CN-121543452-B - Quick surface flooding calculation method based on Fourier neural operator

CN121543452BCN 121543452 BCN121543452 BCN 121543452BCN-121543452-B

Abstract

The invention discloses a fast calculation method of surface flooding based on a Fourier neural operator, and provides a city flooding modeling and numerical calculation method integrating a two-dimensional hydrodynamic model and a physical constraint Fourier neural operator. According to the method, a multi-scale feature mapping and physical constraint mechanism is introduced under the framework of the traditional shallow water equation solving surface flood evolution process, so that nonlinear mapping from low-resolution simulation results and multi-source environment driving data to a high-resolution flood response field is realized, and on the premise of guaranteeing physical rule constraint, the high-precision and rapid prediction of the urban flood process is realized.

Inventors

XING YUN
LIN QIGEN
JIANG TONG
WANG YANJUN
WEI XIKUN
SI LILI
Zhan Mingjin

Assignees

南京信息工程大学
江苏第二师范学院
河北省气象灾害防御和环境气象中心(河北省预警信息发布中心)
江西信息应用职业技术学院

Dates

Publication Date: 20260508
Application Date: 20260119

Claims (5)

1. A fast surface flooding calculation method based on Fourier neural operators is characterized by comprising the following steps: (1) Collecting flood simulation and observation data of a research area, including digital terrain elevation, land utilization type and rainfall data, and carrying out standardized processing on the data to construct a data set for training a nerve operator; (2) Based on a two-dimensional shallow water equation, calculating a low-resolution hydrodynamic solution by using input data, wherein the low-resolution hydrodynamic solution provides hydrodynamic information of flood propagation directions and ponding areas; (3) The method comprises the steps of constructing a Fourier neural operator model, embedding low-resolution hydrodynamic solution into an input layer and a feature coding layer as physical prior information by the model, realizing multi-scale feature fusion through Fourier transformation and multi-scale convolution to learn nonlinear mapping from input data to a high-resolution flood prediction solution, modulating feature response in a frequency domain by the Fourier neural operator model through fast Fourier transformation and inverse transformation, carrying out local feature extraction by combining a multi-layer perceptron to enhance feature representation capability, carrying out dimension alignment by using a resampling layer, carrying out continuous interpolation in time and space dimensions by adopting a three-line interpolation function by the resampling layer, and adopting the following mapping formula: Wherein, the Is an input function; Representing urban terrain, land utilization, building distribution and initial condition static input; Characterizing rainfall, boundary water level external input data, which change with time; Providing important hydrodynamic information of flood propagation direction and ponding region for low-resolution hydrodynamic solution Predictive solutions for high resolution floods, including water depth and flow rate; T is a time variable; The physical priori information of low-resolution hydrodynamic solution and the multi-source environment input are fused in the characteristic extraction process, so that the efficient coupling and physical consistency constraint of multi-scale characteristics are realized; The method is characterized in that the physical background field is embedded into an input layer and a feature coding layer of depth mapping, information fusion is realized through Fourier transformation and multi-scale convolution, and in the Fourier layer, the input relation is expressed as follows: ; Wherein, the The feature function is input for the i-th layer, Is a linear transformation matrix for channel mapping F is a fast Fourier transform FFT, F -1 is an inverse Fourier transform IFFT, For complex weight parameter tensor for modulating the response of selected Fourier mode k, MLP for multi-layer perceptron for jump connection to extract local features, reLU for nonlinear activation function, and method for modulating the response of selected Fourier mode k ; Resampling layer for dimension alignment, denoted as , Continuous interpolation is carried out on three dimensions of time-space for a tri-linear interpolation function; for learning weights, the mapping trunk is fused to realize the fusion of physical constraint and data driving; (4) The Fourier neural operator model is utilized to output a high-resolution water depth field and a high-resolution flow velocity field, and physical consistency constraint correction is carried out on the output result through a residual error correction module, wherein the residual error correction module ensures mass conservation and space continuity of a predicted result based on a shallow water equation balance error and gradient smoothing loss, the shallow water equation balance error in the residual error correction module is used for constraining the mass conservation of the predicted result, the gradient smoothing loss is used for improving the space continuity and gradient consistency of a water surface boundary of a water accumulation area, The output layer adopts a double-channel structure and corresponds to the high-resolution water depth field respectively And flow velocity field Firstly, reconstructing the frequency domain characteristics into a time-space domain solution through an inverse Fourier decoding layer, and then carrying out physical consistency constraint correction through a residual error enhancement module, wherein a residual error term consists of shallow water equation balance errors, and the specific form is as follows: ; Wherein, the Representing the sum of squares error, by minimizing during training To ensure that the prediction result keeps conservation of mass under physical constraint, to increase gradient smooth loss term, R is the external production confluence; wherein Is a gradient; (5) The Fourier neural operator model is trained by minimizing a fusion loss function, wherein the fusion loss function comprises a data driving loss term and a physical constraint loss term, and the collaborative optimization of the data driving and physical mechanism is realized.
2. The fast surface flooding calculation method based on the Fourier neural operator according to claim 1, wherein in the step (2), the two-dimensional shallow water equation comprises a continuous equation and a momentum equation, and the continuous equation and the momentum equation are used for simulating a surface flooding evolution process.
3. The method of claim 1, wherein in the step (5), the fusion loss function is in a form of a plurality of fusion, including mean square error loss, physical constraint loss and gradient smoothing loss of the observation or high-precision simulation result, and each loss item is balanced by an adjustable weight parameter, and the method is as follows: ; Wherein, the Mean square error loss from the observed/high-precision simulation results is represented, , , Is an adjustable weight parameter.
4. An electronic device comprising a memory storing a computer program and a processor implementing the steps of the method of any one of claims 1-3 when the program is executed by the processor.
5. A computer readable storage medium, characterized in that a computer program is stored, which program, when being executed by a processor, carries out the steps of the method according to any one of claims 1-3.

Description

Quick surface flooding calculation method based on Fourier neural operator Technical Field The invention relates to the technical field of intelligent water conservancy and artificial intelligence modeling, in particular to a fast calculation method for surface flooding based on a Fourier neural operator. Background Current urban flood modeling methods rely primarily on two-dimensional hydrodynamic models of physical basis or data-driven machine or deep learning methods. The method has the advantages that the method is high in calculation accuracy, low in calculation efficiency and difficult to realize early warning and forecasting of a high-resolution urban flood process, and the method is capable of quickly forecasting when a large number of observation or numerical simulation samples are provided, but forecasting results depend on representativeness and coverage of training data, and the method is lack of physical consistency and is easy to produce non-physical ponding, abnormal flow rate and other problems. Therefore, the prior method has the technical bottleneck that the physical consistency and the computing efficiency are difficult to be compatible. Disclosure of Invention The invention aims to provide a fast calculation method of surface flooding based on Fourier neural operator, which realizes nonlinear mapping from low-resolution simulation results and multisource environment driving data to a high-resolution flooding response field by introducing a multiscale feature mapping and physical constraint mechanism under the framework of solving the surface flooding evolution process by using a traditional shallow water equation, thereby solving the problems in the background technology on the premise of ensuring the constraint of the physical law. The technical scheme is that the fast surface flooding calculation method based on the Fourier neural operator comprises the following steps: (1) Collecting flood simulation and observation data of a research area, including digital terrain elevation, land utilization type and rainfall data, and carrying out standardized processing on the data to construct a data set for training a nerve operator; (2) Calculating a low-resolution hydrodynamic solution based on a two-dimensional shallow water equation by using the input data, wherein the low-resolution hydrodynamic solution provides hydrodynamic information of a flood propagation direction and a ponding region; (3) Constructing a Fourier neural operator model, embedding low-resolution hydrodynamic solution serving as physical priori information into an input layer and a feature coding layer by the model, and realizing multi-scale feature fusion by Fourier transformation and multi-scale convolution to learn nonlinear mapping from input data to a high-resolution flood prediction solution; (4) Outputting a high-resolution water depth field and a high-resolution flow velocity field by using a Fourier neural operator model, and carrying out physical consistency constraint correction on an output result by a residual error correction module, wherein the residual error correction module ensures mass conservation and space continuity of a predicted result based on shallow water equation balance errors and gradient smooth losses; (5) And training the Fourier neural operator model by minimizing a fusion loss function, wherein the fusion loss function comprises a data driving loss term and a physical constraint loss term, so that the collaborative optimization of the data driving and physical mechanism is realized. Further, in the step (1), the rainfall data is subjected to logarithmic transformation. Further, in the step (2), the two-dimensional shallow water equation includes a continuous equation and a momentum equation, which are used for simulating the surface flooding evolution process. Further, in the step (3), the fourier neural operator model modulates the feature response in the frequency domain through fast fourier transform and inverse transform, and performs local feature extraction by combining a multi-layer perceptron to enhance the feature representation capability. Further, in the step (3), the method further includes performing dimension alignment by using a resampling layer, and the resampling layer performs continuous interpolation in time and space dimensions by adopting a tri-linear interpolation function. Further, in the step (4), the shallow water equation balance error in the residual error correction module is used for restricting mass conservation of the prediction result, and the gradient smoothing loss is used for improving space continuity and gradient consistency of the water surface boundary of the water accumulation area. Further, in the step (5), the fusion loss function is in a multi-term fusion form, including a mean square error loss, a physical constraint loss and a gradient smoothing loss of an observation or high-precision simulation result, and each loss term is balanced through a