing the water flow direction to form autonomously in complete accordance with the real-time hydraulic operation state. After the structured state set is completed and the physical relationships are explicitly encoded to generate a spatiotemporal directed graph with physical attributes, the spatiotemporal recursive prediction stage is carried out. Mass conservation, water level gradient direction, and cross-system exchange continuity related physical constraints are integrated into the entire inference process. This ensures that the rapidly predicted global flood candidate situation follows the established physical rules and constraints throughout the entire process, making up for the lack of corresponding physical constraints in traditional rapid prediction results. To address the shortcomings of the current control mechanism, the subsequent physical consistency closed-loop system is used to conduct physical residual verification and local re-solution of the candidate flood situation and unified state space across the entire region. This allows for timely correction of various physical operational deviations that occur during the simulation process, thereby steadily improving the physical reliability of the simulation results. The entire simulation process relies on a spatiotemporal recursive computation mode to ensure the efficiency of the overall simulation work. Furthermore, the entire process relies on real hydrological physical correlations to complete structural coding and situation simulation, ensuring that each simulation result has corresponding physical logical support and fully guaranteeing the interpretability of the simulation results. Ultimately, this successfully achieves a synergistic balance between simulation efficiency, physical reliability, and result interpretability. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart illustrating the steps of a method for rapidly extrapolating urban rainfall-runoff inundation using physically coded interpretation, as provided in Embodiment 1 of the present invention.

[0060] Figure 2 This is a comparison diagram of spatial inundation distribution at typical flood peak times provided in Embodiment 1 of the present invention;

[0061] Figure 3 This is a comparison diagram of water depth process lines at key locations provided in Embodiment 1 of the present invention;

[0062] Figure 4 This is a stability comparison chart under different foreseeability durations provided in Embodiment 1 of the present invention;

[0063] Figure 5 This is an overall flowchart of a method for rapid extrapolation of urban rainfall-runoff inundation that can be interpreted by physical coding, provided in Embodiment 1 of the present invention.

[0064] Figure 6 This is a structural block diagram of a physical coding-interpretable urban rainfall-runoff inundation rapid projection system provided in Embodiment 2 of the present invention. Detailed Implementation

[0065] This invention provides a physical coding-interpretable method and system for rapid prediction of urban rainfall runoff inundation. It solves the technical problems of insufficient coupling between surface, pipeline and river processes, the flow direction relying on static presets, and the lack of mass conservation, water level gradient direction and cross-system exchange continuity constraints in the rapid prediction results, making it difficult to balance prediction efficiency, physical reliability and interpretability.

[0066] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention. It should be noted that in the optional embodiments of the present invention, the object information and other related data involved require the permission or consent of the object when the embodiments of the present invention are applied to specific products or technologies, and the collection, use, and processing of related data must comply with relevant laws, regulations, and standards. That is to say, if the embodiments of the present invention involve data related to the object, it needs to be obtained with the authorization and consent of the object, the authorization and consent of relevant departments, and in compliance with relevant laws, regulations, and standards. If personal information is involved in the embodiments, the acquisition of all personal information requires the consent of the individual. If sensitive information is involved, the separate consent of the information subject is required, and the embodiments also need to be implemented with the authorization and consent of the object.

[0067] Please see Figure 1 , Figure 1 The flowchart illustrates the steps of a physical coding-interpretable method for rapid extrapolation of urban rainfall-runoff inundation, as provided in Embodiment 1 of the present invention.

[0068] This invention provides a method for rapid extrapolation of urban rainfall-runoff inundation using physically coded and interpretable methods, comprising:

[0069] Step 101: Obtain basic input data for the target urban area and construct a unified state space based on the basic input data for the target urban area.

[0070] The basic input data for the urban target area is divided into two categories: static basic input and dynamic boundary input. Static basic input (i.e., basic static data) includes a two-dimensional digital elevation model (DEM), underground pipe network topology parameters, one-dimensional river cross-sectional geometric parameters, and underlying land use types. The two-dimensional DEM is raster data representing the surface elevation distribution of the target area, providing basic support for surface grid division and surface water accumulation evolution calculations. The underground pipe network topology parameters include information such as pipe node locations, inter-node connections, pipe diameter, and pipe slope, used to construct the topology of the pipe network system and support the solution of the pipe network's transport and drainage processes. The one-dimensional river cross-sectional geometric parameters include the river cross-sectional shape, width, and... Information such as depth and roughness is used to characterize the flow capacity of the river channel, supporting the solution of the one-dimensional water flow evolution process of the river channel; the underlying land use type represents the distribution of different underlying surfaces such as buildings, roads, and green spaces within the target area, providing parameter basis for soil infiltration loss calculation; the dynamic boundary input includes the spatiotemporal rainfall matrix and the boundary water level of the external receiving water body. The spatiotemporal rainfall matrix contains rainfall intensity data at different spatial locations and time steps within the target area, which is the core dynamic input driving the surface runoff generation and confluence process and conducting flood simulation; the boundary water level of the external receiving water body is the water level data of the receiving water body outside the target area, serving as the external boundary condition of the system and directly affecting the hydrodynamic processes of the surface, river channel, and pipe network.

[0071] The unified state space is specifically composed of external boundary state quantities, dynamic hydraulic state data, inter-system net exchange flux, absolute water level difference set, and basic static data from the basic input data of the urban target area. The unified state space serves as an integrated data and physical state carrier for the coupled hydrodynamic simulation of the entire region. The basic static data is taken from the basic input data of the urban target area, serving as the fixed data foundation of the unified state space and providing constant space and basic parameters for the overall hydrodynamic solution. The dynamic hydraulic state data are core hydraulic state quantities updated in real time after completing the coupled solution of two-dimensional surface water flow, soil infiltration, river flow evolution, and pipeline transport and discharge within the unified state space. Specifically, it includes surface water depth, infiltration loss data, river depth, and pipeline node head. The inter-system net exchange flux is dynamically generated interactive state data during the multi-system coupled solution process. Specifically, it includes surface-to-river net exchange flux and surface-to-pipeline net exchange flux, used to characterize the water exchange relationship between the three types of subsystems. The absolute water level difference set is calculated based on real-time updated dynamic hydraulic state data of surface water depth, river water depth, and pipeline node head, and is the core physical variable driving the direction and intensity of water exchange across the entire region. The external boundary state quantity is composed of the boundary water level of the external receiving water body, serving as the external constraint condition for the coordinated updating of hydrodynamics across the entire region. The above five types of data elements are uniformly collected in the same state space, realizing the synchronous storage, coordinated updating, and unified retrieval of the physical state and interaction data of the surface, river, and pipeline subsystems. This provides complete and unified state data support for subsequent spatiotemporal mapping of physical relationships, spatiotemporal recursive prediction of physical constraint embedding, and closed-loop correction of physical consistency.

[0072] It should be noted that this step is used to establish a unified mathematical expression for solving physical mechanisms and sharing data-driven learning during the system initialization phase, and to construct a unified state space structure on which subsequent steps depend. The system first acquires the static basic input and dynamic boundary input of the target area. The static basic input includes the two-dimensional ground digital elevation model (DEM), underground pipe network topology parameters, one-dimensional river cross-sectional geometric parameters, and underlying land use type; the dynamic boundary input includes the spatiotemporal rainfall matrix and the boundary water level of the external receiving water body.

[0073] Based on the above inputs, the system constructs a unified state space and defines the following core state variables: surface water depth, river water depth, pipeline node head, inter-system exchange flux, and absolute water level difference. Among these, the absolute water level serves as the unified driving variable for the system, used to connect the physical solutions and data representation of the surface, river, and pipeline subsystems. These uniformly defined state variables play a dual role in the system's underlying architecture: firstly, they serve as the physical solution target variables for the fluid dynamics control equations; secondly, they directly constitute the node and edge feature vectors of the spatiotemporal directed graph structure. Thus, the system eliminates the heterogeneous barriers between the physical and data domains at the data foundation level, providing a unified variable basis for subsequent structural mapping and constrained recursive prediction.

[0074] It is worth mentioning that the present invention can also construct a unified state space using total head, volumetric water content, nodal storage capacity, cross-sectional average flow velocity, local storage and discharge capacity, or equivalent flood state vectors. As long as the underlying physical solution process and the upper-level rapid derivation process can share the same set of core state variables, and support subsequent graph structure construction, state recursion, and physical verification, the purpose of the present invention can be achieved.

[0075] In this embodiment, two types of basic data—static basic input and dynamic boundary input—are acquired for the target urban area, thus establishing a data foundation for a unified state space. Based on this, surface water depth, river water depth, pipeline node head, inter-system exchange flux, and absolute water level difference are uniformly defined as core state variables, covering key hydrodynamic parameters of the three subsystems: surface, river, and pipeline. Simultaneously, absolute water level is explicitly defined as the unified driving variable for the system, using the absolute water level difference as the basis to connect the physical solution logic and data expression rules of the three subsystems, achieving state correlation across subsystems. These state variables are given a dual role: firstly, they serve as the physical solution target variables for subsequent fluid dynamics control equations, directly supporting the mechanistic solution of hydrodynamic processes; secondly, they directly form the basis for the node feature vectors and edge feature vectors of the subsequent spatiotemporal directed graph structure. This eliminates the heterogeneous barriers between the physical domain and the data domain at the data foundation level, completing the construction of a unified state space and providing a unified variable foundation for subsequent structural mapping and constrained recursive prediction.

[0076] Step 102: Perform a coordinated hydrodynamic coupling solution for the surface-pipeline-river system in the unified state space. Within the unified state space, complete the coordinated update of the system state based on the set of absolute water level differences, the net exchange flux between systems, and the external boundary state quantities, and output a structured state set.

[0077] It should be noted that, relying on the unified state space that has been built, various basic and dynamic state information of the entire domain are integrated, and the hydraulic calculation process corresponding to the three types of water systems, namely surface, pipeline and river, is promoted simultaneously. Throughout the process, the operating status of each water system is adjusted in real time with reference to the absolute water level difference set, the net exchange flux between systems and the external boundary state quantity. The synchronous linkage correction of multi-dimensional state data is completed. After the overall collaborative calculation is completed, all updated hydraulic related data are integrated and summarized into a standardized and complete structured state set, which smoothly connects to the subsequent physical relationship spatiotemporal diagram coding related operations.

[0078] Furthermore, step 102 may include the following sub-steps:

[0079] S21. Solve for the two-dimensional surface water flow and soil infiltration loss in the unified state space to obtain the surface water depth and infiltration loss data.

[0080] S22. Solve the one-dimensional flow evolution process of the river channel in the unified state space based on the surface water depth and infiltration loss data to obtain the river channel depth and the net surface-to-river channel exchange flux.

[0081] S23. Based on the surface water depth, infiltration loss data, river water depth and surface-to-river net exchange flux, solve the underground pipe network transport and discharge process in the unified state space to obtain the pipe network node head and surface-to-pipe network net exchange flux.

[0082] S24. Calculate the set of absolute water level differences based on surface water depth, river water depth, and water head at pipe network nodes;

[0083] S25. The water level at the boundary of the external receiving water body is taken as the external boundary state quantity.

[0084] S26. Integrate surface water depth, river water depth, water head at pipe network nodes, net surface-to-pipe network exchange flux, net surface-to-river exchange flux, absolute water level difference set, and external boundary state quantity to obtain a structured state set;

[0085] S27. Among them, the two-dimensional surface water flow movement, the one-dimensional river flow evolution process, and the underground pipe network transmission and discharge process are updated collaboratively in a unified state space based on the absolute water level difference set, the net exchange flux between systems, and the external boundary state quantity. The solution is coupled through the water exchange feedback between the surface and the pipe network, the surface and the river, and the pipe network and the receiving water body.

[0086] The external receiving water body boundary water level refers to the external hydraulic boundary condition data in the flood simulation of the urban target area. It refers to the water level process data of receiving water bodies outside the target area that have direct hydraulic connections with the internal rivers and drainage networks. Specifically, it includes: water body types covering downstream rivers receiving urban drainage, nearby regulating lakes, ocean tides in coastal cities, or large municipal drainage canals and pumping station forebays that are the final destinations of the urban drainage system; the data format is a time series containing the corresponding water level values ​​at each time step within the simulation period, which can completely present the water level change process of the receiving water body. In this invention, this water level data is included as an external boundary state quantity in a structured state set.

[0087] It should be noted that, based on the unified state space established in step 101, this step performs unified solution and collaborative update of the surface runoff, river flow, and underground pipeline discharge states, simultaneously forming a unified structured state representation. It is important to note that the urban rainfall-runoff-inundation process is a synchronously coupled continuous evolution process, rather than an independent sequential process. Therefore, this step does not simply piece together the surface, river, and pipeline processes step by step, but rather solves the hydrodynamic interactions between the three within a unified state space. This state representation not only characterizes the physical evolution of the system at the current moment but also serves as a shared state carrier in the processes of graph structure construction, spatiotemporal recursive prediction, and residual verification.

[0088] (1) Calculation of two-dimensional surface water balance and absolute water level drive:

[0089] For two-dimensional orthogonal grid cells, the system establishes a partial differential equation for the continuity of surface hydrodynamics:

[0090] ;

[0091] The system defines the real-time absolute water level of the grid. for:

[0092] ;

[0093] Furthermore, the actual direction of surface water flow is no longer preset, but is determined in real time by the partial derivative (i.e., gradient) of the absolute water level in space. This applies to any flow direction in space. Its driving slope descent The analysis is as follows:

[0094] ;

[0095] The system calculates the relative elevation along the absolute water level gradient using the nonlinear Manning-Darcy composite dynamic equation. shaft and Unit width flow rate in the axial direction:

[0096] ;

[0097] ;

[0098] Infiltration loss data Calculations based on the Green-Ampt non-constant infiltration model:

[0099] ;

[0100] In the formula: This represents the real-time water depth of the surface grid (i.e., the surface water depth). For physical evolution time variables; For partial derivative mathematical operators; These are the directions of the two orthogonal spatial coordinate axes of a two-dimensional orthogonal grid; respectively along shaft and Momentum-per-unit-width flux transmitted in the axial direction; The rainfall intensity source term is the external input; This is the non-constant infiltration rate loss term from the surface to the soil (i.e., infiltration loss data). This represents the net exchange flux from the surface grid to the underground pipe network, with outflow being positive and backflow being negative. This represents the net exchange flux from the surface grid to the inland river channel, with outflow being positive and overflow being negative. Real-time absolute water level of the surface grid; This represents the static ground elevation of the surface grid. For hydraulically driven potential energy gradient along any spatial direction; For any flow direction variable in space; The slope composite Manning roughness of the surface grid; This is a sign extraction function used to obtain the sign of the potential gradient to determine the direction of water flow. It is an absolute value operator; The vertical saturated hydraulic conductivity of the soil; For moistened capillary suction; Soil porosity; This refers to the initial soil moisture content; This represents the cumulative infiltration amount at the current time step.

[0101] (2) Calculation of one-dimensional river channel evolution and inter-system water exchange:

[0102] The system solves for the evolution of river flow based on the one-dimensional diffusion wave equation:

[0103] ;

[0104] The system defines the depth of water exceeding the levee in the river channel. With the surface water depth exceeding the levee They are respectively:

[0105] ;

[0106] ;

[0107] When a river overflows its banks and there is backwater downstream, the exchange flux... The calculation is as follows:

[0108] ;

[0109] For the interaction between surface and underground pipe networks, the system executes a macro-microstep operator splitting mechanism. At the macro step size... Contains Micro-computation substep of the pipeline network Net exchange flux is constrained by both the physical available water volume and the feedback from the pipeline overflow. The calculation is as follows:

[0110] ;

[0111] In the formula: The real-time cross-sectional area of ​​the main channel of the river; The transient flow rate of the main channel of the river; The spatial distance variable along the longitudinal direction of the river channel; Lateral exchange flow in the river section; These represent the dynamic over-levee depth on the river channel side and the surface side, respectively. These are the absolute water levels of the river channel and the manholes in the pipeline network, respectively. This refers to the static physical elevation of the riverbank crest. This is a function for maximizing the value, used to truncate negative driving forces generated when the limit is not exceeded; The dimensionless flow coefficient under submerged overflow conditions; The acceleration due to gravity is taken as 9.81 m / s². For the flow coefficient of the pipe network orifice or rainwater inlet; The effective flow area of ​​the orifice or drain outlet; This is a function for finding the minimum value, used to impose a physical upper limit constraint on the amount of water to prevent overdraft; To prevent physical overdraft safety tolerance factor; For the first Real-time water depth of each surface grid cell; For the first The base area of ​​each surface grid cell; For the macroscopic time step of surface hydrodynamic evolution; The time step for microscopic calculation of the hydraulic evolution of the pipeline network; The total number of micro substeps contained within a macro step size; For discrete counting indices of micro-steps; For summation operators; For the first The instantaneous overflow feedback flow from each micro-level sub-pipeline node to the ground surface.

[0112] After solving the hydrodynamic coupling process of the surface-pipeline-river system, the system does not discard the continuous solution results as isolated intermediate variables, but instead incorporates them into the solution at each time step. The following is a unified encapsulation of a structured state set. :

[0113] ;

[0114] In the formula: for A structured set of hydrodynamic states at any given moment; They represent The surface water depth, river water depth, and water head at pipeline nodes at any given time; They represent Net surface-to-pipeline exchange flux and net surface-to-river exchange flux at any given time; for The set of absolute water level differences between all adjacent computing nodes within the time system; for The set of external boundary state variables at time step 1. This structured state set preserves the dynamic information of the physical solution and provides direct input for explicit graph structure encoding. Furthermore, this structured state set serves not only as the coupled solution result but also as a shared state carrier for subsequent spatiotemporal directed graph encoding, recursive prediction, and residual verification.

[0115] Furthermore, the two-dimensional surface water flow movement, the one-dimensional river flow evolution process, and the underground pipeline transportation and discharge process are all uniformly incorporated into a unified state space for synchronous calculation and control. Throughout the calculation process, the set of absolute water level differences obtained from real-time calculations serves as the basis for determining the direction of water flow and the allocation of hydraulic potential energy. The scale of water exchange between various hydrological systems is controlled by the net exchange flux between systems. At the same time, the external constraints of the overall hydrological extrapolation are limited by the external boundary state quantities. After the preliminary calculation of various hydraulic parameters is completed, a data feedback link is formed by the actual water volume interaction changes between the surface and the pipeline, between the surface and the river, and between the pipeline and the external receiving water body. The state change information brought about by the water volume interaction is fed back to each calculation link, and the surface water flow operation parameters, river flow evolution parameters, and underground pipeline transportation and discharge operation parameters are synchronously adjusted and dynamically updated. This enables the various state parameters of the three types of hydrological operation processes to be mutually adapted and linked in real time. The coupled solution work of deep linkage between multiple systems is completed by relying on continuous water volume interaction feedback. This operational mode enables dynamic and synchronous control of three types of hydrological processes, effectively compensating for the shortcomings of traditional simulation methods where each hydrological process is independent and has weak linkage and coupling. It relies on real-time water level differences to dynamically guide the flow trend of the water body, reducing the dependence of the water flow direction setting on static preset conditions. It also relies on water volume interaction feedback to correct the operating status in real time, further ensuring that the overall simulation process closely matches the actual hydrological operation.

[0116] Furthermore, the set of absolute water level differences includes water level differences between adjacent surface units, between the surface and the pipe network, between the surface and the river channel, and between the pipe network and the external receiving water body;

[0117] Absolute water level includes one or more of the following: the sum of surface elevation and dynamic water depth, water head at pipeline nodes, river water level, or boundary water level of external receiving water bodies.

[0118] The absolute water level difference set is used to determine the direction, intensity and spatiotemporal directional graph edge direction of water exchange between surface units, pipeline nodes, river units and external receiving water bodies, so that the flow path can be dynamically updated with the real-time water level status.

[0119] It should be noted that, firstly, the specific calculation and selection methods for various absolute water levels across the entire area should be clarified. The absolute water level corresponding to the surface location is obtained by summing the fixed surface elevation overlaid with the real-time dynamic water depth. For pipeline locations, the pipeline node head is directly used as the corresponding absolute water level. For river areas, the river water level is selected, and for external water bodies, the boundary water level of the external receiving water body is selected. The corresponding water level type can be flexibly selected for calculation according to the simulation scenario. Based on this, a complete set of absolute water level differences is formed. This set fully includes the differences between adjacent surface units, between surface areas and underground pipelines, between surface areas and river areas, and between pipeline bodies. The system calculates all water level differences between the system and external receiving water bodies. After unifying and summarizing all water level differences, it determines the specific flow direction of water exchange between different hydrological units based on the positive and negative relationships of water level differences at different locations. The magnitude of the water level differences determines the actual intensity of water exchange. Simultaneously, the hydraulic flow direction reflected by the water level differences is directly defined as the extension direction of the internal edge structure of the spatiotemporal directed graph. The entire set of absolute water level differences is continuously updated based on real-time water level data across the entire region, thereby driving the flow distribution path of the entire region to autonomously and dynamically update according to the real-time hydraulic operation status, without the need for pre-set fixed flow routes. This system can autonomously control the flow trend of the entire region based on real-time hydraulic conditions, effectively solving the problem of excessive reliance on static presets for water flow direction in traditional simulations. Furthermore, by using real water level differences as the physical basis to build a spatiotemporal directed graph, the graph structure features conform to actual hydrological flow patterns, further improving the physical fit of the overall simulation process.

[0120] It is worth mentioning that this invention employs a collaborative updating mechanism for the two-dimensional hydrodynamic process at the surface, the one-dimensional evolution process of the river channel, and the underground pipeline transportation and discharge process, and achieves cross-timescale exchange through macro-microstep operator splitting and periodic flux backpropagation. As an alternative, the underlying mechanisms of the surface, river channel, and pipeline network can also be solved using two-dimensional shallow water equations, diffuse wave models, local inertial models, the full-dynamic Saint-Venant equations, reduced-order physical models, or lumped equivalent dynamic models, respectively. As long as bidirectional mass exchange and state linkage updates between the surface, pipeline, and river systems can be achieved, the goal of constructing a unified mechanistic foundation can be achieved.

[0121] Furthermore, this invention uses the absolute water level difference, composed of "topographic elevation + dynamic water depth," as a unified driving variable. Alternatively, this driving variable can be the total head difference, the sum of pressure head and position head, the pressure gradient field, the free surface slope field, or a generalized potential energy gradient field incorporating groundwater pressure and pore water pressure terms. As long as the limitations of a static DEM with a fixed flow direction can be overcome, and the dynamic changes in the flow path under conditions of local backwater, buoyancy, and backflow can be accurately reflected, the objective of this invention can be achieved.

[0122] In this embodiment, based on the aforementioned unified state space, the two-dimensional surface water flow movement and soil infiltration loss are simultaneously solved by combining the spatiotemporal rainfall matrix and the infiltration parameters corresponding to the underlying land use type. This yields the surface water depth and corresponding infiltration loss data for each surface grid cell. Subsequently, based on this surface water depth and infiltration loss data, the one-dimensional river flow evolution process is solved. Simultaneously, water exchange is dynamically calculated based on the real-time water level difference between the river and the surface, obtaining the river depth and the net surface-to-river exchange flux. Finally, the surface water depth, infiltration loss data, river depth, and net surface-to-river exchange flux are combined... The system solves the underground pipeline transportation and discharge process through a macro-micro step collaborative mechanism. Based on the real-time water level difference between the surface and the pipeline, it dynamically updates the interactive water volume to obtain the water head at the pipeline nodes and the net exchange flux between the surface and the pipeline. Then, based on the surface water depth, river water depth, and water head at the pipeline nodes, it calculates the set of absolute water level differences between all adjacent computing nodes in the system. The water level at the boundary of the external receiving water body is used as the external boundary state quantity. Finally, all the above solutions and calculation results are encapsulated and integrated according to a unified data structure to obtain a structured state set. This process drives the water volume interaction between subsystems with dynamically updated water level data, replacing the traditional static preset flow direction method.

[0123] Step 103: Explicitly encode the physical relationships of the structured state set into a spatiotemporal graph structure, and output a spatiotemporal directed graph with physical attributes.

[0124] It should be noted that, based on the structured state set obtained above, the surface water depth, river water depth, water head of the pipeline node and absolute water level difference are extracted as node feature vectors, and the surface-to-pipeline net exchange flux, surface-to-river net exchange flux and external boundary state quantities are extracted as edge feature vectors. Based on the hydraulic connectivity between each computing node, a graph structure is constructed to complete the explicit encoding of physical relationships into a spatiotemporal graph structure, and a spatiotemporal directed graph with physical attributes is output.

[0125] Furthermore, step 103 may include the following sub-steps:

[0126] S31. Perform node feature extraction processing on the structured state set to generate node feature vectors;

[0127] S32. Extract edge features from the structured state set to generate edge feature vectors;

[0128] S33. Construct a spatiotemporal directed graph with physical attributes based on the node feature vectors and edge feature vectors;

[0129] S34. Among them, the node feature vector includes one or more of the following: surface water depth, river water depth, pipeline node head, external boundary water level, local storage and discharge status, and absolute water level.

[0130] S35. The edge feature vector includes one or more of the following: absolute water level difference, net exchange flux between surface and pipe network, net exchange flux between surface and river channel, internal connectivity of pipe network, boundary type, flow direction identifier, and exchange continuity identifier.

[0131] S36. The edge directions in a spatiotemporally directed graph with physical attributes are jointly determined by the real-time absolute water level difference, physical connectivity, and inter-system exchange flux, and are used to characterize the dynamic flow direction and cross-system exchange relationships in the flood hydrodynamic process.

[0132] Boundary type is a category attribute used to delineate the interfaces connecting different hydrological regions, and is used to distinguish the actual function of various water body interaction interfaces.

[0133] The flow direction indicator is set based on the laws of hydraulic action and is used to intuitively distinguish the actual flow direction of water bodies.

[0134] The exchange continuity identifier is a parameter used to determine whether the water exchange process between different hydrological systems remains stable and continuous.

[0135] Physical connectivity refers to the spatial connectivity between different hydrological units that enables actual water flow and passage, and is the fundamental condition for realizing water volume interaction.

[0136] It should be noted that this step constructs a spatiotemporal directed graph structure with explicit physical attributes based on the real physical connectivity relationships between state variables in a unified state space, enabling the structured state to be explicitly expressed at the graph topology level. It should also be noted that this invention does not retrospectively correct the physical mechanism by adding constraints after model training, but rather encodes key physical relationships directly into the information transmission paths, state representations, and propagation constraints of the neural network during the graph structure construction stage, thereby achieving pre-embedding and explicit mapping of physical mechanism relationships into the model structure.

[0137] ;

[0138] in, Let be the directed spacetime graph with physical properties at time t; It is a heterogeneous set of nodes in a spatiotemporal directed graph, containing three types of computational nodes: surface grid units, river units, and pipeline nodes, corresponding to the computational units of each hydrodynamic process in the structured state set; X is the set of directed edges in a spatiotemporal directed graph, corresponding to the actual physical connectivity paths between nodes, carrying the hydraulic interactions between nodes, and obtained by mapping water exchange and water level difference information from the structured state set; tLet E be the set of node features at time t, which is the set of all node feature vectors extracted from the structured state set. Each node feature vector contains the surface water depth, river water depth, pipeline head, and associated physical information of the corresponding node; t Let t be the edge feature set at time t. It is the set of all edge feature vectors extracted from the structured state set. Each edge feature vector contains physical information such as the net exchange flux between the surface and the pipeline, the net exchange flux between the surface and the river channel, the absolute water level difference, and the external boundary state quantities of the corresponding connected edge.

[0139] In this step, the physical mechanism relationship is not introduced as a soft constraint posterior during the training phase, but is explicitly encoded as the information transmission path of the neural network when the graph structure is constructed.

[0140] (1) Heterogeneous node state coding:

[0141] The system encodes surface, waterway, and pipeline nodes into a heterogeneous node set. For nodes , its in Node feature vector at time step The encoding is:

[0142] ;

[0143] In the formula: for Time Node A comprehensive feature encoding vector containing both static and dynamic information; For nodes The static elevation of the bottom surface; They are respectively Time Node Real-time water depth (including surface water depth and river water depth) and absolute water level (i.e., water head at pipeline nodes). They are respectively Time affects the node Local rainfall source term and infiltration loss rate; To represent nodes The structural state quantity of the current storage and release capacity.

[0144] (2) Encoding of physical connected edge features:

[0145] The system encodes real physical connected paths as a set of directed edges. In this model, absolute water level difference is encoded as an edge-driven feature, and exchange flux is encoded as an auxiliary state feature. (Directed edge feature vector) The encoding is:

[0146] ;

[0147] In the formula: for From the upstream node at all times Pointing to downstream nodes The directed edge feature vector (i.e., edge feature vector). In the set of absolute water level differences Time Node With nodes The absolute water level difference between them, i.e., the potential energy gradient driving force; For nodes With nodes The actual physical exchange flux between them (including net exchange flux between surface and pipeline network, and net exchange flux between surface and river channel). Variables are used to identify classification types of physical boundary flow states, such as free overflow and submerged outflow. The boundary state identifier variable (i.e., the external boundary state quantity) is used to identify the external acceptance conditions.

[0148] Through the above heterogeneous node encoding and physical connectivity edge encoding, the system directly translates the physical connectivity, water exchange, and boundary-driven relationships in the surface-pipeline-river system into a spatiotemporal directed graph structure that can be computed by neural networks and does not deviate from real physical reachability, providing a graph topology basis for physical constraint spatiotemporal recursive prediction.

[0149] It is worth mentioning that this invention employs a spatiotemporally directed graph, representing nodes as surface grids, channel units, and pipe network nodes, and encoding absolute water level differences, exchange fluxes, boundary types, and local storage and discharge states as node features, edge features, or auxiliary state variables. Alternatively, heterogeneous graphs, dynamic graphs, hypergraphs, message-passing graphs, graph operator networks, or structured connection representations based on tensor fields can also be used. The objective of this invention can be achieved as long as physical connectivity, exchange directions, and boundary states are explicitly embedded into the internal propagation structure of the model, rather than merely provided as external supervision labels.

[0150] In this embodiment, after the structured state set is summarized and integrated, standardized node feature extraction is first performed on the independent state data of various hydrological units stored within the set. The corresponding state parameters are categorized and filtered according to the attributes of the hydrological units themselves. Parameters that reflect the unit's own operation, such as surface water depth, river water depth, pipeline node head, external boundary water level, local storage and discharge status, and absolute water level, are uniformly standardized and formatted, and orderly combined to form standardized node feature vectors. After completing the construction of the unit's own features, edge feature extraction is then performed on the data representing the interaction between different hydrological units within the structured state set. Corresponding parameters that reflect the interaction patterns of units, such as absolute water level difference, net surface-to-pipeline exchange flux, net surface-to-river exchange flux, internal pipeline connectivity, boundary type, flow direction identifier, and exchange continuity identifier, are selected and arranged in a coordinated manner to generate... After acquiring the core feature data of node feature vectors and edge feature vectors, the inherent physical attributes of each hydrological unit node in the graph are defined by the node feature vectors, and the interactive attributes of the connection relationship between different nodes are defined by the edge feature vectors. According to the logic of hydrological spatial distribution, a spatiotemporal directed graph with complete hydrological physical attributes is constructed. In the process of constructing the graph connection structure, the fixed direction is no longer preset by humans. Instead, the specific extension direction of all connecting edges inside the spatiotemporal directed graph is determined by combining the absolute water level difference obtained by real-time measurement of the whole area, the actual physical connectivity of the site, and the inter-system exchange flux formed between various hydrological systems. By using the actual direction of the graph edges, the dynamic flow trend of water bodies naturally formed in the whole process of flood hydrodynamic evolution is accurately restored. At the same time, the various interactive features carried by the edges clearly reflect the various cross-system water exchange connections between different hydrological systems. This construction method directly transforms the real hydraulic operation data obtained through collaborative coupling into feature data that can be directly called by the graphical model. This allows the overall spatiotemporal directed graph architecture to fully conform to the actual hydrological distribution and water flow patterns, completely abandoning the practice of setting fixed flow directions in advance in traditional extrapolation models. It effectively improves the problem of excessive reliance on static presets for flow direction, and comprehensively covers the state parameters of the unit itself and the interaction constraint parameters between units. This gives the completed graphical model complete physical support, enabling it to fully bear the details of flood evolution across the entire region. It provides a physically rigorous and data-driven basic extrapolation model for subsequent spatiotemporal recursive prediction with various physical constraints.

[0151] Step 104: Perform spatiotemporal recursive prediction on the spatiotemporal directed graph with physical attributes, with physical constraints embedded as the core of absolute water level difference driving and inter-system exchange flux linkage, and output the candidate situation of flood in the whole region.

[0152] It should be noted that the extrapolation work is carried out based on the spatiotemporal directed graph with physical attributes that was built in the early stage. The absolute water level difference is used as the core driving basis for the overall extrapolation. The linkage and cooperation between different hydrological units are realized by the exchange flux between systems. Various predetermined physical constraints are integrated into each operational link of the time-series extrapolation. The node attributes and edge associations built into the spatiotemporal directed graph are combined to complete the iterative extrapolation of the hydrological state of the whole region step by step in chronological order. The situation extrapolation work of the whole region is completed in accordance with the natural hydrodynamic evolution logic, and finally the candidate situation of flooding in the whole region is calculated.

[0153] Furthermore, step 104 may include the following sub-steps:

[0154] S41. Along the physical connectivity path of the spatiotemporal directed graph with physical attributes, using the absolute water level difference of nodes as the basis for spatial transmission and the exchange flux between systems as the hydraulic linkage benchmark, perform spatial aggregation of node feature vectors to obtain spatial aggregation features.

[0155] S42. Based on spatial aggregation features, perform time-dimensional recursive updates on the node feature vectors to obtain spatiotemporal recursive intermediate results;

[0156] S43. Apply physical constraints of mass conservation, water level gradient direction, and spatiotemporal smoothing to the intermediate spatiotemporal recursion results to optimize them, and obtain the optimized spatiotemporal recursion results.

[0157] S44. Based on the optimized spatiotemporal recursive results, determine the candidate flood situation for the entire region;

[0158] S45, where the constraint of the water level gradient direction is used to restrict the predicted water flow direction from being consistent with or not conflicting with the hydrodynamic driving direction determined by the real-time absolute water level difference.

[0159] It should be noted that this step, under the combined effect of a unified state space and physical graph topological constraints, employs graph convolutional networks and gated recurrent units to perform spatiotemporal recursive updates of the system state, thereby achieving rapid prediction of future flood conditions. It is also important to clarify that this step is not a purely statistical sequential extrapolation detached from physical mechanisms, but rather a constrained recursive calculation of the continuous evolution of runoff formation, confluence and transmission, and flood expansion during urban rainfall-runoff-inundation processes, based on the unified state representation and physical connectivity relationships established in the previous steps. This recursive process is simultaneously governed by both the spatial physical connectivity structure and the explicit physical constraint loss function, thus avoiding physical distortions such as "water creation out of thin air" or "conduction in the opposite direction of potential energy" that may occur in purely data-driven models under extreme and unknown conditions.

[0160] (1) Characteristic evolution under structural constraints:

[0161] The spatial propagation and temporal evolution equations are expressed as follows:

[0162] ;

[0163] ;

[0164] In the formula: These are the graph convolutional networks of the 1st generation and 2nd generation, respectively. Layer and first The hidden state matrix of the node features of the layer; A directed adjacency matrix containing self-loops and subject to a one-way physical transmission mask applied according to the absolute water level gradient direction in step S3; To and The corresponding degree diagonal matrix, The directed adjacency matrix contains self-loops and is masked by a one-way physical transmission according to the direction of the absolute water level gradient, corresponding to the actual physical connection path between nodes; The negative 1 / 2 power operator of the degree matrix is ​​used to perform symmetric normalization of features; For the network The learnable feature transformation weight matrix of the layer; It is a non-linear activation function; Each is the current Time and the previous The hidden state vector at time t, which is used to proxy the evolution of local physical water storage memory; The update gate feature vector is used to control the proportion of time state inheritance. The candidate hidden state feature vector calculated by the network at the current time; To and A vector of all 1s with the same dimension; This is the Hadamard product operator, which represents the element-wise multiplication of matrices or vectors.

[0165] (2) Constraint loss of physically conserved quantities:

[0166] During the backpropagation parameter optimization process of the model, the system translates the mass balance and hydrodynamic conduction laws into a composite differentiable loss function. :

[0167] ;

[0168] The specific calculation equations for the above four constraint losses are as follows:

[0169] ;

[0170] ;

[0171] ;

[0172] ;

[0173] In the formula: The total loss function for joint network optimization; These are the data fitting loss term, the mass conservation constraint loss term, the absolute water level gradient direction constraint loss term, and the spatiotemporal smoothing regularization constraint loss term, respectively. These correspond to the dynamic weight adjustment coefficients of the losses under the four constraints mentioned above. This represents the total number of sample nodes during the batch training process. They are nodes The network prediction output value and the real label value generated by the underlying physical model; It is the square operator of the L2 norm, i.e., the mean square error distance operator; These are the model predictions. Time and The total physical water storage capacity of the entire region or a local area at any given time; Representing time steps The total inflow rate of external rainfall within the system, the total outflow rate at the system boundary, the total infiltration loss rate, and the net exchange flux between systems; Nodes output by the underlying physics engine To the node The reference exchange flux, with positive and negative signs indicating the physical flow direction; These are the nodes predicted by the inference model. and nodes The absolute water level; These are the corresponding nodes and water depth variables at the corresponding times predicted by the simulation model; It is a smooth decay penalty weighting coefficient constructed based on the physical spatial distance or natural elevation difference between nodes.

[0174] By embedding the above structural constraints and loss constraints together, the system ensures that the spatiotemporal recursion process of the neural network always runs within the physically accessible topological space, and continuously accepts mass conservation and flow consistency constraints during the parameter optimization stage, thereby guaranteeing the physical consistency of the prediction results on a macroscopic scale.

[0175] Specifically, firstly, spatial aggregation of node feature vectors is performed along the physically connected paths of the spatiotemporally directed graph with physical attributes, using the node feature vectors (corresponding to the node in the graph convolutional network) as the basis for the aggregation. Hidden state matrix of node features in layer ( ) is the input, based on the spatial propagation equation in the figure. A directed adjacency matrix containing self-loops and subjected to a unidirectional physical propagation mask based on the absolute water level gradient direction is used. (The actual physical connection path between corresponding nodes), combined with The corresponding degree diagonal matrix ,

[0176] pass Perform symmetric normalization on the node features, and then compare them with the network's... The learnable feature transformation weight matrix of the layer Effect, through nonlinear activation function Processing yields the graph convolutional network of the [missing term]. Hidden state matrix of node features in layer This matrix represents the spatial aggregation feature, which integrates the spatial connectivity between nodes with hydraulic gradient information. Subsequently, based on the spatial aggregation feature, a recursive update of the node feature vectors is performed along the time dimension. The spatial aggregation feature is then used as the input to a gated recurrent unit to generate the candidate hidden state feature vector for the current time step. Then, combined with the update gate feature vector that controls the inheritance ratio of time state, The hidden state vector from the previous time step (the evolution of the proxy's local physical water storage memory) is used in accordance with the time evolution equation. The inheritance and update of the time state are completed through the Hadamard product operation, resulting in the hidden state vector at the current time step. This vector is the intermediate result of spatiotemporal recursion, which integrates spatial aggregation information with the physical water storage state of the preceding time step.

[0177] Next, physical constraint optimizations for mass conservation, water level gradient direction, and spatiotemporal smoothing are performed on the intermediate spatiotemporal recursion results. This is achieved through an iterative optimization process based on model backpropagation parameters. Using the intermediate spatiotemporal recursion results as the optimization base, a unified optimization objective is constructed by integrating multi-dimensional hydrodynamic physical mechanism rules. Constraint correction is completed through a closed-loop approach involving deviation comparison, violation penalties, and parameter back-correction. First, mass conservation constraint optimization is performed. The total rainfall inflow, system boundary discharge, soil infiltration loss, and net exchange between the surface, river, and pipe network systems are extracted from the unified state space for the corresponding time step. Simultaneously, the changes in total and local water storage at different times are extracted from the intermediate spatiotemporal recursion results. The water storage change trend predicted by the model is compared item by item with the actual water balance relationship under the physical mechanism to accurately identify unreasonable deviations such as water surplus or deficit in the prediction results. Violations are penalized. The law of mass conservation imposes constraints and penalties on the output behavior, guiding the internal parameters of the model to adaptively adjust during parameter optimization. This forces the flood simulation process to strictly adhere to the logic of water balance, avoiding physical distortions such as the arbitrary generation or loss of water. Secondly, water level gradient direction constraint optimization is carried out. With the help of the underlying hydrodynamic physics engine, based on the real-time water level status of each node in the spatiotemporal recursive intermediate results, the natural water flow conduction reference direction and hydraulic interaction law between adjacent connected nodes are deduced. Then, the absolute water level between nodes in the model's recursive output are verified one by one. The system checks whether the actual simulated water flow direction matches the natural flow direction of the water level gradient. If water flows from low to high levels in reverse, violating the basic laws of gravity-hydraulic conduction, a constraint penalty mechanism is immediately triggered. The model parameters are corrected through a reverse iteration mechanism to regulate the water flow propagation direction between all connected nodes, ensuring that it always conforms to the inherent physical logic of the water level potential energy gradient. Finally, spatiotemporal smoothing constraint optimization is carried out. In the time dimension, the water depth and head status of individual surface grids, river units, and pipe network nodes are continuously verified to limit abnormal results such as drastic jumps and abrupt fluctuations in water level values ​​at adjacent simulation times for the same node. In the spatial dimension, various computational nodes that are geographically adjacent and have hydraulic connectivity are linked for verification to constrain the irregular numerical discontinuities and abrupt changes in flood water level status between adjacent nodes. By applying regularization penalties to the behavior of state jumps in the time dimension and state abrupt changes in the spatial dimension, the system ensures that the flood situation in the whole region maintains continuous and gentle changes in the process of temporal evolution and spatial spread, which conforms to the objective laws of the natural evolution of actual floods.Based on this, the model's basic data fitting requirements are integrated with the three types of physical constraints. By configuring a reasonable weight ratio, the model's prediction accuracy and the constraint strength of each physical constraint are balanced. During the model's backpropagation optimization iteration process, the gradient is backpropagated by integrating the deviation information generated by each physical constraint. The internal learnable parameters of the spatiotemporal graph convolution module and the time recursion module are corrected layer by layer. Various physical inconsistencies in the intermediate results of spatiotemporal recursion are continuously corrected. After multiple rounds of iteration and convergence, the inference results are always limited to a reasonable topological range that can be accommodated by the hydrodynamic physical rules. Finally, the optimized spatiotemporal recursion results that meet the requirements of multiple physical constraints are obtained.

[0178] Finally, based on the optimized spatiotemporal recursive results, the hydrodynamic state data such as predicted water depth and absolute water level corresponding to each node are extracted, and the evolution information of the state of all nodes in the target area over time is integrated to form flood development process data covering the entire system of surface, river channel and pipeline network, and determine the candidate flood situation of the whole area. This situation satisfies both spatial physical connectivity structure and explicit physical constraints, avoiding the physical distortion problem of pure data-driven model.

[0179] Furthermore, the water level gradient direction constraint, as the core physical constraint condition regulating the logic of water flow extrapolation, is embedded throughout the iterative calculation process of spatiotemporal recursive prediction. In each round of hydrological node state update and water flow path extrapolation, the system retrieves the real-time absolute water level difference between all hydrological units in the entire region. Based on the basic principle of hydrodynamics—the natural transmission of water level potential energy from high to low—it accurately calculates and determines the standard hydrodynamic driving direction at each location within the entire region. Simultaneously, it performs full-coverage verification and mandatory constraints on the predicted water flow direction generated by the model extrapolation, node by node and path by path, strictly limiting all... The simulated water flow direction ensures that the overflow direction between surface units, the cross-system water flow exchange direction between the surface and the pipe network and river channel, and the water transport direction within the pipe network and river channel are all completely consistent with the standard hydrodynamic driving direction determined by the real-time absolute water level difference, or there is no hydraulic logic conflict. This effectively avoids abnormal simulation results that violate natural hydrological laws, such as reverse flow, disordered flow direction, and false water flow movement, which are prone to occur during rapid simulation. It allows the overall flood flow evolution direction to be completely dominated by the real-time dynamic water level gradient physical mechanism, and completely gets rid of the limitations of traditional simulations that rely on fixed static flow direction parameters.

[0180] It is worth mentioning that this invention employs a graph convolutional network and gated recurrent units to jointly model spatial propagation and temporal evolution. As an alternative, graph attention networks, graph Transformers, spatiotemporal convolutional networks, long short-term memory networks, neural operator networks, POD (Proper Orthogonal Decomposition) reduced-order models, or other network structures capable of handling spatiotemporal recursion in graph topology can also be used. As long as the alternative model can rapidly extrapolate the global flood situation over multiple future time steps under a unified state space and physical graph topological constraints, while maintaining physical interpretability, the objective of this invention can be achieved.

[0181] Furthermore, this invention employs a composite loss function consisting of a data fitting term, a global mass conservation term, a water level gradient direction term, and a spatiotemporal smoothing term. Alternatively, physical information operator layers, conservation projection layers, hard constraints based on Lagrange multipliers, penalty function methods, energy consistency constraints, boundary flux continuity constraints, or local equilibrium constraints can be used to embed conservation relationships and flow consistency into the model during the training or forward propagation phase. As long as the model output satisfies fundamental physical laws at both macroscopic and local scales, the objective of this invention can be achieved.

[0182] Step 105: Perform physical residual verification and local re-solution on the candidate flood situation and unified state space of the whole domain through the physical consistency closed-loop method, and output the final flood situation of the whole domain after physical consistency correction.

[0183] It should be noted that after obtaining the candidate flood situation for the entire region in the preceding process, the candidate situation data is compared with the original hydraulic state data stored in the unified state space based on the physical consistency closed-loop operation logic. A comprehensive physical residual verification is carried out to accurately screen out various hydrological physical deviations in the simulation results. For areas with deviations and anomalies identified during the verification process, targeted local re-solution calculations are performed to recalculate and adjust unreasonable hydrological state parameters. After completing all deviation corrections and state adaptation work, the corrected hydrological information for the entire region is integrated, and the final flood situation for the entire region after complete physical consistency correction is output.

[0184] Furthermore, step 105 may include the following sub-steps:

[0185] S51. Based on the physical constraint rules of the unified state space, calculate the macroscopic conservation residual representing the deviation of water balance between the whole region and the local area in the candidate flood situation, the directional conflict residual representing the conflict between the predicted water flow direction and the driving direction of the absolute water level difference, and the exchange continuity residual representing the jump in the flux at the interaction boundary between the surface and the pipe network and the surface and the river channel.

[0186] S52. Determine whether the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the whole region trigger the limit-breaking condition.

[0187] S53. If the over-limit condition is not triggered, the candidate flood situation of the whole region will be taken as the final flood situation of the whole region after physical consistency correction.

[0188] Optionally, it also includes:

[0189] If the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the whole region trigger the limit-breaking condition, then based on the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the whole region, the abnormal spatial sub-region is locked in the target urban area.

[0190] A local re-solution is performed on the abnormal spatial sub-region to obtain the corrected local calculation results;

[0191] The corrected local calculation results are fed back into the unified state space to complete the update, resulting in a new unified state space.

[0192] Jump to execute the step of performing a coordinated hydrodynamic coupling solution of the surface-pipeline-river system in the unified state space and outputting a structured state set until the macroscopic conservation residual, directional conflict residual and exchange continuity residual of the candidate flood situation in the whole area have not triggered the limit condition.

[0193] The candidate state of the whole-domain flood situation determined when the macro-conservation residual, directional conflict residual and exchange continuity residual of the candidate state of the whole-domain flood situation do not trigger the over-limit condition is taken as the final whole-domain flood situation after physical consistency correction.

[0194] Among them, the anomaly space sub-region is determined based on the spatial distribution of macroscopic conservation residuals, directional conflict residuals and exchange continuity residuals, including surface grids, pipeline nodes, river units and their adjacent hydraulic connectivity areas where residuals trigger limit conditions;

[0195] The corrected local calculation results include one or more of the following: corrected surface water depth, water head at pipe network nodes, river water depth, inter-system exchange flux, and absolute water level difference set, which are used for the next round of structured state set generation, spatiotemporal map encoding, and recursive prediction.

[0196] It should be noted that this step constructs a physical residual verification and correction closed-loop mechanism for the predicted output obtained in the above steps. When a physical mismatch occurs in a local region of the recursive result, the system does not directly use pure data output, but triggers a local physical re-solution and forcibly feeds the corrected state back into the prediction basis at the next time step to ensure that the system still has engineering-grade reliability under extreme unknown conditions.

[0197] (1) Calculation of physical residual triggering conditions:

[0198] The system calculates the macroscopic conserved residuals at each time step of the simulation in real time. Directional conflict residuals and the continuity residual of inter-system exchange throughput :

[0199] ;

[0200] ;

[0201] ;

[0202] When the system detects that any of the following physical limit exceedance conditions have been triggered, the local physics re-solver program is started:

[0203] ;

[0204] ;

[0205] ;

[0206] In the formula: To infer the model at time step Internally calculated mass conservation deviation residuals; The edge conflict count residuals that violate the direction of the actual water flow within a global or local region; The physical continuity jump residual of the exchange flux at the system interaction boundary location; To infer the exchange flux of the forward propagation prediction output of the neural network model; This refers to the physical reference flux obtained by predicting water depth based on the current model and by analytical calculation using underlying physical formulas. This is the set of associated edges representing the interaction boundaries between systems, including surface-pipeline connection edges and surface-river connection edges; This is a conditional indicator operator; it takes the value 1 when the condition inside the square brackets is true, and 0 otherwise. These are the physical tolerance threshold constants for the mass conservation residual, directional conflict limit, and flux continuity jump, which are pre-calibrated by the engineering system.

[0207] (2) Local re-solution and physical state refeedback:

[0208] The system locks the spatial sub-regions where physical residuals exceed limits. Calling the underlying physical mechanism to solve the operator Perform local transient re-integration calculation:

[0209] ;

[0210] After the local physical recalculation is completed, the system forcibly performs a state backfeed update operation:

[0211] ;

[0212] In the formula: For spatial target sub-regions that trigger physical residual exceedance limits; It is the set of real state variables that conform to the laws of fluid mechanics after being corrected and calculated by the underlying physical mechanism operator; For the previous calculation time The spatial hydrodynamic state of this sub-region at any given time; This serves as the physical driving input for the rainfall source terms within the computation time step for this sub-region; This refers to the dynamic external accepting boundary conditions of the sub-region within the computation time step; To map the underlying integral solver of all the fluid dynamics partial differential equations in the above steps; This is the operator for forcing state overwrite and matrix variable assignment.

[0213] By correcting the state The data is forcibly overwritten into the system state, and the next round of spatial feature extraction and temporal recursion of the graph convolutional network will continue on the physically consistent state basis. At the same time, the temporal samples of this "failure-physical recalculation-state correction" can be synchronously fed back to the network training and incremental assimilation modules, forming a complete closed loop of physical mechanism and data-driven bidirectional control, bidirectional correction and iterative evolution.

[0214] Specifically, based on the aforementioned candidate flood situation and unified state space, the macroscopic conservation residual, directional conflict residual, and commutative continuity residual of the candidate flood situation are first calculated according to the physical constraint rules of the unified state space. Then, it is determined whether the three types of residuals of the candidate flood situation trigger the limit-breaking condition. This condition is... , , If none of the three types of residuals trigger the limit-breaking condition, the candidate flood situation for the entire region will be taken as the final flood situation for the entire region after physical consistency correction. If any of the three types of residuals triggers the limit-breaking condition, firstly, for the directional conflict residuals and exchange continuity residuals, locate all nodes and interaction edges that trigger the count or flux deviation exceeding the limit, extract the surface grid units, river units and pipeline nodes where these nodes are located, and delineate the connected local spatial range based on their spatial adjacency relationship. At the same time, combine the water imbalance area corresponding to the macroscopic conservation residuals to finally lock the abnormal spatial sub-region that caused the physical residual to exceed the limit. This subregion is a minimal connected space set containing all physically distorted nodes and their neighboring units, ensuring that local resolution can cover all physically inconsistent locations;

[0215] Subsequently, a local re-solution is performed on the anomaly space sub-region, invoking the underlying physical mechanism to solve the operator. According to the formula The hydrodynamic state of the sub-region at the previous calculation time. Rainfall source physical drive input and dynamic external accepting boundary conditions as input This yields the corrected local calculation results, which is the set of true state variables that conform to the laws of fluid mechanics. ;

[0216] Finally, the state backfeedback operation is performed, based on the assignment operator. The corrected set of state variables will directly overwrite the corresponding abnormal sub-region in the unified state space. The original state variables of the location, that is, those belonging to the state matrix in the unified state space. The node dimension performs element-by-element replacement, replacing the original prediction results with the corrected surface water depth, river water depth, pipeline node head, and exchange flux data. The state variables of other non-abnormal areas remain unchanged, completing the update of the unified state space and obtaining a new unified state space. Then, the process jumps to perform a coordinated hydrodynamic coupling solution of the surface-pipeline-river system on the unified state space and outputs a structured state set. This allows subsequent hydrodynamic coupling solutions and spatiotemporal recursive predictions to continue on the physically consistent state basis until the macroscopic conservation residuals, directional conflict residuals, and exchange continuity residuals of the candidate flood situation in the whole region have not triggered the out-of-limit conditions. Finally, the candidate flood situation in the whole region at this time is taken as the final whole flood situation after physical consistency correction.

[0217] It is worth mentioning that this invention employs conservation checks, directional checks, and exchange continuity checks, and triggers local physics re-solution and state reinjection when local mismatches occur. As alternatives, methods such as rule-based threshold triggering, Bayesian correction, ensemble updates, Kalman filtering, particle filtering, online assimilation, local proxy correctors, or error backpropagation correctors can also be used to enhance result consistency. As long as the abnormal regions can be identified, corrected, and the corrected results reintegrated into the subsequent state update process when local physics mismatches occur in the rapid derivation results, the objective of this invention can be achieved.

[0218] In this embodiment, after completing the preliminary simulation of the candidate flood situation across the entire region, residual statistical calculations are carried out strictly according to the predetermined physical constraints within the unified state space. From the generated candidate flood situation data, three types of deviation values ​​with different effects are statistically calculated. Specifically, macroscopic conservation residuals are obtained by combining the overall and local water balance relationships; directional conflict residuals are obtained by statistically analyzing the natural hydraulic flow direction corresponding to the absolute water level difference; and exchange continuity residuals are calculated based on the interaction of water volume changes between the surface and the pipe network, and between the surface and the river channel. After completing all three types of residual calculations, the calculations are performed according to pre-set parameters. A good evaluation criterion verifies the actual values ​​of the three types of residuals one by one, determining whether each residual reaches and triggers the preset limit-breaking conditions. If the verification results show that all residuals do not exceed the limit range, the current candidate flood situation for the entire region is directly determined as the final flood situation for the entire region after physical consistency correction. If any type of residual value exceeds the standard range and triggers the limit-breaking condition, the problem area is located by combining the spatial distribution of the three types of residuals within the urban study area, accurately locking the corresponding abnormal spatial sub-region. This region not only includes the surface grid, pipeline nodes, and river units where residuals exceed the limit, but also... The system incorporates adjacent areas with hydraulic connectivity, and then performs refined local re-solution calculations separately for the locked anomaly space sub-regions. It recalculates various hydrological parameters within the region in conjunction with the surrounding hydraulic environment, obtaining accurate and reliable corrected local calculation results. All corrected local hydrological data are then uniformly fed back into the initial unified state space, completing the overall replacement and synchronous update of various state parameters within the space, forming a new unified state space. After data updates, the system automatically jumps back to the multi-system collaborative hydrodynamic coupling solution process, and the structured state is completed again sequentially. The entire inference process, including set output, spatiotemporal directed graph encoding, and spatiotemporal recursive prediction with physical constraint embedding, continuously performs closed-loop operations such as residual determination, region locking, local recalculation, and data update. It continuously calibrates the inference results with physical rules until all residual values ​​no longer trigger the limit conditions. At this point, the iterative cycle process is terminated, and the candidate flood situation of the entire domain that meets all physical constraint standards is taken as the final output. The various corrected hydrological parameters produced in this iteration can also be directly used in subsequent processes such as structured state set organization, spatiotemporal graph construction, and time series recursive prediction.This closed-loop iterative correction model relies on multi-dimensional physical residuals to complete comprehensive compliance verification. It can accurately identify problems in the preliminary simulation results, such as water imbalance, disordered flow direction, and cross-system flux mutations, which do not conform to natural hydrological laws. It adopts a local recalculation method instead of a full-domain re-simulation to effectively control the overall computational workload and avoid significantly reducing the simulation efficiency. It accurately locates problem areas by relying on the spatial distribution of residuals, effectively making up for the shortcomings of insufficient local state matching in the collaborative simulation of surface, pipeline, and river systems. Through multiple iterative cycles, it continuously corrects the simulation deviations, thoroughly improving the shortcomings of traditional rapid prediction models that lack multi-level physical verification and whose simulation results are prone to violating basic hydrological laws. With the help of data backfeeding, it achieves dynamic synchronous updates of the state information across the entire domain, allowing each round of simulation calculations to be carried out based on the latest calibrated real hydraulic state. While ensuring the efficiency of rapid simulation of flood situation, it continuously improves the degree of fit between the final simulation results and the actual hydrodynamic evolution process. At the same time, the entire correction process is driven by clear physical constraint rules, so that every result adjustment has a corresponding hydrological and physical basis, further enhancing the interpretability of the overall simulation results.

[0219] Furthermore, to verify the technical effectiveness of the Urban Rapid Rainfall-Runoff Inundation Model (URRIM) proposed in this invention under complex urban flooding scenarios, comparative experiments were conducted based on typical rainstorm conditions, and three sets of visualization results were generated. The results show that this invention exhibits significant advantages in characterizing the spatial inundation distribution at typical flood peak times, tracking the dynamic processes at key sensitive locations, and demonstrating predictive stability under different forecast durations. It can effectively balance the mechanistic realism of complex hydrodynamic processes, rapid inference capabilities, and physical consistency of results.

[0220] (1) Comparison of spatial inundation distribution at typical flood peak moments (e.g.) Figure 2 (as shown)

[0221] This figure illustrates the simulation results of spatial inundation distribution in the study area using different methods at typical flood peak times. In the figure, (a) represents the baseline physical results, (b) represents the results driven by ordinary data, and (c) represents the URRIM results; area A is the sensitive area for dynamic changes in flow paths, and area B is the sensitive area for backwater backwater. As can be seen from the figure, the water accumulation distribution in the study area at flood peak times exhibits significant spatial heterogeneity in the baseline physical results: on the one hand, low-lying areas form localized high-water cores; on the other hand, near the boundary between the river channel and the surface system, backwater zones extend along the boundary due to the influence of external high water levels, while significant dynamic changes in flow paths occur in local transition areas. Although the ordinary data-driven method can identify the main water accumulation areas macroscopically, its spatial field exhibits significant smoothing distortion and localized anomalous fluctuations. Particularly in region B, the conventional data-driven results failed to accurately depict the spatial morphology of the backwater ridge, resulting in local patches inconsistent with the actual hydrodynamic connectivity. In region A, the data failed to adequately characterize the core area and directional expansion of the water accumulation zone in the dynamic transition zone of the flow path. This indicates that while this type of method can learn overall statistical characteristics, it struggles to accurately maintain the actual hydrodynamic connectivity under absolute water level-driven conditions in extreme situations. In contrast, the URRIM results showed a high degree of consistency with the baseline physical results in terms of spatial distribution. It preserved the morphology of the backwater ridge developing along the boundary well in region B, and accurately recovered the location and expansion direction of high-value water accumulation areas corresponding to local dynamic transitions in the flow path in region A. Overall, URRIM outperformed conventional data-driven methods in terms of the location of the main water accumulation center, the width of the boundary ridge, and the morphology of local turning zones.

[0222] (2) Comparison of water depth process lines at key locations:

[0223] Figure 3 The results of water depth hydrographs at three representative locations are shown. (a) represents a low-lying water accumulation point, (b) a pipe network backwater node, and (c) a river backwater boundary point. In the figure, the solid black line represents the baseline physical results, the dashed gray line represents the results driven by ordinary data, the dotted gray line represents the PINN method, and the dotted black line represents the URRIM results.

[0224] At low-lying water accumulation points, baseline physical results show that water depth underwent a clear evolutionary process of "rapid rise – peak formation – slow receding". Conventional data-driven methods responded slowly in the early stages of rising water, with significantly lower peak values, indicating insufficient ability to characterize the rapid accumulation and storage of local catchments. PINN-type methods showed improvement over conventional data-driven methods, but still underestimated peak amplitude and the receding phase. In contrast, URRIM results closely followed the baseline physical process line overall, with not only consistent peak times but also good trend consistency during the receding phase, demonstrating a stronger ability to dynamically track the storage and discharge processes in low-lying areas.

[0225] At the pipeline backing node, the baseline physical results exhibit a distinct bimodal characteristic, reflecting the combined response under the combined effects of rainfall inflow and underground pipeline backing feedback. Ordinary data-driven methods provide the weakest characterization of the bimodal structure, with both peaks showing underestimation of amplitude and periodic shifts. While PINN-type methods can identify the bimodal characteristics, they are insufficient in recovering the localized enhanced response at the second peak caused by backing feedback. The URRIM results, however, track the bimodal process well, particularly accurately characterizing the localized uplift response near the second peak. This indicates that the present invention maintains higher process consistency when dealing with complex node dynamic responses caused by underground pipeline pressure feedback.

[0226] At the backwater boundary point, the baseline physical results show a significant rise in boundary water level and a delayed recession process. Ordinary data-driven methods significantly underestimate the rise in water level and lag behind during the recession phase. While PINN-type methods recover the overall trend to some extent, they still deviate from the baseline physical results during the peak plateau and tail-end decline phases. URRIM most closely matches the baseline results throughout the entire process, especially in the middle stage when the backwater influence is strongest, effectively preserving the high-water-level plateau characteristics caused by the boundary backwater.

[0227] (3) Comparison of stability under different forecast durations (e.g.) Figure 4 (as shown)

[0228] This figure shows a comparison of the stability of different methods under different forecast durations. (a) shows the RMSE (Real Mean Squared Error) curve as a function of forecast duration, and (b) shows the peak time error curve as a function of forecast duration. Figure 4 As shown in (a), the water depth error of all models increases with the gradual increase of the forecast period from short to long. This is a common error accumulation phenomenon in rapid flood forecasting, but the error growth rate varies significantly among different methods. The RMSE of the ordinary data-driven method increases the fastest, indicating that it is more prone to state drift and error propagation outside of short-term forecasts. The growth trend of PINN-type methods is slower than that of the ordinary data-driven method, but the error still continues to increase with the forecast period. In contrast, URRIM's RMSE remains the lowest and its growth rate is the slowest, indicating that it has stronger state preservation and error suppression capabilities under long forecast conditions.

[0229] from Figure 4As shown in (b), the peak occurrence time error gradually increases with the increase of the forecast duration. Ordinary data-driven methods exhibit a rapid increase in peak occurrence time deviation after the forecast duration increases, demonstrating a significant decrease in peak tracking capability. While PINN-type methods outperform ordinary data-driven methods, they still exhibit significant bias under longer forecast periods. In contrast, URRIM shows the slowest increase in peak occurrence time error, indicating that it can still maintain a relatively stable ability to capture the flood peak time series under long-term recursive conditions. Overall, this invention demonstrates good error control capability and process stability under different forecast duration conditions, making it more suitable for meeting the requirements of result stability and engineering reliability in scenarios of rapid urban flood forecasting and short-term risk assessment.

[0230] As a comparison of technical effectiveness, existing technologies can be used as a reference. In the field of urban stormwater flooding simulation and rapid risk assessment, how to achieve urban rainfall-runoff-inundation process modeling under complex hydrodynamic conditions that combines physical rationality, computational efficiency, and interpretability of results is a key technical problem that urgently needs to be solved. The main contradiction of existing technologies lies in the difficulty of simultaneously balancing the realism of the expression of complex hydrodynamic process mechanisms, the real-time nature of rapid flood situation extrapolation, and the physical reliability of model output results. This results in a significant disconnect between urban flood simulation, rapid extrapolation, and the expression of physical mechanisms.

[0231] Under extreme and sudden rainstorm scenarios, rainfall input, runoff formation, confluence and transport, and surface inundation expansion are not independent sequential processes, but rather continuous hydrodynamic evolution processes that occur simultaneously and influence each other under the combined effects of surface accumulation, underground pipe network discharge, river water level backwater, and external receiving boundaries. Under complex urban underlying surface conditions, there is a significant and strongly nonlinear hydrodynamic coupling process between surface runoff, underground pipe network flow, and river flow. This linkage directly affects the formation and evolution of phenomena such as water diffusion, pipe network backwater, node overflow, backflow, and dynamic changes in local flow paths. Therefore, accurately describing these processes typically requires physical models that can characterize the dynamic driving mechanism of absolute water level and the water exchange and hydrodynamic feedback relationships between the surface-pipeline-river system. However, such models often involve numerical solutions to high-dimensional partial differential equations or complex discrete equations, resulting in high computational complexity and making it difficult to meet the timeliness requirements of rapid urban flood forecasting and short-term risk identification.

[0232] On the other hand, to improve inference efficiency, existing methods often employ purely data-driven deep learning models for flood situation prediction. Although these models have a fast response speed, they lack explicit physical constraints such as mass conservation, water level gradient driving, and consistency of water exchange across systems. When facing extreme nonlinear flood processes, they are prone to physical distortions such as local water volume non-conservation, deviation of water flow direction from the actual water level gradient, and local abrupt changes in the predicted field. This weakens the credibility and interpretability of the model results in engineering applications.

[0233] Therefore, there is an urgent need to construct a unified technical framework to achieve rapid simulation and interpretable representation of the overall flood situation while ensuring the physical rationality of the urban rainfall-runoff-inundation process. Specifically, it is necessary to construct a physically coded interpretable model that can explicitly encode the absolute water level driving mechanism, the water exchange and hydrodynamic feedback relationship in the surface-pipeline-river system, and conservation constraints within the model, thereby achieving the unification of process mechanism expression, rapid state simulation, and physical consistency constraints within the same system.

[0234] Specifically, under the combined influence of global climate change and rapid urbanization, urban flooding disasters induced by extreme heavy rainfall exhibit characteristics such as suddenness, complex evolutionary processes, and significant spatial differentiation, seriously threatening the operation of urban infrastructure and regional security. Currently, urban flood prevention research is gradually shifting from post-disaster response to rapid simulation, risk assessment, and proactive defense throughout the entire process. The core technology lies in how to achieve a unified model that combines mechanistic accuracy, extrapolation efficiency, and interpretability across the entire urban rainfall-runoff-inundation process. Furthermore, the urban rainfall-runoff-inundation process is a synchronously coupled, continuous evolutionary process, rather than an independent, sequential process. However, existing scientific research and engineering practices mainly follow two paths, which still have significant limitations.

[0235] (1) Traditional physical mechanism simulation: In the field of urban flood simulation, traditional physical mechanism models are still the main technical means to describe complex hydrodynamic processes. However, existing methods generally suffer from "process fragmentation" and "feedback deficiency" in terms of system architecture and underlying mechanism expression. From a system architecture perspective, commonly used underground drainage models in the industry, such as the SWMM (Storm Water Management Model), while capable of describing the hydraulic processes of pipe networks relatively well, often employ lumped or simplified methods such as the nonlinear reservoir method during the formation and confluence of surface runoff. This makes it difficult to accurately depict the two-dimensional water diffusion process in complex urban roads, low-lying areas, and boundary transition zones. While one-dimensional-two-dimensional integrated models, such as the MIKE URBAN (MIKE Urban Water System Model), introduce a coupling framework between the surface and the pipe network to some extent, the interactions between the surface, pipe network, and waterways are still largely based on loose coupling, unidirectional driving, or offline exchange methods. This makes it difficult to accurately reflect the transient feedback relationships between surface water inflow, pipe network overload overflow, external high water levels, and local backflow under heavy rainfall conditions. Furthermore, regarding flow path description mechanisms, existing distributed models in surface water flow calculations often rely on predefined static flow direction fields based on initial digital elevation models, such as using the D8 flow direction algorithm to determine fixed flow directions. These methods fail to fully consider the dynamic adjustment effect of real-time changes in the absolute water level gradient on the flow direction after water accumulation, making it difficult to accurately simulate key physical phenomena such as dynamic changes in local flow paths, peak overflow in depressions, and backwater under extreme rainfall conditions. Overall, traditional physical models, when describing the continuous evolution of urban rainfall-runoff-inundation processes, still treat runoff formation, confluence and transport, and inundation expansion as separate steps, lacking a modeling method that can comprehensively express the hydrodynamic coupling process and absolute water level driving mechanism within the surface, pipe network, and river system under a unified framework.

[0236] (2) Data-driven rapid simulation: Given that traditional physical models typically involve large computational loads in large-scale urban flood simulations, deep learning methods, represented by Long Short-Term Memory (LSTM) networks, graph neural networks, and related surrogate models, have been widely used in recent years for rapid simulation of flood conditions. These methods, by learning the input-output mapping relationship in historical samples, can provide predictions of water depth, water level, or flow rate for future periods in a short time, demonstrating a significant advantage in computational efficiency. However, most existing deep learning models are based on black-box mapping driven by statistical correlation. Their internal state representation, spatial propagation paths, and dynamic update processes often lack clear physical meaning, and they do not explicitly embed fundamental hydrodynamic laws such as mass conservation, water level gradient driving, and consistency of water exchange between the surface, pipe network, and river channels into the model structure and state evolution process. Especially when facing extreme rainstorm conditions that exceed the distribution of training samples, such models are prone to phenomena such as local water volume non-conservation, water flow direction deviating from the true water level gradient, and local abrupt changes in the prediction field, thereby weakening the physical credibility and engineering interpretability of the prediction results. Although some studies have attempted to enhance the consistency of the model mechanism by introducing physical information neural networks or physical constraint loss terms, existing methods still focus on fitting the residuals of local equations or enhancing the physical constraints under single process or single boundary conditions. They are still difficult to uniformly express the continuous evolution characteristics of runoff formation, confluence and transmission and inundation expansion in the entire process of urban rainfall-runoff-inundation under the same framework, and are also difficult to uniformly characterize the hydrodynamic coupling process, absolute water level driving mechanism and its corresponding interpretable state evolution process in the surface, pipe network and river system.

[0237] As can be seen from the above, existing technologies, when addressing the need for modeling and rapid extrapolation of complex urban rainfall-runoff-inundation processes, generally suffer from a separation between the representation of underlying physical mechanisms and efficient predictive calculations, exhibiting an overall "process fragmentation" characteristic and making it difficult to form a unified modeling and extrapolation framework. First, in terms of the representation of underlying mechanisms, traditional numerical models typically separate surface runoff evolution, river flow evolution, and underground pipe network transport and discharge processes into relatively independent modules for processing. They often use step-by-step calculations, loose coupling, or offline exchange methods to transmit information, thus failing to accurately reflect the continuous water exchange and hydrodynamic feedback processes between the surface, pipe network, and river channels under conditions where rainfall input, runoff formation, and inundation expansion occur simultaneously. They also lack the ability to uniformly characterize transient mass exchange, boundary backwater effects, and local reverse effects. Meanwhile, existing surface water flow calculation methods are mostly based on static digital elevation models that pre-determine flow directions. This makes it difficult to reflect complex phenomena such as dynamic adjustments in flow paths, backflow, and reverse overflow caused by localized water accumulation, pipeline overload, high river level backflow, or changes in external receiving boundaries under extreme rainfall conditions. This affects the accuracy of depicting the overall hydrodynamic evolution process. Secondly, in terms of situational prediction and computational efficiency, high-fidelity physical models typically require solving high-dimensional partial differential equations or complex discrete control equations, resulting in high computational complexity. This makes it difficult to meet the timeliness requirements of rapid urban flood forecasting and short-term risk identification. To improve extrapolation efficiency, some methods employ purely data-driven deep learning models for rapid prediction. However, these methods typically lack explicit physical constraints such as mass conservation, water level gradient driving, and consistency of water exchange between the surface, pipe network, and river channel. Therefore, when facing highly nonlinear flood evolution processes, they are prone to problems such as local water volume non-conservation, deviations of flow direction from the actual water level gradient, and local abrupt changes in prediction results, thereby weakening the physical rationality and engineering credibility of the results. In summary, existing technologies still lack a unified coordination mechanism for the mechanistic representation, rapid situation extrapolation, and physical consistency of results in complex urban rainfall-runoff-inundation processes. It is difficult to simultaneously ensure the accuracy of complex hydrodynamic process characterization, computational response efficiency, and the physical consistency and interpretability of model output results within the same system.

[0238] Furthermore, existing urban rainfall-runoff-inundation simulation technologies still have significant limitations in terms of the synergy between mechanism realism, real-time simulation, and physical consistency of results. In terms of representing underlying mechanisms, traditional numerical models often employ a step-by-step or loosely coupled approach to surface runoff, underground pipe network discharge, and river flow, making it difficult to comprehensively depict the continuous water exchange and hydrodynamic feedback processes between the surface, pipe networks, and rivers within a unified framework. Simultaneously, existing flow path calculation logic is mostly based on predefined flow direction fields derived from static topography, failing to fully consider the dynamic adjustment effect of real-time changes in absolute water level gradients on flow direction after water accumulation. Therefore, it is difficult to accurately describe complex urban rainfall-runoff-inundation processes such as dynamic changes in local flow paths, backwater, node overflows, and backflow under extreme rainfall conditions. On the other hand, traditional physical models typically require solving high-dimensional partial differential equations or complex discrete control equations, resulting in high computational complexity and making it difficult to meet the timeliness requirements for rapid urban flood prediction and short-term risk identification. To improve simulation efficiency, some existing methods employ purely data-driven models or neural networks incorporating physical constraints for rapid prediction. However, these methods typically rely on statistical mapping or local equation fitting, failing to encode the absolute water level driving mechanism, the hydrodynamic coupling process within the surface-pipeline-channel system, and the overall state evolution within the model. Consequently, when facing highly nonlinear flooding processes, issues such as local water volume non-conservation, deviations of flow direction from the actual water level gradient, and insufficient interpretability of results may still arise. In summary, current technologies lack a model framework capable of uniformly expressing the entire urban rainfall-runoff-inundation process within the same system, enabling rapid situational simulations while maintaining physical consistency and interpretability.

[0239] To address the aforementioned problems, this invention provides a physically coded and interpretable rapid extrapolation method for urban rainfall-runoff inundation. The aim is to provide a physically coded and interpretable rapid extrapolation model for urban rainfall-runoff inundation (URRIM) to achieve the mechanistic expression of the entire urban rainfall-runoff-inundation process, rapid extrapolation of the overall flood situation, and physical consistency constraints of the results within a unified technical framework. To achieve the above objectives, this invention constructs a simulation module for the hydrodynamic coupling process of the surface-pipeline-river system, used to uniformly express the continuous water exchange and hydrodynamic feedback relationships between the systems; constructs a physically coded and interpretable rapid extrapolation module, used to efficiently extrapolate the overall flood situation in the future under explicit physical constraints; and constructs a physical consistency verification and iterative update module, used to review the physical consistency of candidate extrapolation results and perform local corrections and state recharge when necessary, thereby improving the stability, physical reliability, and engineering interpretability of the model output results.

[0240] Specifically, addressing the shortcomings of existing technologies in expressing complex urban flooding mechanisms, rapidly extrapolating overall situations, and lacking physical consistency and interpretability of results, this invention constructs an overall technical approach comprised of a unified state space construction module, a simulation module for the hydrodynamic coupling process of the surface-pipeline-river system, a physically encoded interpretable rapid extrapolation module, and a physical consistency verification and iterative update module. The unified state space construction module serves as the foundation for system initialization and shared state representation, providing unified state variable definitions, boundary condition descriptions, and structured input carriers for subsequent core modules. Based on this, the surface-pipeline-river system hydrodynamic coupling process simulation module, the physically encoded interpretable rapid extrapolation module, and the physical consistency verification and iterative update module together constitute a unified technical architecture.

[0241] In this technical architecture, the urban rainfall-runoff-inundation process is viewed as a synchronously coupled, continuously evolving holistic process, rather than sequential, independent stages. The three core modules operate collaboratively within a unified state space, revolving around the same set of state variables: the hydrodynamic coupling process simulation module generates a physically based, structured state representation; the physically encoded, interpretable, and rapid deduction module performs rapid recursion of future states under explicit physical constraints; and the physical consistency verification and iterative update module reviews the conservation, directionality, and exchange continuity of the deduction results, triggering local corrections and state refeedback when necessary. Through the synergistic cooperation of the above technical routes and architecture, this invention achieves a unified system for expressing the entire process mechanism, rapid spatiotemporal deduction, and physical consistency constraints of the results. A schematic diagram of its overall architecture is shown below. Figure 5 As shown.

[0242] Based on the shared state representation provided in the unified state space construction phase, the core mechanisms of this invention mainly include a simulation module for the hydrodynamic coupling process of the surface-pipeline-river system, a physically encoded interpretable rapid deduction module, and a physical consistency verification and iterative update module. The following sections will describe these three core modules respectively.

[0243] (1) Simulation module for hydrodynamic coupling process of surface-pipeline-river system:

[0244] This module constructs the physical framework for the entire urban rainfall-runoff-inundation process. Its core lies in using absolute water level difference as a unified driving variable to solve the hydrodynamic coupling process of surface runoff, underground pipe network flow, and river flow within the same state framework. The system takes rainfall, topography, land use, river boundary conditions, and underground pipe network topology as inputs to collaboratively update the two-dimensional surface hydrodynamic process, the one-dimensional river evolution process, and the underground pipe network transport and discharge process. The urban rainfall-runoff-inundation process is a synchronously coupled continuous evolution process, rather than an independent serial process; therefore, this module does not simply piece together the sub-processes step by step, but continuously expresses their overall evolutionary relationship within a unified state space. Furthermore, the surface water flow direction is no longer determined by a predefined static flow field, but by the real-time determination of the absolute water level formed by the superposition of topographic elevation and dynamic water depth. This allows the system to characterize key nonlinear phenomena such as dynamic changes in local flow paths, peak overflow in depressions, and backwater under extreme rainfall conditions. Simultaneously, the system establishes dynamic water exchange and feedback relationships between the surface and the pipe network, and between the surface and the river channel, through physical mechanisms such as orifice flow, overflow, and overtopping exchange. This allows complex processes such as pipe network overflow, local backflow, river overtopping, and water diffusion to be uniformly expressed within the same continuous framework. To achieve cross-timescale water exchange and coordinated updates, this module employs a macro-microstep coupled operator splitting mechanism: within a macro-time step of surface and river channel, the underground pipe network module is synchronously driven to execute multiple micro-steps. After each synchronization cycle, the inflow from the surface to the pipe network and the overflow feedback from the pipe network to the surface are rewritten back into the unified state update process. The exchange volume from the surface to the pipe network is determined based on the local absolute water level difference and orifice flow relationship. To avoid local water overdraft under numerical discrete conditions, the system further applies available water constraints after flux calculation. When internal pressure in the pipe network causes node overflow, the system integrates and averages the instantaneous overflow rate in the micro-step over the synchronization cycle and feeds it back to the surface state update process. By coupling the aforementioned macroscopic step-size drive, microscopic sub-step solution, and periodic flux backpropagation, a closed loop of transient mass exchange across time scales is achieved between the surface, pipeline, and river systems. The result generated by this module is not a single water level value, but a structured physical state set including surface water depth, river water depth, pipeline node head, inter-system exchange flux, local absolute water level gradient, and boundary states. This state set not only represents the physical evolution of the system at the current moment but also constitutes a unified state carrier upon which rapid deduction, physical verification, and local correction processes all depend, thus ensuring the continuous connection between the physical mechanism and subsequent state recursion processes under the same mathematical semantics.

[0245] (2) Physically encoded interpretable fast deduction module:

[0246] This module enables rapid projection of future flood conditions across the entire region while maintaining physical meaning and consistency. Its core lies in not providing physical mechanism results as posterior labels for data-driven model fitting, but rather explicitly encoding key physical relationships already formed in a unified state space into the model structure and state update process, constructing an interpretable rapid projection mechanism. Specifically, the system constructs a spatiotemporally directed graph with physical attributes based on the real physical connectivity relationships between state variables within the unified state space. Nodes represent the local hydrodynamic states of surface grids, river units, and pipe network nodes; edges represent the physical connectivity relationships and water exchange directions between surfaces, between surfaces and rivers, between surfaces and pipe networks, and between nodes within the pipe network. Simultaneously, absolute water level difference, exchange flux, boundary type, and local storage / discharge states are encoded as node features, edge features, or auxiliary state variables. Thus, the physical relationships in the system no longer exist merely as supervisory signals but are directly translated into the graph structure, feature representation, and propagation constraints within the rapid projection module, achieving explicit embedding of mechanistic relationships into the model structure. Building upon this foundation, the system employs a graph convolutional network to extract spatial propagation features and a gated recurrent unit to describe the temporal evolution of the hydrodynamic state. Specifically, the graph convolutional layer aggregates neighborhood information along the physical connectivity paths in the spatiotemporally directed graph, ensuring that spatial feature propagation strictly follows the actual possible flow paths. The gated recurrent unit updates the hidden states of local nodes based on historical states, current inflows, and exchange relationships, thereby achieving the recursive evolution of the system state over multiple future time steps. Furthermore, this module introduces a composite physical loss function, incorporating data fitting, global mass conservation, water level gradient direction, and spatiotemporal smoothing terms into a unified optimization objective. The mass conservation term constrains global water storage changes to be consistent with external rainfall, boundary outflows, infiltration losses, and the inter-system water exchange between the surface, pipe network, and river channel. The water level gradient direction term constrains the predicted flow direction from conflicting with the absolute water level gradient. The spatiotemporal smoothing term restricts non-physical abrupt changes in the local state field. Through a dual approach of explicit structural encoding and synchronous constraint embedding, the system translates key physical relationships in the simulation module of the hydrodynamic coupling process of the surface-pipeline-river system into internal representations and state update rules for rapid extrapolation. This enables the model output to not only quickly provide global water accumulation, water level, or flow results for future time periods, but also to characterize the dynamic spatiotemporal evolution of runoff formation, confluence and transmission, and inundation expansion during urban rainfall-runoff-inundation processes, which occur simultaneously and influence each other. The module outputs candidate global flood scenarios for multiple future time steps, including predictions of surface water accumulation, water level, flow, and corresponding exchange fluxes. Because these candidate scenarios simultaneously retain information such as node states, edge exchanges, and flow direction relationships, they possess clear physical meaning and can be directly incorporated into the physical consistency verification and iterative update process.

[0247] (3) Physical consistency verification and iterative update module:

[0248] This module performs physical consistency checks on the rapid simulation results and, when necessary, executes local corrections and state reinjection to ensure the stability, reliability, and engineering usability of the entire system output. The system does not directly treat the candidate states output by the rapid simulation module as the final result; instead, it performs conservation checks, directional checks, and exchange continuity checks. The conservation check determines whether the water storage changes at a certain time step or in a certain area match rainfall, infiltration, boundary outflow, and inter-system exchange fluxes. The directional check determines whether the candidate flow direction is consistent with the absolute water level gradient. The exchange continuity check determines whether there are abrupt changes, breaks, or non-physical jumps in the exchange fluxes at system interaction boundaries such as between the surface and river channels, and between the surface and pipe networks. When the system detects significant conservation residuals, directional conflicts, or exchange anomalies in a local area or specific time window, it triggers a local physical re-check and correction mechanism. This mechanism identifies anomalous regions based on a unified state space and calls upon the surface-pipeline-river system hydrodynamic coupling process simulation module to recalculate the target region, obtaining a corrected local state. Subsequently, the corrected result is fed back into the rapid extrapolation module as the basis for updating the state recursion at subsequent time steps, and can also be used simultaneously as incremental training samples or online assimilation information in subsequent model updates. Through this approach, a closed loop is formed among the three modules, with a unified state space as the core link, encompassing physical mechanism constraints, rapid extrapolation execution, physical consistency verification, local correction, and state feedback. This improves the model's stability, reliability, and interpretability under extreme operating conditions and long-term predictions.

[0249] Furthermore, this invention addresses the need for urban stormwater flooding simulation and rapid risk assessment. It is applicable to urban areas with continuous hydrodynamic interactions, including surface runoff evolution, underground pipe network discharge, river flow evolution, and external boundary backwater. It is particularly suitable for urban flood simulation and rapid extrapolation scenarios under conditions of overlapping stormwater and high external water levels, such as low-lying flood-prone areas, tidal river networks, areas with complex drainage zone boundaries, and urban flooding simulation and rapid extrapolation scenarios. It should be noted that in the above scenarios, the urban rainfall-runoff-inundation process is a synchronously coupled continuous evolution process, rather than an independent serial process. Addressing the problems of insufficient expression of complex hydrodynamic process mechanisms, limited efficiency in global situation extrapolation, and insufficient physical consistency and interpretability of model output results in traditional methods, this invention relies on a surface-pipeline-river system hydrodynamic coupling process simulation module, a physically encoded interpretable rapid extrapolation module, and a physical consistency verification and iterative update module. Under a unified state space, it achieves closed-loop collaborative operation of physical mechanism expression, rapid spatiotemporal extrapolation, and dynamic correction, enabling the following functions and demonstrating corresponding technical advantages.

[0250] (1) To realize the integrated mechanism expression of the entire process of urban "rainfall-runoff-inundation":

[0251] Based on a simulation module for the hydrodynamic coupling process of the surface-pipeline-river system, this invention can provide a unified mechanistic representation of the entire urban rainfall-runoff-inundation process. Unlike traditional methods that treat surface runoff, underground pipeline discharge, river flow evolution, and boundary backwater effects step by step or loosely connect them, this invention, under a unified state space, takes absolute water level as the core and portrays rainfall input, runoff formation, confluence and transmission, and inundation expansion as a continuous hydrodynamic evolution process that occurs simultaneously and influences each other, thereby achieving a unified expression of the complex urban flood evolution mechanism.

[0252] Specifically, this invention comprehensively considers the interrelationships between key processes such as surface water diffusion, underground pipe network response, river level evolution, and external boundary backwater within the same framework, enabling a consistent description of complex phenomena such as dynamic changes in local flow paths, backwater backwater, node overflow, backflow, and river overflow. Because the system no longer relies on a static flow field to pre-determine the local flow direction, but instead determines the flow direction in real time based on the absolute water level gradient, it can more accurately reflect the true dynamic characteristics of urban flooding processes under extreme rainfall conditions.

[0253] Its technological advantages lie in its ability to overcome the problems of fragmented mechanism expression and lack of feedback relationships under the traditional step-by-step processing method, and to achieve overall modeling and consistent expression of the entire process of urban rainfall-runoff-inundation within the same technical system, providing a unified and reliable physical framework for subsequent rapid simulation and physical consistency verification.

[0254] (2) To achieve rapid simulation of the entire flood situation with physical coding and interpretable features:

[0255] By leveraging a physically encoded, interpretable, and rapid extrapolation module, this invention enables rapid extrapolation of the overall flood situation across multiple future time steps, constrained by a unified state space and real physical connectivity. The system explicitly encodes key physical relationships such as absolute water level difference, exchange flux, boundary type, and local storage and discharge states into a spatiotemporal directed graph structure, node features, edge features, and auxiliary state variables. This ensures that physical mechanisms are no longer merely external supervisory information but are directly integrated into the internal representation and state update process of the rapid extrapolation model. Furthermore, the system combines graph convolutional networks to model the spatial propagation process and gated recurrent units to model the temporal evolution process, thereby achieving efficient prediction of overall water accumulation, water level, flow rate, and exchange flux.

[0256] Meanwhile, this invention introduces a composite physical loss function that includes a data fitting term, a global mass conservation term, a water level gradient direction term, and a spatiotemporal smoothing term. This allows the rapid extrapolation model to simultaneously receive the combined effects of two types of physical information—explicit structural encoding and explicit constraint embedding—during both training and recursion. As a result, the model output not only provides a global flood situation for future periods but also characterizes the dynamic spatiotemporal evolution of runoff formation, confluence and transmission, and inundation expansion during the urban rainfall-runoff-inundation process, exhibiting simultaneous occurrence and mutual influence, and possessing a clear physical interpretive basis.

[0257] Compared with traditional high-fidelity numerical models, which suffer from high computational costs and insufficient deduction efficiency, and pure data-driven models, which are prone to problems such as local nonconservation, flow distortion, and abnormal abrupt changes in the state field, this invention can significantly shorten the deduction time while effectively improving the physical rationality and stability of the results.

[0258] Its technological advantage lies in the fact that it can improve the timeliness, physical rationality, and interpretability of prediction results while meeting the needs of rapid urban flood forecasting and short-term risk identification.

[0259] (3) Implement physical consistency verification and iterative updates for result credibility:

[0260] Based on the physical consistency verification and iterative update module, this invention can perform three types of physical consistency checks on the candidate flood situation obtained by rapid simulation: conservation, directionality, and exchange continuity. It can also perform local state correction and state recharge updates when necessary. Specifically, the system determines whether the water storage change in a certain area or at a certain time step matches rainfall, infiltration, boundary outflow, and inter-system exchange flux; verifies whether the candidate flow direction is consistent with the absolute water level gradient; and checks whether there are abrupt changes, breaks, or non-physical jumps in the exchange flux at system interaction boundaries such as between the surface and the river channel, and between the surface and the pipe network. This allows the system to identify abnormal areas or abnormal time windows in the candidate situation.

[0261] When conserved residuals, directional conflicts, or exchange anomalies are detected, the system triggers a local physical re-verification and correction mechanism. This mechanism calls the surface-pipeline-river system hydrodynamic coupling process simulation module to recalculate the abnormal region and feeds the corrected local state back into the unified state update process, serving as the state basis for subsequent rapid time-step extrapolations. Simultaneously, the relevant correction information can also be used as incremental training samples or online assimilation information in subsequent model updates. Through these methods, the system maintains its rapid extrapolation capabilities while continuously suppressing non-physical offset problems caused by error accumulation.

[0262] Compared with traditional rapid inference methods that only output one-time prediction results and lack subsequent consistency guarantees, this invention can continuously maintain the consistency between the results and the underlying physical constraints under complex boundary conditions, extreme rainfall conditions and long forecast periods.

[0263] Its technical advantages lie in its ability to enhance the credibility, generalization ability, and engineering interpretation value of the model output results, making the prediction results not only more timely, but also more physically consistent and stable.

[0264] Based on the aforementioned unified technical architecture, this invention focuses on the overall modeling, rapid deduction, and dynamic correction of the entire urban rainfall-runoff-inundation process. It forms a five-step progressive closed-loop implementation process consisting of: "basic input and unified state space construction, hydrodynamic solution and structured state output, explicit encoding of physical relationships into a spatiotemporal graph structure, spatiotemporal recursive prediction with embedded physical constraints, and physical residual verification and local re-solution." These five steps are not isolated linear sequences, but rather interconnected and collaboratively operate under unified state space constraints, jointly serving the mechanistic expression, rapid deduction, and physical consistency maintenance of the entire urban rainfall-runoff-inundation process.

[0265] In summary, the key points of this invention are:

[0266] 1. A modeling framework for the entire urban rainfall-runoff-inundation process based on a unified state space.

[0267] One of the key points of this invention is that it first establishes a unified state space for solving physical mechanisms and sharing data-driven learning. State variables such as surface water depth, river water depth, pipeline node head, inter-system exchange flux, and absolute water level difference are defined uniformly under the same mathematical semantics. This allows the same set of state variables to serve as both target variables for underlying physical solutions and direct input carriers for subsequent graph structure construction, rapid deduction, and physical verification, thereby solving the problem of the separation between the state representation of the traditional physical domain and data domain.

[0268] 2. A hydrodynamic coupling process of a surface-pipeline-river system driven by absolute water level.

[0269] One of the key points of this invention is that it uses the absolute water level difference instead of the static flow field as a unified driving variable, and solves the hydrodynamic coupling process between surface runoff, underground pipe network flow and river flow in a unified manner under the same state framework. It also realizes the transient mass exchange closed loop across time scales through orifice flow, overflow, overtopping exchange and macro-micro step operator splitting mechanism, so as to accurately characterize the strong nonlinear flooding process such as local flow path dynamic transformation, backwater backing, node overflow and backflow.

[0270] 3. An interpretable and fast derivation mechanism that explicitly encodes physical relationships into the model structure.

[0271] One of the key points of this invention is that instead of using physical mechanism results as posterior labels for data-driven model fitting, it explicitly encodes the real physical connectivity, absolute water level difference, exchange flux, boundary type, and local storage and discharge states in a unified state space as node features, edge features, and propagation constraints in a spatiotemporal directed graph. It then combines graph convolutional networks and gated recurrent units to complete rapid recursion for multiple future time steps, thereby achieving a direct mapping of mechanism relationships to model structures.

[0272] 4. A rapid derivation method for composite physical constraints that involves explicit structural encoding and synchronous embedding of constraints.

[0273] One of the key points of this invention is that, during the rapid deduction process, composite physical loss functions such as data fitting terms, global mass conservation terms, water level gradient direction terms, and spatiotemporal smoothing terms are introduced simultaneously, so that the model recursion is always carried out within the physically reachable topological space, avoiding problems such as local water volume non-conservation, flow direction distortion, and abrupt state changes that may occur in purely data-driven models under extreme conditions.

[0274] 5. A physical consistency verification and iterative update mechanism oriented towards result credibility.

[0275] One of the key points of this invention is that it implements three types of physical consistency checks on the candidate flood situation obtained by rapid inference: conservation, directionality, and exchange continuity. When significant conservation residuals, directional conflicts, or system exchange anomalies are detected in a local area, local physical re-solution and state refeedback are triggered. The corrected local state is written back into the unified state update process and can be used as an incremental training sample or online assimilation information to participate in subsequent model updates, thereby forming an integrated closed loop of physical mechanism constraints, rapid inference execution, physical verification, and local correction.

[0276] Compared with existing technologies, this invention has the following significant advantages. The core of existing technologies lies in using neural networks to replace some discrete solution steps in the two-dimensional shallow water equations, thereby improving the computational efficiency of surface flood evolution and enhancing the rationality of the solution results through local physical constraints. However, the focus of such schemes is mainly on the rapid replacement solution of two-dimensional shallow water processes. Their interaction between the surface and the pipe network is mostly based on unidirectional exchanges using local condition judgments, and a unified mechanistic framework for the entire urban rainfall-runoff-inundation process has not yet been formed. Furthermore, it fails to explicitly express the hydrodynamic coupling process, absolute water level driving mechanism, and corresponding interpretable state evolution process within the same system of the surface, pipe network, and river system.

[0277] This invention overcomes the aforementioned shortcomings. It is not simply a method for accelerating solutions to two-dimensional shallow water processes, but rather a unified modeling method for urban rainfall-runoff inundation that uses a unified state space as a link, encompassing the expression of the hydrodynamic coupling process of the surface-pipeline-river system, explicit encoding of physical relationships, and physical consistency verification and iterative updates. Because this invention first establishes a hydrodynamic coupling process of the surface, pipeline, and river systems driven by absolute water level at the bottom layer, and further embeds real physical connectivity, exchange flux, and conservation constraints directly into the spatiotemporal directed graph structure and state update rules, it can not only rapidly extrapolate the overall flood situation in the future, but also maintain stronger physical consistency and interpretability under extreme conditions and long-term forecasts. Furthermore, this invention effectively suppresses non-physical offsets caused by error accumulation by introducing conservation, directionality, and exchange continuity verification, and triggering re-solution and state re-injection when local mismatches occur. Therefore, compared with existing technologies, this invention has more significant comprehensive advantages in terms of the ability to express the entire process mechanism, the stability of rapid extrapolation, and the reliability of results.

[0278] In this embodiment of the invention, a method for rapid extrapolation of urban rainfall-runoff inundation with physically coded interpretable features is provided. This method acquires basic input data for a target urban area and constructs a unified state space based on this data. The unified state space is then used for a coordinated hydrodynamic coupling solution of the surface-pipeline-river system. Within this unified state space, the system state is updated collaboratively based on the absolute water level difference set, the net exchange flux between systems, and the external boundary state variables, resulting in a structured state set. The structured state set is then explicitly encoded into a spatiotemporal graph structure based on physical relationships, outputting a spatiotemporal directed graph with physical attributes. A spatiotemporal recursive prediction method is used, driven by absolute water level difference and with the linkage of inter-system exchange flux as the core, to embed physical constraints and output the candidate flood situation for the entire region. Through a physical consistency closed-loop approach, physical residual verification and local re-solution are performed on the candidate flood situation and the unified state space, outputting the final flood situation for the entire region after physical consistency correction. Based on the above scheme, a unified state space is built as the unified carrier for the hydraulic calculation of the entire region. Combined with multi-system state collaborative update calculations based on the absolute water level difference set, the net exchange flux between systems, and the external boundary state quantities, this method completely changes the previous independent nature of surface, pipeline, and river hydrological processes. The implementation mode of the calculation uses the absolute water level difference obtained in real time as the core driving condition for the overall inference. It abandons the traditional method of relying on static presets to determine the direction of water flow, allowing the water flow direction to form autonomously in complete accordance with the real-time hydraulic operation state. After the structured state set is completed and the physical relationships are explicitly encoded to generate a spatiotemporal directed graph with physical attributes, the spatiotemporal recursive prediction stage is carried out. Mass conservation, water level gradient direction, and cross-system exchange continuity related physical constraints are integrated into the entire inference process. This ensures that the rapidly predicted full-area flood candidate situation follows the established physical rules and constraints throughout the entire process, making up for the lack of corresponding physical constraints in traditional rapid prediction results. To address the shortcomings of the current control mechanism, the subsequent physical consistency closed-loop system is used to conduct physical residual verification and local re-solution of the candidate flood situation and unified state space across the entire region. This allows for timely correction of various physical operational deviations that occur during the simulation process, thereby steadily improving the physical reliability of the simulation results. The entire simulation process relies on a spatiotemporal recursive computation mode to ensure the efficiency of the overall simulation work. Furthermore, the entire process relies on real hydrological physical correlations to complete structural coding and situation simulation, ensuring that each simulation result has corresponding physical logical support and fully guaranteeing the interpretability of the simulation results. Ultimately, this successfully achieves a synergistic balance between simulation efficiency, physical reliability, and result interpretability.

[0279] Please see Figure 6 , Figure 6 This is a structural block diagram of a physical coding-interpretable urban rainfall-runoff inundation rapid projection system provided in Embodiment 2 of the present invention.

[0280] This invention provides a physical coding-interpretable urban rainfall-runoff inundation rapid projection system, comprising:

[0281] The acquisition module 601 is used to acquire basic input data of the target urban area and construct a unified state space based on the basic input data of the target urban area.

[0282] Solver module 602 is used to perform coordinated hydrodynamic coupling solution of surface-pipeline-river system in unified state space. Within the unified state space, it completes the coordinated update of system state based on the set of absolute water level differences, net exchange flux between systems and external boundary state quantities, and outputs a structured state set.

[0283] Encoding module 603 is used to explicitly encode the physical relationships of the structured state set into a spatiotemporal graph structure, and output a spatiotemporal directed graph with physical attributes;

[0284] Prediction module 604 is used to perform spatiotemporal recursive prediction of spatiotemporal directed graphs with physical attributes, with physical constraints embedded as the core of absolute water level difference driving and inter-system exchange flux linkage, and output the candidate situation of flood in the whole region.

[0285] The closed-loop verification module 605 is used to perform physical residual verification and local re-solution on the candidate flood situation and unified state space of the whole domain through the physical consistency closed-loop method, and output the final flood situation of the whole domain after physical consistency correction.

[0286] Those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system and modules described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here.

[0287] This invention also provides a computer device, including a memory and a processor, wherein the memory stores a computer program; when the computer program is executed by the processor, the processor performs the steps of the physical coding interpretable rapid extrapolation method for urban rainfall runoff inundation as described in the above embodiments.

[0288] This invention also provides a computer-readable storage medium storing a computer program / instructions thereon, which, when executed by a processor, implements the steps of the physical coding-interpretable rapid extrapolation method for urban rainfall runoff inundation as described in the above embodiments.

[0289] This invention also provides a computer program product, including a computer program stored on a non-transitory computer-readable storage medium, the computer program including program instructions, wherein when the program instructions are executed by a computer, the computer performs the steps of the physically encoded interpretable rapid extrapolation method for urban rainfall runoff inundation as described in the above embodiments.

[0290] In the several embodiments provided in this application, it should be understood that the disclosed systems and methods can be implemented in other ways. For example, the device embodiments described above are merely illustrative; for instance, the division of units is only a logical functional division, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between devices or units may be electrical, mechanical, or other forms.

[0291] The units described as separate components may or may not be physically separate. The components shown as units may or may not be physical units; that is, they may be located in one place or distributed across multiple network units. Some or all of the units can be selected to achieve the purpose of this embodiment according to actual needs.

[0292] Furthermore, the functional units in the various embodiments of the present invention can be integrated into one processing unit, or each unit can exist physically separately, or two or more units can be integrated into one unit. The integrated unit can be implemented in hardware or as a software functional unit.

[0293] If the integrated unit is implemented as a software functional unit and sold or used as an independent product, it can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or all or part of the technical solution, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the steps of the methods of the various embodiments of the present invention. The aforementioned storage medium includes various media capable of storing program code, such as USB flash drives, portable hard drives, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0294] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for rapid extrapolation of urban rainfall-runoff inundation using physically coded interpretable methods, characterized in that, include: Acquire basic input data for the target urban area, and construct a unified state space based on the basic input data for the target urban area; The unified state space is used to perform a coordinated hydrodynamic coupling solution for the surface-pipeline-river system. Within the unified state space, the system state is updated collaboratively based on the set of absolute water level differences, the net exchange flux between systems, and the external boundary state quantities, and a structured state set is output. The structured state set is explicitly encoded into a spatiotemporal graph structure based on physical relationships, outputting a spatiotemporal directed graph with physical attributes, including: The structured state set is subjected to node feature extraction processing to generate node feature vectors; Edge features are extracted from the structured state set to generate edge feature vectors; Based on the node feature vectors and the edge feature vectors, a spatiotemporal directed graph with physical attributes is constructed. The node feature vector includes one or more of the following: surface water depth, river water depth, pipeline node head, external boundary water level, local storage and discharge status, and absolute water level. The edge feature vector includes one or more of the following: absolute water level difference, net surface-to-pipeline exchange flux, net surface-to-river exchange flux, internal connectivity of the pipeline network, boundary type, flow direction identifier, and exchange continuity identifier. The edge directions in the spatiotemporal directed graph with physical attributes are jointly determined by the real-time absolute water level difference, physical connectivity, and net exchange flux between systems, and are used to characterize the dynamic flow direction and cross-system exchange relationship in the flood hydrodynamic process. The spatiotemporal directed graph with physical attributes is subjected to spatiotemporal recursive prediction based on physical constraints driven by absolute water level difference and linkage of net exchange flux between systems, outputting candidate flood situations for the entire region, including: Along the physical connectivity path of the spatiotemporal directed graph with physical attributes, using the absolute water level difference between nodes as the basis for spatial transmission and the net exchange flux between systems as the hydraulic linkage benchmark, spatial aggregation of node feature vectors is performed to obtain spatial aggregation features. Based on the spatial aggregation features, the node feature vectors are recursively updated in the time dimension to obtain the spatiotemporal recursive intermediate results. Physical constraints of mass conservation, water level gradient direction, and spatiotemporal smoothing are applied to the intermediate spatiotemporal recursion results to optimize them, resulting in optimized spatiotemporal recursion results. Based on the optimized spatiotemporal recursive results, candidate flood situations for the entire region are determined; The constraint of the water level gradient direction is used to restrict the predicted water flow direction from being consistent with or not conflicting with the hydrodynamic driving direction determined by the real-time absolute water level difference. The candidate global flood situation and the unified state space are physically residual checked and locally resolved using a physical consistency closed-loop method, outputting the final global flood situation after physical consistency correction, including: Based on the physical constraint rules of the unified state space, the following residuals are calculated: macroscopic conservation residuals representing the deviation of water balance between the whole region and the local area in the candidate flood situation; directional conflict residuals representing the conflict between the predicted water flow direction and the driving direction of the absolute water level difference; and exchange continuity residuals representing the jump in flux at the interaction boundary between the surface and the pipe network and the surface and the river channel. Determine whether the macroscopic conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the entire region trigger the limit-breaking condition; If the aforementioned limit-crossing condition is not triggered, the candidate global flood situation will be taken as the final global flood situation after the physical consistency correction. If the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the whole region trigger the limit-breaking condition, then based on the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate flood situation in the whole region, an abnormal spatial sub-region is locked in the target urban area. Perform a local re-solution on the aforementioned abnormal spatial sub-region to obtain the corrected local calculation results; The corrected local calculation results are fed back into the unified state space to complete the update, resulting in a new unified state space. Jump to execute the step of performing a coordinated hydrodynamic coupling solution of the surface-pipeline-river system in the unified state space and outputting a structured state set until the macroscopic conservation residual, directional conflict residual and exchange continuity residual of the candidate flood situation in the whole region do not trigger the over-limit condition; The candidate state of the global flood situation determined when the macro-conservation residual, directional conflict residual, and exchange continuity residual of the candidate state of the global flood situation do not trigger the above-mentioned over-limit conditions is taken as the final global flood situation after the physical consistency correction. The abnormal spatial sub-region is determined based on the spatial distribution of the macroscopic conservation residual, the directional conflict residual, and the exchange continuity residual, and includes the surface grid, pipeline nodes, river units, and their adjacent hydraulic connectivity regions where the residuals trigger the limit-breaking conditions; The corrected local calculation results include one or more of the following: corrected surface water depth, water head at pipe network nodes, river water depth, net exchange flux between systems, and absolute water level difference set, which are used for the next round of structured state set generation, spatiotemporal map encoding, and recursive prediction.

2. The method for rapid extrapolation of urban rainfall-runoff inundation using physically coded interpretation as described in claim 1, characterized in that, The unified state space is specifically composed of external boundary state quantities, dynamic hydraulic state data, net exchange flux between systems, absolute water level difference set, and basic static data in the basic input data of the urban target area.

3. The method for rapid extrapolation of urban rainfall-runoff inundation using physically coded interpretation as described in claim 1, characterized in that, The inter-system net exchange flux includes river depth, surface-to-river net exchange flux, and surface-to-pipeline net exchange flux; the unified state space is used to perform a surface-pipeline-river system coordinated hydrodynamic coupling solution, and the system state is coordinatedly updated within the unified state space based on the absolute water level difference set, inter-system net exchange flux, and external boundary state quantities, outputting a structured state set, including: The surface water flow motion and soil infiltration loss in the unified state space are solved to obtain the surface water depth and infiltration loss data. The one-dimensional evolution process of the river channel within the unified state space is solved based on the surface water depth and the infiltration loss data to obtain the river channel depth and the net surface-to-channel exchange flux. Based on the surface water depth, the infiltration loss data, the river water depth and the surface-to-river net exchange flux, the underground pipeline transportation and discharge process in the unified state space is solved to obtain the pipeline node head and the surface-to-pipeline net exchange flux. Based on the surface water depth, the river water depth, and the water head at the pipeline nodes, calculate the set of absolute water level differences; The water level at the boundary of the external receiving water body is taken as the external boundary state quantity. By integrating the surface water depth, the river water depth, the water head of the pipeline node, the net exchange flux between the surface and the pipeline, the net exchange flux between the surface and the river, the absolute water level difference set, and the external boundary state quantity, a structured state set is obtained; The two-dimensional surface water flow movement, the one-dimensional river flow evolution process, and the underground pipeline transportation and discharge process are all updated collaboratively within the unified state space based on the absolute water level difference set, the net exchange flux between systems, and the external boundary state quantity. The solution is achieved through coupled solutions via water exchange feedback between the surface and the pipeline, the surface and the river, and the pipeline and the receiving water body.

4. The method for rapid extrapolation of urban rainfall-runoff inundation using physically coded interpretation according to claim 3, characterized in that, The set of absolute water level differences includes the water level differences between adjacent surface units, between the surface and the pipe network, between the surface and the river, and between the pipe network and the external receiving water body; Absolute water level includes one or more of the following: the sum of surface elevation and dynamic water depth, water head at pipeline nodes, river water level, or boundary water level of external receiving water bodies. The absolute water level difference set is used to determine the direction, intensity and spatiotemporal directional graph edge direction of water exchange between surface units, pipeline nodes, river units and external receiving water bodies, so that the flow path can be dynamically updated with the real-time water level status.

5. A physically coded, interpretable urban rainfall-runoff inundation rapid projection system, applied to the physically coded, interpretable urban rainfall-runoff inundation rapid projection method of claim 1, characterized in that, include: The acquisition module is used to acquire basic input data of the target urban area and construct a unified state space based on the basic input data of the target urban area. The solution module is used to perform a coordinated hydrodynamic coupling solution of the surface-pipeline-river system in the unified state space. Within the unified state space, it completes the coordinated update of the system state based on the set of absolute water level differences, the net exchange flux between systems, and the external boundary state quantities, and outputs a structured state set. The encoding module is used to explicitly encode the physical relationships of the structured state set into a spatiotemporal graph structure, and output a spatiotemporal directed graph with physical attributes. The prediction module is used to perform spatiotemporal recursive prediction on the spatiotemporal directed graph with physical attributes, with physical constraints embedded as the core of absolute water level difference driving and inter-system net exchange flux linkage, and output the candidate situation of flood in the whole region. The closed-loop verification module is used to perform physical residual verification and local re-solution on the candidate flood situation of the whole domain and the unified state space through a physical consistency closed-loop method, and output the final flood situation of the whole domain after physical consistency correction.

6. An electronic device, characterized in that, The system includes a memory and a processor, wherein the memory stores a computer program that, when executed by the processor, causes the processor to perform the steps of the physical coding interpretable rapid extrapolation method for urban rainfall runoff inundation as described in any one of claims 1-4.

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