An interpolation method in high-dimensional space based on tree structure

Abstract

A tree-based interpolation method in high-dimensional space includes the following steps: constructing a feature tree data structure, wherein each layer of the feature tree stores a feature, and each linked list from the root node to the leaf node records a feature chain and its corresponding value; inserting the feature value to be interpolated into the feature tree; and calculating the value corresponding to the newly inserted feature chain. This tree-based interpolation method in high-dimensional space improves algorithm efficiency by deleting unnecessary interpolations and merging interpolation operations in the same dimension of the lookup table.

Description

Technical Field

[0001] The present invention relates to the technical field of integrated circuit automated design, and in particular to an interpolation method in a high-dimensional space based on a tree structure. Background Art

[0002] Library Characterization, library feature parameter extraction, referred to as K library, is the basis of digital back-end synthesis, layout and routing, verification, and signoff. It is used to extract timing, noise, power, and other information of basic modules such as standard cells, memory, IO, and IP. This information will be integrated into the Liberty file in the form of a lookup table. Then the engineer will perform interpolation operations based on the lookup table to quickly estimate the module's timing and other information. Generally, the data in the lookup table is appropriately transformed, and there can be good linearity between adjacent data points to ensure accuracy. When we are in the AIK library, we also need to interpolate the lookup table to enhance the data to improve the stability of AI prediction.

[0003] However, the time complexity of conventional interpolation methods increases exponentially with the dimensionality of the lookup table. In the AI ​​K library, even the time required to interpolate a two-dimensional lookup table exceeds the time required to train the AI ​​model, which is completely unacceptable. Summary of the Invention

[0004] In order to address the deficiencies in the prior art, the present invention aims to provide an interpolation method in high-dimensional space based on a tree structure, which can improve the efficiency of the algorithm by deleting unnecessary interpolations and merging interpolation operations of the same dimension in the lookup table.

[0005] To achieve the above object, the present invention provides a tree-structured interpolation method in a high-dimensional space, comprising the following steps:

[0006] Construct a data structure of a feature tree, wherein each layer of the feature tree stores a feature, and each linked list from the root node to the leaf node records a feature chain and its corresponding value;

[0007] Insert the feature value to be interpolated into the feature tree;

[0008] Calculate the value corresponding to the newly inserted feature chain.

[0009] Furthermore, the step of constructing the data structure of the feature tree also includes:

[0010] Read the lookup table and generate a data matrix. Each row of matrix data contains a feature chain and its corresponding value. Insert each data in the obtained data matrix to create a feature tree.

[0011] Furthermore, it also includes adding a row of data to the feature tree, including:

[0012] 21) The pointer is at the root node, and the data to be inserted is

[0013] 22) If If the length is greater than 1, go to step 23), otherwise go to step 28);

[0014] 23) If x[0] is in the child nodes of the current node, execute step 24), otherwise execute step 25);

[0015] 24) Get the child node t corresponding to x[0] and jump to step 26);

[0016] 25) Create child node t with x[0];

[0017] 26) The pointer moves to the child node t;

[0018] 27) Re-align Assignment Return to step 22);

[0019] 28) Create a leaf node with (x[0], y), completing the insertion of this feature chain.

[0020] Furthermore, the step of inserting the feature value to be interpolated into the feature tree further includes:

[0021] Sort, insert and prune the feature tree;

[0022] Define the feature list l that needs to be interpolated. Each element of l is a list of feature values ​​that need to be inserted for the corresponding feature. Insert the feature list l into the feature tree.

[0023] Furthermore, the steps of sorting, inserting and pruning the feature tree further include:

[0024] Define the number of neighbors and sort the eigenvalues ​​by size. Neighbors are the left and right adjacent elements closest to the interpolation point.

[0025] Sort the first-layer features and insert the feature values ​​to be inserted, retaining only the inserted feature value and its neighbors, and pruning the remaining child nodes;

[0026] Sort the second-layer features, keep only the interpolation points, and cut off the rest of the child nodes;

[0027] Sort the third-layer features and insert the feature values ​​to be inserted, retaining the neighbors of the inserted feature values. The third layer is the leaf node, and the interpolation points in the newly inserted key-value pairs are filled with NULL.

[0028] Furthermore, the step of calculating the value corresponding to the newly inserted feature chain also includes:

[0029] Starting from the bottom leaf node, interpolation is performed layer by layer, completing the interpolation calculation of one feature each time.

[0030] Furthermore, the step of calculating the value corresponding to the newly inserted feature chain also includes:

[0031] Save the bottom tree node into a list l;

[0032] Create an empty training matrix X train_tot and the prediction matrix X pred_tot ;

[0033] Traverse each node in list 1 and get its training matrix X train and the prediction matrix X pred , respectively appended to X train_tot and X pred_tot middle;

[0034] Utilize X train_tot and X pred_tot , customize the interpolation function, do the interpolation calculation together, and use the obtained results to update the nodes in list 1;

[0035] If the previous layer is not the root node, initialize list 1, save all nodes of the previous layer in 1, and complete the interpolation operation of each layer.

[0036] Furthermore, the training matrix X is obtained by traversing each node in the list 1. train and the prediction matrix X pred The steps also include,

[0037] 31) Pointer to a tree node t in list l;

[0038] 32) Create empty training and prediction matrices X train , X pred ;

[0039] 33) Determine whether the child nodes of node t contain NULL. If so, execute steps 34)-37). Otherwise, jump to step 38);

[0040] 34) Create a list u to store child nodes containing NULL;

[0041] 35) Take the first node in list u and assign it to variable u ele ;

[0042] 36) Get u ele Neighbors, generate training matrix X train_sub and the prediction matrix X pred_sub, respectively appended to X train and X pred middle;

[0043] 37) If u ele Is the last element of list u, execute step 38), otherwise, take the next element of list u and assign it to u ele , return to step 36);

[0044] 38) Return to X train and X pred .

[0045] To achieve the above-mentioned purpose, the present invention also provides an electronic device, comprising a memory and a processor, wherein the memory stores a program running on the processor, and when the processor runs the program, the steps of the above-mentioned tree-structure-based interpolation method in high-dimensional space are executed.

[0046] To achieve the above object, the present invention further provides a computer-readable storage medium having computer instructions stored thereon, which, when executed, execute the steps of the above-mentioned tree-structure-based interpolation method in high-dimensional space.

[0047] The interpolation method based on the tree structure in high-dimensional space of the present invention has the following beneficial effects:

[0048] 1) A tree data structure is used to store features. The depth of the tree is unlimited, and interpolation of lookup tables of any dimension can be easily implemented.

[0049] 2) The tree data structure records neighbor information, which allows for easy finding of neighbors during interpolation calculations. It also promptly deletes unnecessary eigenvalues, avoiding unnecessary interpolation calculations. This is particularly effective when only a small number of eigenvalues ​​are interpolated.

[0050] 3) All interpolation calculations for a feature are merged, which essentially solves the dimensionality curse when interpolating high-dimensional lookup tables.

[0051] Other features and advantages of the present invention will be set forth in the description which follows, and in part will be obvious from the description, or may be learned by practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] The accompanying drawings are used to provide a further understanding of the present invention and constitute a part of the specification. Together with the embodiments of the present invention, they are used to explain the present invention and do not constitute a limitation of the present invention. In the accompanying drawings:

[0053] Figure 1 Flowchart of the tree-structure-based interpolation method in high-dimensional space of the present invention;

[0054] Figure 2 Schematic diagram of the process of constructing and interpolating a feature tree in accordance with the first embodiment of the present invention;

[0055] Figure 3 Schematic diagram of the training and prediction matrices of a leaf node and a subtree in accordance with an embodiment of the present invention;

[0056] Figure 4 This is a schematic diagram of the process of inserting a feature chain into a feature tree according to the first embodiment of the present invention;

[0057] Figure 5 This is a flow chart of inserting a new feature value into a feature tree according to the first embodiment of the present invention;

[0058] Figure 6 This is a flow chart of obtaining a training and prediction matrix for a node according to the first embodiment of the present invention. DETAILED DESCRIPTION

[0059] The preferred embodiments of the present invention are described below with reference to the accompanying drawings. It should be understood that the preferred embodiments described herein are only used to illustrate and explain the present invention, and are not used to limit the present invention.

[0060] Figure 1 The following is a flow chart of the interpolation method based on the tree structure in the high-dimensional space according to the present invention. Figure 1 , the interpolation method based on tree structure in high-dimensional space of the present invention is described in detail.

[0061] In step 101, a data structure of a feature tree is constructed.

[0062] Preferably, the lookup table is read to generate a data matrix, each row of data contains a feature chain and its corresponding value, and each data in the obtained data matrix is ​​inserted to create a feature tree.

[0063] In this embodiment of the present invention, a Liberty file is a library file used to describe information such as timing, power, and noise for physical units. This file utilizes a hierarchical structure, combining basic attributes and lookup tables to record the responses of each timing path under various combinations of input signals and output loads. Later tools utilize this library file to find the data that best reflects the actual unit conditions and calculate information such as timing, power, and noise.

[0064] Lookup table: records the functional relationship between physical information such as timing and input signal and output load. The table has indexes ranging from one to four dimensions and the corresponding values ​​for each index value combination.

[0065] Feature: An index in a lookup table is called a feature.

[0066] Feature chain: Take a value from each feature in the lookup table to get a combination. This combination is called a feature chain, which corresponds to a value in the lookup table.

[0067] Feature tree: All feature chains in a lookup table form a feature tree.

[0068] In the embodiment of the present invention, it is assumed that there is a three-dimensional lookup table, which contains three features A, B, and C. The original features and value values ​​and the feature values ​​to be inserted are shown in Table 1:

[0069] Label Original eigenvalues Eigenvalues ​​to be inserted A <![CDATA[a1,a2,a3]]> x B <![CDATA[b1,b2,b3,b4]]> <![CDATA[b1,b3,b4]]> C <![CDATA[c1,c2,c3,c4]]> <![CDATA[z1,z2]]> value <![CDATA[v 11 ,v 12 ,v 13 ,v 14 ,v 21 ...]]> -

[0070] In the embodiment of the present invention, the feature tree corresponding to the original lookup table in Table 1 is as follows: Figure 2 As shown in the figure, it has the following features: 1) The root node of the tree is a pointer, denoted by t. Node t has three child nodes, corresponding to the three values ​​of feature A; 2) The three child nodes have similar structures, each with four child nodes, corresponding to the four values ​​of feature B; 3) The feature tree is constructed in this way until the last feature; 4) In Figure 2 In the last feature C, we use the key-value pair (c k , v ik )Build leaf nodes, c k is the value of feature C, v ik It is the value corresponding to the feature chain. The subscripts k and i represent the sequence numbers of the leaf node and the previous level tree node respectively.

[0071] In the embodiment of the present invention, the algorithm for constructing the feature tree can be specifically implemented as follows: a data matrix is ​​generated from the lookup table, and each row of the matrix contains a feature chain and a corresponding value. For example, in the lookup table of Table 1, the first row of data is represented as

[0072] In the embodiment of the present invention, each row of data is Figure 4 The process is added to the feature tree. The steps to add a row of data are as follows: 1) The pointer is at the root node. The data to be inserted is 2) If If the length is greater than 1, execute step 3), otherwise execute step 8); 3) If x[0] is in the child node of the current node, execute step 4); otherwise execute step 5); 4) Get the child node t corresponding to x[0] and jump to step 6); 5) Create child node t with x[0]; 6) Move the pointer to child node t; 7) Re-align Assignment Return to step 2); 8) Create a leaf node with (x[0], y), completing the insertion of this feature chain.

[0073] In step 102, the feature value to be interpolated is inserted into the feature tree.

[0074] Preferably, define a feature list l that needs to be interpolated, where each element of l is a list of feature values ​​that need to be interpolated for the corresponding feature, such as Figure 5 As shown, insert feature list l into the feature tree.

[0075] In the embodiment of the present invention, the feature tree is sorted, inserted and pruned to obtain the following Figure 3 The result shown. It can be specifically implemented as follows: 1) Define the number of neighbors: first sort the eigenvalues ​​by size, and the neighbors are the adjacent elements closest to the interpolation point on the left and right. The present invention uses 2 neighbors. For extrapolation interpolation, take the two elements on the left or right closest to the interpolation point; for interpolation, take one element on the left and one on the right; 2) Sort feature A and insert x, retain only x and its neighbors, and cut off the child node a1; 3) Sort feature B, retain only the interpolation point, and cut off the child node b2; 4) Sort feature C and insert z1, z2, retain z1’s neighbors c1, c2 and z2’s neighbors c3, c4. Because this layer is a leaf node, the interpolation point is filled with NULL (null pointer) in the newly inserted key-value pair; 5) The insertion of the new feature is completed. The feature chain that needs to be interpolated (that is, its leaf node contains NULL value) is marked as a gray short dashed line.

[0076] In an embodiment of the present invention, an algorithm for inserting new feature values ​​in a feature tree includes: when inserting new feature values, unlike the method of inserting data one by one when constructing a feature tree, all values ​​of a feature are inserted at one time; when inserting new feature values, the features are sorted and pruned to facilitate finding neighbors and avoid unnecessary interpolation operations.

[0077] In the embodiment of the present invention, the step of inserting a new feature value into the feature tree can be specifically performed as follows: 1) The pointer is at the root node. The list of features to be interpolated is Each element of is a list of corresponding features to be interpolated. As shown in Table 1 2) From the children of the current node, get the neighbors of all elements in y[0]. 3) Obtain the union u of the neighbors and y[0] and sort it. 4) Create an empty list l to store the child nodes. 5) Take the first element in u and assign it to the variable u. ele 6) If the length of u is equal to 1, execute steps 7)-10); otherwise, execute steps 11)-12). 7) If u ele If it is already in the child nodes of the current node, then take out the corresponding child node t; otherwise, use (u ele , NULL) Create a new leaf node t. Execute step 8). 8) Save t in list l. 9) If u eleIf it is not the last element of list l, assign the next element to variable u ele , execute step 7); otherwise, execute step 10). 10) If u ele Is the last value of list l, update the child nodes of the current node with list l. Complete the insertion of new feature values ​​for the current node. 11) If u ele If it is already in the child nodes of the current node, then take out the corresponding child node t; otherwise, use u ele Create a new child node t. 12) The pointer moves to the child node t and reassigns the value Execute step 2) and recursively insert the feature list into subsection t until it is completed Then execute steps 8)-10).

[0078] In step 103, the value corresponding to the newly inserted feature chain is calculated.

[0079] Preferably, starting from the bottom leaf node, interpolation is performed layer by layer, and the interpolation calculation of one layer (ie, one feature) is completed each time.

[0080] Preferably, a) a custom interpolation function is used, the input of which is a data matrix containing multiple interpolation operation units; b) the following steps are performed: Figure 5 The process shown in the figure goes to the last layer of the feature tree and generates the training and prediction matrices for this layer's data; c) interpolates the resulting data matrix using the interpolation function and updates the node values ​​at this layer; d) moves up the feature tree once and repeats step c) to interpolate the newly inserted feature values; e) repeats step d) until the entire feature tree is interpolated; f) generates a data matrix based on feature list l, with each row corresponding to a feature chain to be interpolated; g) based on the feature tree generated in step e, reads the value of each feature chain in step f). This completes the interpolation.

[0081] In the embodiment of the present invention, the algorithm for interpolating the newly inserted feature chain can be specifically implemented as follows: a) save the bottom tree node to a list l; b) create an empty training matrix X train_tot and the prediction matrix X pred_tot ; c) traverse each node in list l, press Figure 6 The process gets its training matrix v train and the prediction matrix X pred , respectively appended to X train_tot and X pred_tot Each node’s v train and X pred ,according to Figure 6 The process shown is obtained as follows: 1) Point to a tree node t in the list l; 2) Create an empty training and prediction matrix X train , X pred3) Determine whether any of the child nodes of node t contain NULL. If so, execute steps 4)-7). Otherwise, jump to step 8). 4) Create a list u to store the child nodes containing NULL. 5) Take the first node in list u and assign it to variable u. ele 6) Get u ele Neighbors, generate training matrix X train_sub and the prediction matrix X pred_sub , respectively appended to X train and X pred The matrix contains the entire feature chain, such as Figure 3 shows the matrix of a leaf node and a subtree; 7) If u ele Is the last element of list u, execute step 8); otherwise, take the next element of list u and assign it to u ele , return to step 6); 8) return to X train and X pred d) Using X train_tot and X pred_tot , customize the interpolation function, and perform the interpolation calculation together. Use the result to update the nodes in list l. e) If the previous layer is not the root node, initialize list l and save all the nodes in the previous layer in l. Perform steps a)-d) to complete the interpolation calculation for each layer.

[0082] In the embodiment of the present invention, the value corresponding to the new feature is calculated as shown in Table 1. Feature B does not have a new value to be inserted, but only a subset of it is taken.

[0083] In the embodiment of the present invention, 1) scan each leaf node at the bottom layer and process feature C. For a leaf node containing NULL, search for neighbors among its sister nodes (shared parent nodes). 2) If a neighbor is found, save the neighbor's key-value pair in X train In the , save the leaf node in X pred If no neighbor is found, no further processing is done. 3) Continue to the next leaf node containing NULL and append the data to X train and X pred middle. Figure 3 (a) shows Figure 2 The training and prediction matrices corresponding to the rightmost subtree in (b). Figure 3 X in (a) train In the figure, the two lines enclosed by the wireframe represent a unit for interpolation operation, which is used to calculate X pred Here we use (c1, v i1 ) and (c2, v i2 )Calculate (z1, w i1 ) in the value. 4) All leaf node information is stored in X trainand X pred , calculate X red w in ik value. Figure 2 (c) indicates that the interpolation calculation of the bottom feature C has been completed. The feature chain that has completed the interpolation calculation is marked with a black long dashed line. 5) Move to the previous layer to process feature B. Nodes containing NULL have no neighbors. They are not processed for now. 6) Move to the previous layer to process feature A. The node to be interpolated and its neighbors are found, and the corresponding feature chain data information is stored in X train and X pred In, such as Figure 3 As shown in (b), the interpolation calculation of feature A is completed.

[0084] The present invention provides a method for interpolating a lookup table in a Liberty library file in the automated design of integrated circuits. The method is characterized in that a feature tree data structure is constructed to store lookup table data; a feature tree-based tracing algorithm is developed to generate an interpolated data matrix. The feature tree data structure stores one feature at each layer, and a linked list is used to record the feature chain and value of a piece of data, as well as the adjacent relationships between each piece of data. The tracing algorithm includes a method for constructing a feature tree, finding neighbors of an interpolation point, pruning the feature tree, and merging interpolation operations for a feature.

[0085] The present invention provides a library characterization solution for the SOC design process in the field of integrated circuit automated design, and constructs a feature tree data structure. Each layer of the feature tree stores a feature, and each linked list from the root node to the leaf node records a feature chain and its corresponding value. This structure is compatible with feature chains of any length and can recursively interpolate lookup tables of various dimensions. In addition, this structure records the adjacent relationship of each piece of data and can provide neighbors of the interpolation point for the interpolation algorithm. Second, based on the tracing algorithm of the feature tree structure, unnecessary data is clipped and interpolation operations are merged. Specifically, it includes: building a high-dimensional feature space to record the adjacent relationship of data points; finding neighbors of the interpolation point, clipping the feature tree, and avoiding unnecessary interpolation; merging the interpolation data of a feature, operating on it, and completing the interpolation of a feature at one time, which essentially solves the dimensionality curse.

[0086] This invention enables fast and accurate interpolation of high-dimensional lookup tables. This makes interpolation possible in AI K libraries. Furthermore, this algorithm may be useful in other scenarios involving interpolation of lookup tables.

[0087] The present invention also provides an interpolation device based on a tree structure in a high-dimensional space, comprising a memory and a processor, wherein the memory stores a program running on the processor, and when the processor runs the program, the steps of the above-mentioned interpolation method based on a tree structure in a high-dimensional space are executed.

[0088] The present invention also provides a computer-readable storage medium having computer instructions stored thereon, which, when executed, execute the steps of the above-mentioned interpolation method based on a tree structure in a high-dimensional space. The interpolation method based on a tree structure in a high-dimensional space is described in the introduction of the previous section and will not be repeated here.

[0089] Those skilled in the art will understand that the foregoing descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art will be able to modify the technical solutions described in the foregoing embodiments or substitute equivalents for some of the technical features. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included within the scope of protection of the present invention.

Claims

1. A tree-based interpolation method in high-dimensional space, characterized in that: The following steps are involved: Construct a data structure of a feature tree, where each layer of the feature tree stores a feature, and each directed edge from the root node to the leaf node records a feature chain and its corresponding value through a linked list. The nodes of the linked list store the feature value and a pointer to the feature of the next level; Inserting feature values ​​to be interpolated into a feature tree and performing hierarchical difference pruning on the feature tree; the hierarchical difference pruning includes: retaining the inserted feature values ​​and their neighboring nodes in the first layer, retaining only the interpolation points in the second layer, and retaining the neighboring nodes and filling missing values ​​with null pointers in the third layer; Calculate the value corresponding to the newly inserted feature chain, including: interpolating layer by layer starting from the bottom leaf node, and generating the training matrix and prediction matrix by merging the interpolation operations of the same feature; The step of constructing the data structure of the feature tree also includes: Read the lookup table and generate a data matrix. Each row of matrix data contains a feature chain and its corresponding value. Insert each data in the data matrix into the feature tree to complete the creation of the feature tree. The lookup table records the physical information of the basic module as a function of the input signal and output load, and contains indexes of multiple dimensions and the values ​​corresponding to each index value combination; the basic module includes standard cells, memory, IO, and IP; the physical information includes timing, noise, and power consumption.

2. The interpolation method based on tree structure in high-dimensional space according to claim 1, characterized in that: Also includes adding a row of data to the feature tree, including: 21) The pointer is at the root node, and the data to be inserted is ( ), is the feature chain corresponding to the lookup table, and y is the eigenvalue corresponding to the feature chain; 22) If the number of remaining dimensions in the feature chain is greater than 1, go to step 23), otherwise go to step 28); 23) If x[0] is in the child nodes of the current node, go to step 24), otherwise go to step 25); 24) Get the child node t corresponding to x[0] and jump to step 26); 25) Create child node t with x[0]; 26) The pointer moves to the child node t; 27) Assign to the remaining feature chain , return to step 22); 28) ) creates a leaf node and completes the insertion of this feature chain.

3. The interpolation method based on tree structure in high-dimensional space according to claim 1, characterized in that: The step of inserting the feature value to be interpolated into the feature tree also includes: Sort, insert and prune the feature tree; Define the feature list l that needs to be interpolated. Each element of l is a list of feature values ​​that need to be inserted for the corresponding feature. Insert the feature list l into the feature tree.

4. The interpolation method based on tree structure in high-dimensional space according to claim 3, characterized in that: The steps of sorting, inserting and pruning the feature tree also include: Define the number of neighbors and sort the eigenvalues ​​by size. Neighbors are the left and right adjacent elements closest to the interpolation point. Sort the first-layer features and insert the feature values ​​to be inserted, retaining only the inserted feature value and its neighbors, and pruning the remaining child nodes; Sort the second-layer features, keep only the interpolation points, and cut off the rest of the child nodes; Sort the third-layer features and insert the feature values ​​to be inserted, retaining the neighbors of the inserted feature values. The third layer is the leaf node, and the interpolation points in the newly inserted key-value pairs are filled with NULL.

5. The interpolation method based on tree structure in high-dimensional space according to claim 1, characterized in that: The step of calculating the value corresponding to the newly inserted feature chain also includes: Save the bottom tree node into a list l; Create an empty training matrix and the prediction matrix ; Traverse each node in list l and get its training matrix and the prediction matrix , respectively appended to and middle; use and , customize the interpolation function, do the interpolation calculation together, and use the obtained results to update the nodes in list l; If the previous layer is not the root node, initialize the list l, save all the nodes of the previous layer in l, and complete the interpolation operation of each layer.

6. The interpolation method based on tree structure in high-dimensional space according to claim 5, characterized in that: The traversal of each node in the list l obtains its training matrix and the prediction matrix The steps also include, 31) Pointer in list A tree node in ; 32) Create empty training and prediction matrices , ; 33) Judgment Node Does the child node contain NULL? If so, execute steps 34)-37). Otherwise, jump to step 38); 34) Create a list , save the child nodes containing NULL; 35) Get list The first node in the array is assigned to the variable ; 36) Get Neighbors, generate training matrix and the prediction matrix , respectively appended to and middle; 37) If is a list The last element of the list, execute step 38), otherwise, take the list The next element of , return to step 36); 38) Return and .

7. An electronic device, characterized in that: The invention comprises a memory and a processor, wherein the memory stores a program running on the processor, and the processor executes the steps of the tree structure-based interpolation method in high-dimensional space according to any one of claims 1 to 6 when running the program.

8. A computer-readable storage medium having computer instructions stored thereon, characterized in that: When the computer instructions are executed, the steps of the tree-structure-based interpolation method in high-dimensional space according to any one of claims 1 to 6 are executed.

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