A flow field representation method, system and medium based on high-order network

Abstract

The present invention discloses a flow field representation method, system and medium based on a high-order network. The method includes: constructing a distribution matrix based on the high-order dependency and distribution information of particles in the connected data blocks in the local flow field; performing aggregation processing on the distribution matrix to aggregate the particles in the distribution matrix from high-order states to high-order nodes to obtain an aggregation matrix; constructing a probability transfer matrix based on the transfer relationship between particles in the aggregation matrix under the global flow field; constructing a three-layer high-order network model based on the distribution matrix, the aggregation matrix and the probability transfer matrix; optimizing the three-layer high-order network model, and generating a flow field representation result based on the optimized model. The present invention can improve the display quality of flow field visualization results under the global flow field by establishing a three-layer high-order network model and optimizing the model. As a flow field representation method, system and medium based on a high-order network, the present invention can be widely used in the field of flow field visualization technology.

Description

Technical Field

[0001] The present invention relates to the field of flow field visualization, and in particular to a flow field representation method, system and medium based on a high-order network. Background Art

[0002] Flow fields are important data fields generated in scientific and engineering simulations, such as atmospheric and ocean simulations, numerical simulations of aircraft and automobiles, and combustion simulations. Flow field visualization can make these data simulations more intuitively understandable. Flow field visualization has always been a hot topic and a challenge in scientific visualization. Existing graph-based technologies typically follow a similar construction process, only addressing underestimated long-term dependencies. They fail to provide detailed behavioral information within each block and fail to incorporate connections between high-order dependencies. They only capture local high-order patterns in the flow field but cannot describe its global structure. Consequently, existing technologies are not easily extended to support tasks such as data partitioning, workload balancing, and flow field decomposition. Summary of the Invention

[0003] In order to solve the above technical problems, the purpose of the present invention is to provide a flow field representation method, system and medium based on a high-order network, which can improve the quality of flow field visualization display results under the global flow field.

[0004] The first technical solution adopted by the present invention is: a flow field representation method based on a high-order network, comprising the following steps:

[0005] Based on the high-order dependency and distribution information of particles in the connected data blocks in the local flow field, a distribution matrix is ​​constructed;

[0006] Aggregate the distribution matrix, aggregate the particles in the distribution matrix from high-order states to high-order nodes, and obtain an aggregate matrix;

[0007] Based on the transfer relationship between particles in the aggregation matrix under the global flow field, a probability transfer matrix is ​​constructed;

[0008] Based on the distribution matrix, aggregation matrix and probability transfer matrix, a three-layer high-order network model is constructed;

[0009] The three-layer high-order network model is optimized, and the flow field representation result is generated based on the optimized model.

[0010] Furthermore, the step of constructing a distribution matrix based on the high-order dependency and distribution information of particles in the connected data blocks in the local flow field specifically includes:

[0011] Based on the high-order dependency relationship between particles, a transfer relationship between connected data blocks of particles in the local flow field is obtained to obtain a first transfer relationship;

[0012] estimating the number of particles of the data connection block based on the first transfer relationship and constructing a first vector;

[0013] Obtaining distribution information of particles from the connected data block to the higher-order state based on the first transition relationship to obtain first distribution information;

[0014] estimating the number of particles in the high-order state based on the first distribution information and constructing a second vector;

[0015] Performing an inverse operation on the first vector and the second vector by matrix multiplication to obtain an inverse operation value;

[0016] Based on the inverse operation value, a distribution matrix is ​​constructed.

[0017] Furthermore, the step of constructing a probability transfer matrix based on the transfer relationship between particles in the aggregation matrix under the global flow field specifically includes:

[0018] Based on the global flow field, the transfer information of particles between high-order nodes is obtained and classified to obtain effective transfer and ineffective transfer;

[0019] If it is determined to be a valid transfer, the change in the number of particles at the two intersecting nodes at two adjacent moments is calculated to obtain the first transfer probability of the particles;

[0020] If it is determined to be an ineffective transfer, it is converted into an effective transfer through the mask matrix, the transfer probability of the particle is calculated, and the second transfer probability of the particle is obtained;

[0021] Combining the first transition probability and the second transition probability, the particle transition probability is obtained by estimating the number of particle changes of two adjacent high-order nodes at two adjacent moments through the column vector;

[0022] Based on the particle transfer probability, a probability transfer matrix is ​​constructed.

[0023] Furthermore, the three-layer high-order network includes a distribution layer, an aggregation layer, and a transfer layer.

[0024] Furthermore, the step of optimizing the three-layer high-order network model and generating a flow field representation result based on the optimized model specifically includes:

[0025] Based on the loss function, the error of particle distribution on the connected data blocks of the three-layer high-order network model is estimated to obtain the error analysis value;

[0026] The three-layer high-order network model is optimized based on the error analysis value to obtain the optimized model;

[0027] Generate flow field representation results based on the optimized model.

[0028] Furthermore, the formula of the loss function is expressed as follows:

[0029]

[0030] In the above formula, L is the error analysis value, t is the number of steps, and i is the connection data block. Indicates the number of particles in the connected data block, represents the estimated number of particles in the connected data block, and k and ∈ are constants.

[0031] Furthermore, the step of optimizing the three-layer high-order network model based on the error analysis value to obtain the optimized model specifically includes:

[0032] Based on the error analysis value, the distribution matrix is ​​initialized through an approximate allocation strategy to obtain the initial value of the distribution matrix;

[0033] Based on the error analysis value, the aggregation matrix is ​​initialized through hierarchical clustering to obtain the initial value of the aggregation matrix;

[0034] Based on the initial value of the aggregation matrix, the probability transfer matrix is ​​optimized by the gradient descent algorithm to obtain the optimized probability transfer matrix;

[0035] Based on the optimized probability transfer matrix, the aggregation matrix is ​​updated by the gradient descent algorithm to obtain an updated aggregation matrix;

[0036] Based on the optimized probability transfer matrix and the updated aggregation matrix, the optimized model is obtained.

[0037] The second technical solution adopted by the present invention is: a flow field representation system based on a high-order network, comprising:

[0038] The distribution module is used to obtain the high-order dependency and distribution information of particles in the connected data blocks in the local flow field and obtain the distribution matrix;

[0039] Aggregation module, used to aggregate particles in the distribution matrix to obtain an aggregation matrix;

[0040] The transfer module is used to calculate the transfer probability of high-order node particles and obtain the probability transfer matrix;

[0041] A building module is used to combine the distribution matrix, aggregation matrix and probability transfer matrix to obtain a three-layer high-order network model;

[0042] The optimization module is used to optimize the constructed three-layer high-order network model to obtain an optimized model.

[0043] The third technical solution adopted by the present invention is: a storage medium for flow field representation based on a high-order network, including a memory, a processor and a computer program stored in the memory and executable on the processor, wherein the processor implements the above-mentioned method when executing the program.

[0044] The beneficial effects of the method, system and medium of the present invention are: the present invention applies graph visualization flow field technology, establishes a three-layer high-order network model, and then optimizes the three-layer high-order network model. According to the different flow behaviors and flow pattern conversions of particles between connected data blocks and the subdivision behavior of the high-order network on the flow field, the fine structure of the flow field can be studied from a global scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0045] Figure 1 It is a flow chart of the steps of a flow field representation method based on a high-order network of the present invention;

[0046] Figure 2 It is a structural block diagram of a flow field representation system based on a high-order network of the present invention;

[0047] Figure 3 It is a partial local flow field diagram of the present invention;

[0048] Figure 4 It is a diagram of the transfer relationship of particles in a partial local flow field of the present invention;

[0049] Figure 5 is a transition probability graph of the particle of the present invention;

[0050] Figure 6 It is a network structure diagram of a three-layer high-order network of the present invention;

[0051] Figure 7 This is a flow field visualization result diagram obtained by applying the method of the present invention. DETAILED DESCRIPTION

[0052] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are provided for ease of description only and do not limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted based on the understanding of those skilled in the art.

[0053] The present invention utilizes graph visualization flow field technology, establishes a three-layer high-order network model, and optimizes the model to improve the quality of flow field visualization display results under the global flow field.

[0054] Reference Figure 1 The present invention provides a flow field representation method based on a high-order network, the method comprising the following steps:

[0055] S1. Construct a distribution matrix based on the high-order dependency and distribution information of particles in the connected data blocks in the local flow field;

[0056] S11, obtaining a transfer relationship between particles connecting data blocks in a local flow field based on a high-order dependency relationship between particles to obtain a first transfer relationship;

[0057] S12, estimating the number of particles in the data connection block based on the first transfer relationship, and constructing a first vector;

[0058] Specifically, refer to Figure 3 and Figure 4 Assume a local flow field whose streamlines exhibit two motion patterns for connected data block particles: the particle's trajectory starting from connected data block (2,1) and the particle's trajectory starting from connected data block (3,2). In this hypothetical local flow field, it can be concluded that the probability of the next connected data block to be visited depends not only on the connected data block the particle is currently in, but also on the series of connected data blocks that the particle has previously visited. Based on the high-order dependency between particles, we can obtain that the particles in the connection data block (2,3) come from (2,2) and (2,1), so the transition probability of the particles in the connection data block (2,3) can be written as p((2,3)|(2,2).(2,1)→(2,4))=0.2 and p((2,3)|(2,2).(2,1)→(1,3))=0.8, where (2,3)|(2,2).(2,1) records the connection data block where the particle is currently located (on the left side of the "|") and the series of connection data blocks that the particle has previously visited (on the right side of the "|"), obtaining the first transition relationship, estimating the number of particles in the data connection block at this time, and constructing the first vector.

[0059] S13. Obtain distribution information of particles from the connected data block to the higher-order state based on the first transition relationship to obtain first distribution information;

[0060] S14, estimating the number of particles in the high-order state based on the first distribution information, and constructing a second vector;

[0061] S15. Perform an inverse operation on the first vector and the second vector by matrix multiplication to obtain an inverse operation value;

[0062] S16. Construct a distribution matrix based on the inverse operation value.

[0063] Specifically, based on the obtained first transition relationship, the particles in the connected data block are distributed to the corresponding high-order states to obtain the first distribution information. Let the first vector b and the second vector s represent the number of particles in the connected data block and the high-order state respectively, where each element b i and s jdenote the number of particles in the i-th block and the j-th higher-order state, respectively. The distribution matrix D estimates the second vector s according to the matrix multiplication s = D·b. Each element D in the distribution matrix D j,i can all be regarded as the proportion of particles in the corresponding high-order state in the data connection block, and the matrix D meets two requirements. First, each column of the matrix D is a unified partition, that is, the sum of the number of particles in the high-order state is the number of particles in the corresponding connection data block. Second, each row of the matrix D is a single vector, that is, only one position has a value of 1, and the values ​​of other positions are 0, which means that the particles in the high-order state can only come from the corresponding connection data block. In summary, the distribution matrix D is constructed.

[0064] S2. Aggregate the distribution matrix, aggregate the particles in the distribution matrix from high-order states to high-order nodes, and obtain an aggregate matrix;

[0065] Specifically, the particles in the distribution matrix are aggregated from high-order states to high-order nodes to reduce the size of the three-layer high-order network model to be constructed later. Let vector n represent the number of particles on the high-order node, and the aggregation matrix A is estimated by calculating n = A s. The aggregation matrix A only contains binary values ​​(0 / 1). If the j-th high-order state is assigned to the i-th high-order node, then the element A of the aggregation matrix A is i,j = 1. Only high-order states that share the same current data connection block can be aggregated to the same high-order node. Since particles in each high-order state can only be aggregated to one high-order node, each column of the aggregation matrix A is a single vector, and the aggregation matrix is ​​output.

[0066] S3. Based on the transfer relationship between particles in the aggregation matrix under the global flow field, a probability transfer matrix is ​​constructed;

[0067] S31. Based on the global flow field, the transfer information of particles between high-order nodes is obtained and classified to obtain effective transfer and ineffective transfer;

[0068] S32: If it is determined to be a valid transfer, the change in the number of particles at the two intersecting nodes at two adjacent moments is calculated to obtain the first transfer probability of the particles;

[0069] S33, if it is determined to be an ineffective transfer, it is converted into an effective transfer through the mask matrix, and the transfer probability of the particle is calculated to obtain the second transfer probability of the particle;

[0070] S34. Combining the first transfer probability and the second transfer probability, estimating the number of particle changes of two adjacent high-order nodes at two adjacent moments by using a column vector to obtain a particle transfer probability;

[0071] S35. Based on the particle transfer probability, a probability transfer matrix is ​​constructed.

[0072] Specifically, the probability transfer matrix is ​​constructed to approximate the movement of particles between high-order nodes. Assume that a column vector n is given (t) Represents the number of particles in each high-order node at time t, and the probability transfer matrix T is based on n (t+1) =T·n (t) Estimate the number of particles in the high-order node at time t+1, where each element T of the probability transition matrix T i,j represents the transition probability from the jth high-order node to the ith high-order node. However, the transition between any two high-order states is not necessarily valid. To determine an invalid transition, two constraints need to be enforced. One is that the transition between two spatially disjoint blocks violates the physical rules, and the other is that the valid transition should satisfy the semantic meaning of the high-order state. For example, it is legal to transition from state A|BC to state *|AB. These two constraints are enforced by a mask matrix M, where each element M i,j It indicates whether the particle transfer between the i-th and j-th high-order nodes is effective, and further outputs the probability transfer matrix.

[0073] S4. Construct a three-layer high-order network model based on the distribution matrix, aggregation matrix and probability transfer matrix;

[0074] Specifically, refer to Figure 5 and Figure 6 The three-layer high-order network model includes a distribution layer, an aggregation layer, and a transfer layer. The distribution layer is represented by the distribution matrix D, the aggregation layer is represented by the aggregation matrix A, and the transfer layer is represented by the probability transfer matrix T. The high-order dependency only describes the local transformation pattern of the flow field. In order to further capture the global structure of the flow field, the transition between high-order states must be considered. A higher-order network (HON) is a directed graph whose nodes are higher-order states and edges encode the transition probabilities between nodes. Particles start from the first-order state (3,2). After moving to (2,2), these particles have a second-order state (2,2)|(3,2). An edge is added to the graph to connect the two states (3,2) and (2,2)|(3,2). The node (2,3) is divided into two nodes (2,3)|(2,2).(3,2) and (2,3)|(2,2).(2,1). The edge from node (2,2) to (2,3) is split into two different edges because the particles moving from node (2,2) to node (2,3) come from different initial nodes (3,2) and (2,1), respectively.

[0075] S5. Optimize the three-layer high-order network model and generate a flow field representation result based on the optimized model.

[0076] S51, estimating the error of particle distribution on the connected data blocks of the three-layer high-order network model based on the loss function, and obtaining an error analysis value;

[0077] Specifically, the error of the particle distribution on the data connection block is estimated using the three-layer network model through the loss function evaluation to obtain the error analysis value. Given the initial number of particles b in the step 0 block (0) , use the distribution matrix D, aggregation matrix A and probability transfer matrix T to estimate the number of particles in the data connection block to the kth step, respectively Represents, and then uses KL-Divergence (KL divergence, KDL) to track the actual number of particles b (1) ,…,b (k) Compare. Where vector b and Each component in should be divided by the total number of particles in order to convert the vector b into a distribution for KDL calculation. The loss function is as follows:

[0078]

[0079] In the above formula, L is the error analysis value, t is the number of steps, and i is the connection data block. Indicates the number of particles in the connected data block, represents the estimated number of particles in the connected data block, and k and ∈ are constants.

[0080] By vector The distribution matrix D, aggregation matrix A and probability transfer matrix T are estimated respectively. Assuming that the initial number of particles b of the given data connection block is (0) , the number of particles in high-order states and high-order nodes can be represented by s (0) =D·b (0) and n (0) =A·s (0) =A·D·b (0) Then the probability transfer matrix T is used to estimate the number of particles in the high-order node at step t (The symbol t here represents factorial, and the t in brackets above represents the number of steps), according to And in order to reduce the computational overhead of matrix inversion, use The number of particles in the high-order nodes is aggregated into the number of particles in the data connection block for comparison in the loss function, where nonzero(·) is a function that sets the non-zero elements in the matrix to 1. Therefore, the estimated number of particles in the t-th step block is:

[0081]

[0082] In the above formula, represents the estimated number of particles in the connected data block, represents the probability transfer matrix T estimating the number of particles in the high-order node at step t, b (0) Indicates the initial number of particles in the data connection block, DT represents the t-th step of the distribution matrix, A T represents the t-th step of the aggregation matrix, T t represents the t-th step of the probability transfer matrix, A represents the aggregation matrix, and D represents the distribution matrix.

[0083] From the above formula, it can be concluded that the loss function only depends on the distribution matrix D, the aggregation matrix A and the probability transfer matrix T.

[0084] S52, optimizing the three-layer high-order network model based on the error analysis value to obtain an optimized model;

[0085] S521. Based on the error analysis value, the distribution matrix is ​​initialized by an approximate allocation strategy to obtain an initial value of the distribution matrix;

[0086] Specifically, the distribution matrix D converts the particles in each data connection block into the number of particles in each high-order state. The initial value of the distribution matrix D is obtained by initializing it using an approximate distribution strategy. This strategy uses statistical data from sampled particles to determine the proportion of particles corresponding to high-order states in a data connection block. Since the distribution from data connection blocks to high-order states does not participate in subsequent state aggregation and node transfer, the distribution matrix D remains unchanged after initialization.

[0087] S522. Based on the error analysis value, the aggregation matrix is ​​initialized by hierarchical clustering to obtain an initial value of the aggregation matrix;

[0088] Specifically, the aggregation matrix A has more columns than rows, which reduces the number of high-order nodes. The hierarchical clustering method is used to group similar high-order states in each block. Hierarchical clustering starts with a cluster of a single high-order state. If the distance between two clusters is less than a predefined threshold, the two clusters are merged in the iterative process. The distance between the high-order states of two clusters is defined as the Euclidean distance between the corresponding transition probability distributions of the two clusters, and the distance between two clusters is defined as the distance between the two clusters c i and c j Additive group average between middle and high order states:

[0089]

[0090] In the above formula, w u represents the number of transitions related to the higher-order state u, w v represents the number of related transitions to the higher-order state v, p u Represents the transition probability distribution information from the high-order state u to the next data connection block, p v Represents the transition probability distribution information from the high-order state v to the next data connection block, c i and c jRepresent two clusters respectively.

[0091] Each element M in the mask matrix M i,j It records whether the transition between the i-th and j-th high-order nodes is valid. By counting the number of transitions between two high-order nodes in the sampled data, if this number is zero, the value of the element at the corresponding position in the mask matrix M is set to zero. Since the mask matrix M depends on the aggregation matrix A, once the aggregation matrix A is updated, the mask matrix M should also be updated.

[0092] S523. Based on the initial value of the aggregation matrix, optimize the probability transfer matrix by a gradient descent algorithm to obtain an optimized probability transfer matrix;

[0093] Specifically, the probability transfer matrix T encodes the edges between high-order nodes in the high-order network. Unlike the previous method that does not consider the dynamic mode of particle transition and adopts a fixed probability transfer matrix T, the probability transfer matrix T is learned in the iterative process, and the probability transfer matrix T of the sampled particles is obtained from the probability transfer matrix T of the sampled particles. (0) First, the probability transfer matrix T is updated using the gradient descent algorithm. The update process uses the following formula:

[0094]

[0095] In the above formula, T (i) represents the i-th probability transfer matrix, T (i+1) represents the probability transfer matrix after optimization of the i-th matrix, α represents the learning rate, ⊙ represents element-wise multiplication, L is the error analysis value, and M represents the mask matrix.

[0096] This formula multiplies each element in the corresponding position of the two matrices.

[0097] S524. Based on the optimized probability transfer matrix, update the aggregation matrix by using a gradient descent algorithm to obtain an updated aggregation matrix;

[0098] Specifically, high-order states should be aggregated into high-order nodes with the most similar transition behaviors. Therefore, after updating the probability transition matrix T of the high-order nodes, the aggregation from high-order states to high-order nodes, i.e., the aggregation matrix A, should be updated accordingly. Let matrix T be s Each column of represents the transition probability from a high-order state to a high-order node, and each column of the probability transfer matrix T represents the transition probability from a high-order node to a high-order node. Therefore, a scheme similar to updating the matrix T is used to update T. s , for each high-order state, by comparing T using the Euclidean distance S The corresponding columns in T can identify the most similar high-order nodes to construct the aggregation matrix A and obtain the updated aggregation matrix.

[0099] S525: Based on the optimized probability transfer matrix and the updated aggregation matrix, an optimized model is obtained.

[0100] S53. Generate a flow field representation result based on the optimized model.

[0101] Specifically, refer to Figure 7 By optimizing a three-layer high-order network model, we find the optimal aggregation between high-order states and the optimal transfer between high-order nodes. This allows us to distinguish different flow behaviors between individual data connection blocks through high-order dependencies, and to capture the global structure of the flow field by establishing a high-order network. This approach is well-suited for downstream tasks such as tracking particle density and partitioning the flow field for data management. By dividing the dataset into several data blocks, the proposed high-order network allows us to aggregate different high-order nodes into different categories, corresponding to different types of streamline segments in the flow field. The flow field visualization results reveal the transitions of particles between data connection blocks, allowing us to understand the structure of the flow field at a global scale.

[0102] Reference Figure 2 , a flow field representation system based on high-order networks, including:

[0103] The distribution module is used to obtain the high-order dependency and distribution information of particles in the connected data blocks in the local flow field and obtain the distribution matrix;

[0104] Aggregation module, used to aggregate particles in the distribution matrix to obtain an aggregation matrix;

[0105] The transfer module is used to calculate the transfer probability of high-order node particles and obtain the probability transfer matrix;

[0106] A building module is used to combine the distribution matrix, aggregation matrix and probability transfer matrix to obtain a three-layer high-order network model;

[0107] The optimization module is used to optimize the constructed three-layer high-order network model to obtain an optimized model.

[0108] The present invention also provides a computer storage medium having a computer program stored thereon. If the method of the present invention is implemented in the form of a software functional unit and sold or used as a standalone product, it can be stored in the computer storage medium. Based on this understanding, the present invention can implement all or part of the process steps in the above-mentioned method embodiments by instructing the relevant hardware through a computer program. The computer program can be stored in a computer storage medium, and when executed by a processor, the computer program can implement the steps of each of the above-mentioned method embodiments. The computer program includes computer program code, which can be in source code form, object code form, executable file, or some intermediate form. The computer storage medium can include: any entity or device capable of carrying the computer program code, recording medium, USB flash drive, mobile hard drive, magnetic disk, optical disk, computer memory, read-only memory, random access memory, electric carrier signal, telecommunication signal, and software distribution medium. It should be noted that the content contained in the computer storage medium can be appropriately increased or decreased based on the requirements of legislation and patent practice in a jurisdiction. For example, in some jurisdictions, according to legislation and patent practice, computer storage media do not include electric carrier signals and telecommunication signals.

[0109] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0110] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A flow field representation method based on a high-order network, characterized in that: The following steps are involved: Based on the high-order dependency and distribution information of particles in the connected data blocks in the local flow field, a distribution matrix is ​​constructed; Aggregate the distribution matrix, aggregate the particles in the distribution matrix from high-order states to high-order nodes, and obtain an aggregate matrix; The aggregation matrix A contains only binary values ​​(0 / 1), and the j-th high-order state is assigned to the i-th high-order node, then the element A of the aggregation matrix A is i,j =1; According to the definition that only high-order states that share the same current data connection block can be aggregated to the same high-order node and since each particle in the high-order state can only be aggregated to one high-order node, it is determined that each column of the aggregation matrix A is a single vector, and the aggregation matrix A is output; Based on the transfer relationship between particles in the aggregation matrix under the global flow field, a probability transfer matrix is ​​constructed; Based on the distribution matrix, aggregation matrix and probability transfer matrix, a three-layer high-order network model is constructed; The three-layer high-order network model is optimized, and the flow field representation result is generated based on the optimized model.

2. The flow field representation method based on a high-order network according to claim 1, characterized in that: The step of constructing a distribution matrix based on the high-order dependency and distribution information of particles in the connected data blocks in the local flow field specifically includes: Based on the high-order dependency relationship between particles, a transfer relationship between connected data blocks of particles in the local flow field is obtained to obtain a first transfer relationship; estimating the number of particles of the data connection block based on the first transfer relationship and constructing a first vector; Obtaining distribution information of particles from the connected data block to the higher-order state based on the first transition relationship to obtain first distribution information; estimating the number of particles in the high-order state based on the first distribution information and constructing a second vector; Performing an inverse operation on the first vector and the second vector by matrix multiplication to obtain an inverse operation value; Based on the inverse operation value, a distribution matrix is ​​constructed.

3. The flow field representation method based on a high-order network according to claim 2, characterized in that: The step of constructing a probability transfer matrix based on the transfer relationship between particles in the aggregation matrix under the global flow field specifically includes: Based on the global flow field, the transfer information of particles between high-order nodes is obtained and classified to obtain effective transfer and ineffective transfer; If it is determined to be a valid transfer, the change in the number of particles at the two intersecting nodes at two adjacent moments is calculated to obtain the first transfer probability of the particles; If it is determined to be an ineffective transfer, it is converted into an effective transfer through the mask matrix, the transfer probability of the particle is calculated, and the second transfer probability of the particle is obtained; Combining the first transition probability and the second transition probability, the particle transition probability is obtained by estimating the number of particle changes of two adjacent high-order nodes at two adjacent moments through the column vector; Based on the particle transfer probability, a probability transfer matrix is ​​constructed.

4. The flow field representation method based on a high-order network according to claim 3, characterized in that: The three-layer high-order network includes a distribution layer, an aggregation layer, and a transfer layer.

5. The flow field representation method based on a high-order network according to claim 4, characterized in that: The step of optimizing the three-layer high-order network model and generating a flow field representation result based on the optimized model specifically includes: Based on the loss function, the error of particle distribution on the connected data blocks of the three-layer high-order network model is estimated to obtain the error analysis value; The three-layer high-order network model is optimized based on the error analysis value to obtain the optimized model; Generate flow field representation results based on the optimized model.

6. The flow field representation method based on a high-order network according to claim 5, characterized in that: The formula of the loss function is as follows: In the above formula, L is the error analysis value, t is the number of steps, and i is the connection data block. Indicates the number of particles in the connected data block, represents the estimated number of particles in the connected data block, and k and ∈ are constants.

7. The flow field representation method based on a high-order network according to claim 6, characterized in that: The step of optimizing the three-layer high-order network model based on the error analysis value to obtain the optimized model specifically includes: Based on the error analysis value, the distribution matrix is ​​initialized through an approximate allocation strategy to obtain the initial value of the distribution matrix; Based on the error analysis value, the aggregation matrix is ​​initialized through hierarchical clustering to obtain the initial value of the aggregation matrix; Based on the initial value of the aggregation matrix, the probability transfer matrix is ​​optimized by the gradient descent algorithm to obtain the optimized probability transfer matrix; Based on the optimized probability transfer matrix, the aggregation matrix is ​​updated by the gradient descent algorithm to obtain an updated aggregation matrix; Based on the optimized probability transfer matrix and the updated aggregation matrix, the optimized model is obtained.

8. A flow field representation system based on a high-order network, characterized in that: Used to execute the flow field representation method based on a high-order network as claimed in claim 1, comprising the following modules: The distribution module is used to obtain the high-order dependency and distribution information of particles in the connected data blocks in the local flow field and obtain the distribution matrix; Aggregation module, used to aggregate particles in the distribution matrix to obtain an aggregation matrix; The transfer module is used to calculate the transfer probability of high-order node particles and obtain the probability transfer matrix; A building module is used to combine the distribution matrix, aggregation matrix and probability transfer matrix to obtain a three-layer high-order network model; The optimization module is used to optimize the constructed three-layer high-order network model to obtain an optimized model.

9. A computer-readable storage medium having a computer program stored thereon, characterized in that: When the program is executed by a processor, the steps of the method according to any one of claims 1 to 7 are implemented.

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