Irregular grid-based heterogeneous underground water permeability coefficient inversion method

Abstract

The invention discloses a heterogeneous underground water permeability coefficient inversion method based on irregular grids, and belongs to the technical field of permeability coefficient calculation, and the method comprises the following steps: S1, carrying out space segmentation on an underground water field to generate irregular grids; s2, frequency domain generation is carried out aiming at a groundwater site constructive polynomial radial basis function, a multi-head self-attention mechanism encoder-decoder architecture is adopted to search frequency weight, and a water level field is described finely; and S3, determining a neighborhood space of each irregular grid, and performing underground water permeability coefficient inversion. According to the method, information aggregation is realized on irregular grids, and the limitation that the convolutional neural network must operate on regular grids is overcome; the range of a single grid sensing field is expanded through power expansion of an adjacent matrix, and the permeability coefficient can be accurately captured by utilizing large-range local information; and more sufficient information is obtained by combining a physical formula and the code of the statistical characteristics, so that the predicted underground water permeability coefficient is more accurate.

Description

Technical Field

[0001] The invention belongs to the technical field of permeability calculation, and in particular to an inversion method for permeability of non-homogeneous groundwater based on irregular grids. Background Art

[0002] In the field of groundwater flow inversion, gridding technology is the core means to solve partial differential equation (PDE) problems. Establishing an inverse operator based on the grid to obtain the response relationship between the observed data and the model parameters is the mainstream parameter direct inversion method.

[0003] Existing groundwater parameter inversion methods based on convolutional neural networks usually rely on regular grids for feature extraction and model training. However, in many practical problems, the spatial distribution of the computational domain is irregular and non-Euclidean, including administrative divisions, parameter distribution, and water layer structure. This irregularity brings a series of challenges to groundwater environmental simulation and predictive modeling, especially in the inversion of groundwater parameters with extremely high heterogeneity, where regular grid models are difficult to meet high-precision requirements.

[0004] Based on the above defects, a method for inversion of heterogeneous groundwater permeability coefficient based on irregular grids is proposed. Summary of the invention

[0005] The purpose of the present invention is to provide a method for inverting the inhomogeneous groundwater permeability coefficient based on an irregular grid to solve the problems in the background technology.

[0006] To achieve the above object, the present invention provides a method for inverting the inhomogeneous groundwater permeability coefficient based on an irregular grid, comprising the following steps:

[0007] S1. Collect groundwater site data and water level observation point data at multiple time points, use constrained Delaunay triangulation to perform spatial segmentation on the groundwater site, generate triangular irregular grids, and obtain the position information and adjacency matrix of the irregular grids;

[0008] The water level observation point data at multiple time points are defined using the Mercator (EPSG:900913) projection coordinate system as follows:

[0009] P i =(x i ,y i ,h t ,h t+1 ,h t+2 );

[0010] Among them, x i is the longitude, y i is latitude, h t is the water level at the first time point of the water level observation point, ht+1 is the water level at the water level observation point at the second time point, h t+2 is the water level of the water level observation point at the third time point;

[0011] S2. Based on the results of S1, a polynomial radial basis function is constructed for the groundwater site to generate the frequency domain, and the frequency domain distribution of the initial water level at the first time point in different spaces is obtained. The encoder-decoder architecture of the multi-head self-attention mechanism is used to search the frequency weights, and the frequency domain weights of each frequency domain are generated. The initial water level frequency domain distribution and the frequency domain weights are weighted summed to obtain the global water level field at the first two time points.

[0012] S3. Process the adjacency matrix in S1 to determine the neighborhood space of each irregular grid. Based on the neighborhood space and the global water level field data of the first two time points in S2, use statistical characteristics to encode the information of each irregular grid to obtain the encoding features. Use the attention mechanism and feedforward neural network to decode the encoding features and output the global groundwater permeability coefficient.

[0013] Preferably, in S1, the specific process of space segmentation is:

[0014] 1) Based on the collected groundwater site data, constraint data I = (IV, IC) is defined, where the constraint data I includes the regional boundary node coordinates IV and the constraint boundary coordinates IC;

[0015] Among them, the coordinates of the region boundary nodes are expressed as:

[0016] IV={(vx1,vy1),(vx2,vy2),...}∈R 2 ;

[0017] Where R is a real number;

[0018] The constraint boundary coordinate IC is expressed as:

[0019] IC={[(cx1,cy1),(cx2,cy2),...,(cx vn ,cy vn )],...}∈R 2vn ;

[0020] Where vn is the number of nodes in a constraint edge;

[0021] 2) Process the coordinates of the region boundary nodes to generate initial triangulation without considering the constraint edges, so as to avoid meshing that destroys the constraint edges;

[0022] 3) Traversing each constraint edge in the triangulation, inserting the constraint edges that are not correctly segmented and not included in the triangulation, and then performing edge flipping operation on the triangulation that does not satisfy the Delaunay property to restore the Delaunay property;

[0023] The insertion operation includes cropping and flipping; the Delaunay property is that the circumscribed circle does not contain other points;

[0024] 4) Repeat step 3) until all constraint edges are correctly divided, and obtain a set of irregular grids of triangles (TV, TG, A), which contains position information and adjacency matrix;

[0025] Where TV = {tv i |tv i ∈R 2} represents the triangular irregular grid node coordinates tv i A collection of , storing spatial coordinates in longitude and latitude;

[0026] TG={(tv i ,tv j ,tv k )|tv i ,tv j ,tv k ∈TV} represents a triangular irregular grid, each of which stores three nodes;

[0027] Represents the adjacency matrix of a triangular mesh, where A ij =1 means tv i With tv j Two irregular grids are connected, A ij =0 means not connected, |TE| represents the number of irregular grids.

[0028] Preferably, in S2, the specific process of frequency domain generation is:

[0029] 1) According to the multi-time point water level observation data collected by S1, a polynomial radial basis function based on spatial position is established. The polynomial radial basis function is expressed as:

[0030] φ(r)=(r 2 +c 2 ) α ;

[0031] Where φ(r) is the polynomial radial basis function value of the known distance r between water level observation points, r is the distance between known water level observation points, c represents the offset constant set to avoid calculating infinity when the distance is 0, and α is the order of the polynomial, which determines the frequency domain of water level change;

[0032] 2) Based on different frequency domains, radial interpolation is performed on the global groundwater site to obtain the initial water level frequency domain distribution.

[0033] Preferably, the calculation formula of the initial water level frequency domain distribution is:

[0034]

[0035] Where h(x, y, α) represents the water level of an irregular grid with the center of the grid at (x, y) in the frequency domain α, N is the number of water level observation points, and φ(r i , α) represents the distance r between the i-th observation point and the observation point to be determined in the frequency domain α i The polynomial radial basis function value, ω i is the weight of the i-th water level observation point. Based on the symmetry of the radial basis matrix, a linear relationship is established between the distance radial basis matrix between the water level observation points and the water level of the observation point. The weight ω is solved by inverting the Cholesky decomposition. i ;

[0036] The weight ω of the i-th water level observation point i The calculation formula is:

[0037]

[0038] In the formula, φi j is the radial basis value of the distance between the i-th observation point and the j-th observation point, h i is the water level value of the i-th water level observation point.

[0039] Preferably, in S2, the specific process of searching the frequency weight is:

[0040] 1) Perform layer normalization on the water level observation point data collected by S1 at the first two time points, use the normalized distance of the water level observation point and the water level difference at the first two time points to couple the data, and loop the encoder n e times, and get the encoding result;

[0041] Among them, layer normalization is to use the Z-score normalization method to transform the data into a distribution form with a mean of 0 and a standard deviation of 1;

[0042] The encoder process is expressed as:

[0043]

[0044] In the formula, is the information flow of the encoder at the layer, Embedding(·) represents the encoding layer, BatchNorm(·) represents batch normalization, where the multiple points of a single batch input are regarded as multiple batches; CONCAT(·) represents feature concatenation, wx is the longitude of all water level observation points, wy is the latitude of all observation wells, and h t+1 is the water level of all water level observation points at the second time point, head enc，i is the i-th self-attention weight in the encoder, Softmax(·) represents the normalized exponential function, is the learnable query weight matrix in the i-th attention head in the encoder, is the learnable key weight matrix in the i-th attention head, is the learnable value weight matrix in the ith attention head, h is the number of attention heads in multi-head self-attention, LayerNorm(·) represents layer normalization, FFN 1,bias represents a fully connected layer with bias, represents the learnable attention output matrix in the l-2th encoding layer, FFN 1，ReLU,bias represents a single-layer fully connected feedforward neural network with bias and ReLU activation function, d k is the number of features of the data input, the number of features is 3;

[0045] Encoder cycle n e times, the number of layers used is l = 2n e The final encoding result is d e is the feature dimension of the encoder result;

[0046] 2) Input the encoding result, the normalized distance of the water level observation point, and the water level of the water level observation point at the first time point into the decoder, and the decoder loops n times. d Second, the decoder result is passed through the Softmax layer to output the frequency domain weights;

[0047] The decoder processing is expressed as:

[0048]

[0049] In the formula, is the information flow of the decoder at layer l, is the learnable query weight matrix in the i-th attention head in the decoder, is the learnable key weight matrix in the i-th attention head, is the learnable value weight matrix in the i-th attention head, head dec，i is the i-th self-attention weight in the decoder, head dec，enc，irepresents the weight of the result of the i-th fusion encoder and the input of the decoder, is the learnable attention output matrix in the l-3 decoder layers;

[0050] Decoder cycle n d times, the number of layers used is l = 3n d , the decoder output Output frequency domain weights through the Softmax layer;

[0051] The calculation formula of frequency domain weight is:

[0052]

[0053] Where W (l) is the frequency domain weight. The dimension of the frequency domain weight is equal to the frequency domain number. After being processed by the normalized exponential function, the sum of all dimensional values ​​is 1.

[0054] Preferably, in S2, the calculation formula for weighted summation is:

[0055]

[0056] In the formula, h(x,y) represents the water level of the irregular grid with the center position (x,y) at the current time point, n f is the number of frequency domains, h(x,y,α i ) represents the frequency domain α i The water level of the irregular grid with the center position (x, y) at the previous time point; ⊙ represents the Hadamard product, which means element-by-element multiplication. is the weight of the i-th frequency domain;

[0057] The global water level h at the first two time points t and t+1 can be obtained from the water levels of the observation points at time t, t+1, and t+2. t (x,y) and h t+1 (x,y).

[0058] Preferably, in S3, the processing process of the adjacency matrix is ​​specifically as follows: the adjacency matrix in S1 is subjected to multiple power expansions, and a mask matrix is ​​used to eliminate the adjacency values ​​obtained during the power expansion process, the neighborhood space of each irregular grid is determined, and the coding information in the neighborhood space is obtained. The power expansion is expressed as:

[0059]

[0060] A k =M[(A+E) k ];

[0061] Where M(x) is the conditional mask function of the adjacency relationship d, which means that all relationships with values ​​greater than 0 are set to 1, M(·) is the conditional mask function, E is the unit matrix, the adjacency value on the diagonal of the unit matrix is ​​1, and the adjacency values ​​in other areas are all 0, A k is the adjacency matrix under the k-order power expansion, A k ∈R |TE|×|TE| , A k Each row and column of represents a grid. The row and column values ​​1 represent that the two grids belong to the same neighborhood space, and 0 represents that the grids are independent of each other in the neighborhood space.

[0062] Preferably, in S3, the specific process of information encoding is:

[0063] 1) Physical information calculation: Darcy's law is used to calculate the flow information of adjacent irregular grids in the neighborhood space;

[0064] 2) Information coding: Extract the statistical characteristics of traffic information, perform dimension splicing and coding on the statistical characteristics and data that affect traffic transmission to obtain coding characteristics; the statistical characteristics are the maximum, mean, minimum, root mean square and median of various types of traffic information in the neighborhood space.

[0065] Preferably, the formula for calculating the physical information is:

[0066]

[0067] In the formula, e is the flow information that the activation function Softabs(·) needs to process, ep is a constant set to avoid negative infinity results, and the flow information that the activation function needs to process includes the instantaneous flow per unit time between adjacent grids i and j at time point t The traffic lost by grid i between time t+1 and time t The flow lost by grid j between time t+1 and time t

[0068] Among them, the instantaneous flow per unit time between adjacent grids i and j at time point t is The calculation formula is:

[0069]

[0070] In the formula, is the water level of grid j at time point t, is the water level of grid i at time point t, a i is the area of ​​grid i, a j is the area of ​​grid j, sy i is the water supply degree of grid i, sy jis the water supply degree of grid j, and the purpose of the activation function SoFtabs(·) is to eliminate negative numbers;

[0071] The traffic lost by grid i between time t+1 and time t The calculation formula is:

[0072]

[0073] The flow lost by grid j between time t+1 and time t The calculation formula is:

[0074]

[0075] Preferably, the coding feature is expressed as:

[0076] In the formula, is the total coded information of the i-th irregular grid in the neighborhood space expanded by k-order power, W k is the encoding matrix in the neighborhood space expanded by k order power, represents the set of statistical and physical information of the neighborhood space belonging to i under the k-order power expansion;

[0077] The collection of statistical and physical information belonging to the neighborhood space of i under the k-order power expansion The calculation formula is:

[0078]

[0079] Among them, AGGR(·) represents the aggregation of information set, including the maximum value, mean value, minimum value, root mean square and median of statistical characteristics, A k (i) is the set of irregular grids in the neighborhood space of grid i under the k-order power expansion, j is the irregular grid adjacent to grid i, X i，j is the set of physical information between two grids i and j, T t，t+1 is the interval from the first time point t to the second time point t+1, r i,j is the distance between the center points of grids i and j, ln(·) means taking the logarithm with natural logarithm as the base to accelerate convergence;

[0080] Among them, the set of physical information between the two grids i and j is X i，j The calculation formula is:

[0081]

[0082] Preferably, in S3, the specific decoding process is: by using the attention mechanism and the feedforward neural network, the encoding features and the encoding information of each irregular grid in the neighborhood space expanded by different orders are subjected to n o The aggregation is repeated times. The more times the aggregation is performed, the more complete the information is. The aggregation result is normalized into a single dimension after passing through a feedforward neural network, which is equivalent to the natural logarithm of the groundwater permeability coefficient, and the groundwater permeability coefficient is obtained.

[0083] Preferably, the polymerization process is expressed as:

[0084]

[0085] In the formula, H i is the total coded information of the ith irregular grid under all power expansion orders, N k is the set of order of k, α k Represents the learnable attention weight in the neighborhood space expanded to k order power; is the information of all neighborhood spaces of grid i, FFN 2，ReLU，bias It is a two-layer fully connected feedforward neural network with a ReLU activation function in the middle and a bias term. is the information used to learn the attention weights, W atten，Q is the weight matrix of the query feature, W atten,K is the weight matrix of key features.

[0086] Therefore, the present invention provides a method for inverting the inhomogeneous groundwater permeability coefficient based on an irregular grid, which has the following beneficial effects:

[0087] (1) By adopting constrained Delaunay triangulation for space segmentation and realizing information aggregation on the generated irregular grid, the limitation of convolutional neural networks that they must run on regular grids is overcome.

[0088] (2) The power expansion of the adjacency matrix expands the range of the perception field of a single grid. Even if the time span between observations is long, the permeability coefficient can be accurately captured by utilizing large-scale local information.

[0089] (3) By combining the physical formula with the statistical characteristics of the code, more complete information can be obtained, making the predicted groundwater permeability coefficient more accurate.

[0090] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0091] Figure 1 It is a schematic diagram of a flow chart of an embodiment of the present invention;

[0092] Figure 2 1 is an encoder-decoder architecture diagram of a multi-head self-attention mechanism according to an embodiment of the present invention, wherein (a) is an encoder architecture diagram and (b) is a decoder architecture diagram;

[0093] Figure 3 A schematic diagram of a flow chart of generating a permeability coefficient from a water level field according to an embodiment of the present invention;

[0094] Figure 4 A schematic diagram of a neighborhood space of a single irregular grid according to an embodiment of the present invention;

[0095] Figure 5 An irregular grid distribution diagram of an embodiment of the present invention;

[0096] Figure 6 : is a water level field distribution diagram of an embodiment of the present invention, wherein (a) is a schematic diagram of the water level expression in different frequency domains and the frequency domain weight represented in the global, and (b) is a water level field distribution diagram of the first time point generated by weighting;

[0097] Figure 7 This is a global groundwater permeability coefficient distribution map inverted by an embodiment of the present invention. DETAILED DESCRIPTION

[0098] The technical solution of the present invention is further described below through the accompanying drawings and embodiments.

[0099] In order to make the purpose, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments.

[0100] Example

[0101] like Figure 1 As shown, the present invention provides a method for inverting the permeability coefficient of heterogeneous groundwater based on irregular grids. A simulation test is conducted on this method to verify the effect of the irregular grid on the accuracy of the permeability coefficient. The steps are as follows:

[0102] S1. Collect the boundary data and observation point data of the groundwater site, and use the constrained Delaunay triangulation to perform spatial segmentation on the groundwater site. In this embodiment, 36 water level observation point data of automatic monitoring are input, and 3900 irregular triangular grids are generated, with an average grid area of ​​248m 2 , the area mean square error is 63m 2 The resulting irregular grid is as follows Figure 5 shown.

[0103] S2. Frequency domain generation: First, the groundwater site is divided into 32 frequency domains based on the power of 0 to 4, and the frequency domain α is evenly divided from 0 (constant component) to 4 (high frequency component). In each frequency domain, the grid data is input into the model. Here, the polynomial radial basis function is used for point distance expansion, and the offset constant c of the polynomial radial basis function is set to 1m.

[0104] After expanding the basis function, a linear equation system of "basis function-observation point weight-observation point water level" is established, and the inverse solution is obtained by Cholesky. It is brought into the grid position of other unknown water levels to solve the initial water level frequency domain distribution. The result is as follows Figure 6 shown.

[0105] Search frequency domain weights: Figure 2 As shown in the figure, the positions of 36 water level observation points and their water levels at the previous two time points are input into the encoder-decoder architecture of the multi-head self-attention mechanism. The number of cycles of the encoder and decoder are set to 6, that is, the number of encoder layers is 12, the number of decoder layers is 18, and the encoding layer dimension is 32. The hidden layer dimension in the feedforward neural network is uniformly set to 64. Under this setting, the model has a total of 65248 neuron parameters, and the final output dimension is the same as the above frequency domain number, that is, the output of 32 variables represents the global weights of 32 frequency domains. The output result is as follows Figure 6 As shown in (a), the frequency domain weights (ω) represented by nine different frequency domains are listed. The frequency domain value with the highest weight is 0.5161, and its weight is 0.4365.

[0106] The initial water level frequency domain distribution and frequency domain weight are weighted and summed to obtain the global water level field at the first two time points. The global water level field at the first time point is as follows: Figure 6 (b)

[0107] S3, the adjacency matrix A of the current 3900 grids records 15641 grid adjacency relationships. Figure 3 As shown, A is expanded multiple times and the mask matrix is ​​used to eliminate the adjacent values ​​obtained during the expansion process. After a single grid is expanded, the neighborhood space of the adjacency matrix changes as shown in Figure 4 As shown in the figure, the calculation amount will double for higher-order settings. After weighing the pros and cons, the power terms are set to 4, namely k = 1, 4, 7, and 10. The sum of the number of adjacencies between the grids obtained after the adjacency matrix is ​​expanded is 11536, 113772, 315640, and 610690 respectively.

[0108] The physical and statistical characteristics of each grid neighborhood space in each frequency domain are encoded. The information aggregation method AGGR is set to two categories, which take the mean and maximum value of the information in the neighborhood space respectively. The constant ep set to avoid negative infinity results is set to 1e-6. The final encoded information dimension of each grid in each frequency domain is 32.

[0109] Aggregate the coded information of all grids. In this embodiment, the aggregation is performed once. Considering that the computing resources do not need to be cycled multiple times, the maximum value and the mean value are used for aggregation in the information aggregation method to obtain the natural logarithm of the groundwater permeability coefficient. Finally, the permeability coefficient of each grid is output. The result is as follows: Figure 7 shown.

[0110] In practical applications, in order to make the data conform to the normal distribution and facilitate modeling and data analysis, the logarithmic transformation of the permeability coefficient is used instead of the permeability coefficient for processing. The permeability coefficient represents the permeability of water in the groundwater body. The value of the permeability coefficient determines the difficulty of water flowing through soil or rock. The larger the permeability coefficient, the faster the water flows; conversely, the slower it is.

[0111] Therefore, the present invention provides a method for inverting the inhomogeneous groundwater permeability coefficient based on an irregular grid, which overcomes the limitation that the convolutional neural network must run on a regular grid by using constrained Delaunay triangulation for space segmentation and realizing information aggregation on the generated irregular grid.

[0112] The power expansion of the adjacency matrix expands the range of the sensing field of a single grid, and even if the time span between observations is long, the permeability coefficient can be accurately captured using a large range of local information;

[0113] By combining the physical formula with the statistical characteristics of the code, more sufficient information can be obtained, making the predicted groundwater permeability coefficient more accurate.

[0114] Finally, it should be noted that the above embodiments are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solution of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solution to deviate from the spirit and scope of the technical solution of the present invention.

Claims

1. A method for inverting the permeability coefficient of heterogeneous groundwater based on irregular grids, characterized in that: The following steps are involved: S1. Collect groundwater site data and water level observation point data at multiple time points, use constrained Delaunay triangulation to perform spatial segmentation on the groundwater site, generate triangular irregular grids, and obtain the position information and adjacency matrix of the irregular grids; S2. Based on the results of S1, a polynomial radial basis function is constructed for the groundwater site to generate the frequency domain, and the frequency domain distribution of the initial water level at the first time point in different spaces is obtained. The encoder-decoder architecture of the multi-head self-attention mechanism is used to search the frequency weights, and the frequency domain weights of each frequency domain are generated. The initial water level frequency domain distribution and the frequency domain weights are weighted summed to obtain the global water level field at the first two time points. S3. Process the adjacency matrix in S1 to determine the neighborhood space of each irregular grid. Based on the neighborhood space and the global water level field data of the first two time points in S2, use statistical characteristics to encode the information of each irregular grid to obtain the encoding features. Use the attention mechanism and feedforward neural network to decode the encoding features and output the global groundwater permeability coefficient.

2. The method for inverting the inhomogeneous groundwater permeability coefficient based on an irregular grid according to claim 1, characterized in that: In S1, the specific process of space segmentation is: 1) defining constraint data based on the collected groundwater site data, wherein the constraint data includes coordinates of regional boundary nodes and coordinates of constraint boundaries; 2) Processing the coordinates of the region boundary nodes to generate an initial triangulation without considering the constraint edges; 3) Traverse each constraint edge in the triangulation, insert the constraint edges that are not correctly divided, and then perform edge flipping operation on the triangulation that does not satisfy the Delaunay property to restore the Delaunay property; 4) Repeat step 3) until all constraint edges are correctly divided, and obtain the position information and adjacency matrix of the triangular irregular grid.

3. The method for inversion of heterogeneous groundwater permeability coefficient based on irregular grid according to claim 1, characterized in that: In S2, the specific process of frequency domain generation is: 1) According to the multi-time point water level observation data collected by S1, a polynomial radial basis function based on spatial position is established. The polynomial radial basis function is expressed as: φ(r)=(r 2 +c 2 ) α ; Where φ(r) is the polynomial radial basis function value of the known distance r between water level observation points, r is the distance between known water level observation points, c is the offset constant, and α is the different frequency domains set; 2) Based on different frequency domains, radial interpolation is performed on the global groundwater site to obtain the initial water level frequency domain distribution.

4. The method for inverting the inhomogeneous groundwater permeability coefficient based on irregular grids according to claim 3 is characterized in that: The calculation formula of the initial water level frequency domain distribution is: In the formula, h(x,y,α) represents the water level of an irregular grid with the center position of the grid (x,y) in the frequency domain α, N is the number of water level observation points, and φ(r i ,α) represents the distance r between the i-th observation point and the observation point to be determined in the frequency domain α i The polynomial radial basis function value, ω i is the weight of the i-th water level observation point.

5. The method for inversion of heterogeneous groundwater permeability coefficient based on irregular grid according to claim 1, characterized in that: In S2, the specific process of searching the frequency weight is as follows: 1) Perform layer normalization on the water level observation point data collected by S1 at the first two time points, use the normalized distance of the water level observation point and the water level difference at the first two time points to couple the data, and loop the encoder n e times, and get the encoding result; 2) Input the encoding result, the normalized distance of the water level observation point, and the water level of the water level observation point at the first time point into the decoder, and the decoder loops n times. d Second, the decoder result is passed through the Softmax layer to output the frequency domain weights.

6. The method for inversion of heterogeneous groundwater permeability coefficient based on irregular grid according to claim 1, characterized in that: In S3, the processing process of the adjacency matrix is ​​specifically as follows: the adjacency matrix in S1 is expanded multiple times by power, and a mask matrix is ​​used to eliminate the adjacency values ​​obtained in the power expansion process, the neighborhood space of each irregular grid is determined, and the encoding information in the neighborhood space is obtained. The power expansion is expressed as: A k =M[(A+E) k ]; Where M(x) is the conditional mask function of the adjacency relation d, M(·) is the conditional mask function, A is the adjacency matrix, E is the identity matrix, and A k is the adjacency matrix under the k-order power expansion, A k ∈R |TE|×|TE| , R is a real number, |TE| is the number of triangular irregular grids.

7. The method for inverting the inhomogeneous groundwater permeability coefficient based on irregular grids according to claim 6, characterized in that: In S3, the specific process of information encoding is as follows: 1) Physical information calculation: Darcy's law is used to calculate the flow information of adjacent irregular grids in the neighborhood space; 2) Information coding: Extract the statistical characteristics of traffic information, perform dimension splicing and coding on the statistical characteristics and data that affect traffic transmission to obtain coding features.

8. The method for inversion of heterogeneous groundwater permeability coefficient based on irregular grid according to claim 7, characterized in that: The encoding feature is expressed as: In the formula, is the total coded information of the i-th irregular grid in the neighborhood space expanded by k-order power, W k is the encoding matrix in the neighborhood space expanded by k orders of magnitude, BatchNorm(·) represents batch normalization, represents the set of statistical and physical information of the neighborhood space belonging to i under the k-order power expansion; The collection of statistical and physical information belonging to the neighborhood space of i under the k-order power expansion The calculation formula is: Among them, CONCAT(·) represents feature concatenation, AGGR(·) represents the aggregation of information sets, and A k (i) is the set of irregular grids in the neighborhood space of grid i under the k-order power expansion, j is the irregular grid adjacent to i, X i,j is the set of physical information between two grids i and j, T t,t+1 is the interval from the first time point t to the second time point t+1, r i,j is the distance between the center points of grids i and j, and ln(·) represents the logarithm with the natural logarithm as the base.

9. The method for inverting the inhomogeneous groundwater permeability coefficient based on irregular grids according to claim 8, characterized in that: In S3, the specific decoding process is: through the attention mechanism and the feedforward neural network, the encoded features and the encoded information of each irregular grid in the neighborhood space expanded by different orders are n- o The aggregation is repeated times, and the aggregation results are normalized into a single dimension after passing through a feedforward neural network, which is equivalent to the natural logarithm of the groundwater permeability coefficient, and the groundwater permeability coefficient is obtained.

10. The method for inverting the inhomogeneous groundwater permeability coefficient based on irregular grids according to claim 9, characterized in that: The aggregation is represented by: In the formula, is the information of all neighborhood spaces of the entire grid i, FFN 2,ReLU,bias is a feedforward neural network, Softmax(·) is a normalized exponential function, is the information used to learn the attention weights, W atten,Q is the weight matrix of the query feature, W atten,K is the weight matrix of key features, d k is the number of features of the data input, H i It is the sum of the encoded information in the neighborhood space expanded by all power orders of grid i.

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