Power transmission network impedance envelope fast prediction method based on graph structure learning and electronic device thereof

Abstract

The present application relates to a kind of power transmission network impedance envelope fast prediction method based on graph structure learning and its electronic equipment, for the fast performance evaluation under complex environment, method includes: first, according to standard unit cell theory, PDN is discretized into Unit cell, and training and test data set containing different environment and process parameters are constructed by EDA tool simulation.First, pre-processing is carried out to data, relevant parameters are extracted from PDN netlist file, and they are abstracted as graph structure: node represents Unit cell, includes L, C, position and five attributes of distance from port distance;Edge indicates connection relationship and contains R attribute.Subsequently, graph data is normalized and converted into node feature vector, and graph neural network model is constructed, with the second upper envelope line of impedance-frequency curve as label, graph level regression training is carried out using training set.Finally, the model is verified using test set, to realize the fast, high-precision prediction of PDN impedance under unknown parameters.The method has good generalization and universality.

Description

[Technical Field]

[0002] This invention belongs to the field of semiconductor design and power integrity optimization technology, specifically involving a fast impedance prediction method for power delivery network (PDN) based on graph neural network (GNN), which is particularly suitable for system-technology co-optimization (STCO) and rapid power integrity assessment in complex packaging structures and multi-chip integrated scenarios. [Background Technology]

[0004] With the increasing complexity of integrated circuit systems and the development of advanced packaging technologies such as chiplets, System-Technology Co-Optimization (STCO) is becoming increasingly critical in achieving high-performance, high-reliability system designs. STCO requires comprehensive consideration of process technology, packaging architecture, and system performance in the early design stages to optimize the overall solution. The Power Delivery Network (PDN), as a key component of the chip and package, directly affects power quality, signal integrity, and system stability due to its impedance characteristics.

[0005] Traditionally, PDN impedance assessment relies on electromagnetic simulation tools (such as HFSS and SIwave), requiring extensive simulations in the frequency domain for each design point to obtain the impedance versus frequency curve. However, this method is computationally expensive and time-consuming, making it difficult to support the frequent design iterations and optimizations in STCO. Especially in multi-port, complex stack-up, and heterogeneous integration scenarios, full-wave simulation efficiency becomes a design bottleneck.

[0006] In recent years, machine learning methods have been applied to accelerate the prediction of PDN impedance and related electromagnetic properties, such as using multilayer perceptrons (MLPs) or convolutional neural networks (CNNs) for parametric modeling. However, such methods often struggle to effectively handle the graph-structured topology of PDNs, and most studies focus on directly predicting raw impedance data without considering how to extract key features that provide design guidance.

[0007] Graph Neural Networks (GNNs), as machine learning models specifically designed for processing graph-structured data, possess efficient modeling capabilities for non-Euclidean data. By abstracting PDNs into a graph structure (nodes representing circuit units and edges representing electrical connections), GNNs can effectively aggregate local and global topological information, achieving accurate modeling of complex circuit behavior. Furthermore, traditional prediction methods often neglect impedance envelope characteristics, which are more practically significant for design. The "secondary upper envelope," as a feature curve intelligently sampled and smoothed, can provide a more conservative and robust design reference while preserving key resonance peaks and trend information.

[0008] Therefore, given the shortcomings of existing PDN impedance simulation and prediction methods in terms of efficiency, structural modeling capabilities, and design friendliness, there is an urgent need to develop an efficient and high-precision impedance prediction method that can combine graph structure modeling and key feature extraction to support rapid power integrity assessment and system optimization in advanced packaging and Chiplet integration environments. [Summary of the Invention]

[0010] The purpose of this invention is to address the shortcomings of existing PDN impedance simulation calculations or predictions, such as low efficiency, insufficient exploitation of graph structure data characteristics, and lack of design-friendly characterization. This invention provides a fast prediction method for power transmission network impedance envelopes based on graph structure learning. It aims to achieve high-precision and high-efficiency prediction of the "secondary upper envelope" of complex power transmission network impedances, and has excellent generalization ability to support rapid design iteration and power integrity assessment in System and Process Co-optimization (STCO).

[0011] To achieve the above objectives, the technical solution adopted by this invention is a fast prediction method for the impedance envelope of a power transmission network based on graph structure learning, comprising the following steps:

[0012] A fast prediction method for the impedance envelope of power transmission networks based on graph structure learning is proposed to avoid time-consuming electromagnetic simulations and achieve rapid evaluation in complex environments. Its key features include the following steps:

[0013] S1. Data Preparation and Feature Extraction: Based on the standard unit theory, the power transmission network (PDN) of the intermediate layer and the core layer is discretized into multiple basic units; within the range of different environmental and process parameters, the original impedance frequency response data of multiple detection ports under different conditions are obtained using simulation tools; for each piece of the original data, a secondary upper envelope that can retain the main resonance peak and smooth the secondary fluctuations is extracted to form the initial dataset.

[0014] S2. Graph Structure Modeling and Attribute Definition: Using standard cell theory, the power transmission network in step S1 is discretized and modeled as a combination of connections of different United cells, and abstracted into a graph data structure. Each basic cell is a node in the graph, and five attributes are defined for each node, including inductance L, capacitance C, position coordinates, and distance from the current detection port. The electrical connection relationship between United cells is used as an edge, and a resistance R attribute is defined for each edge.

[0015] S3. Feature Engineering and Label Generation: The graph data structure defined in step S2 is normalized to generate node feature vectors. At the same time, each of the quadratic upper envelope lines extracted in step S1 is fitted into a transfer function coefficient vector of a linear time-invariant system using a vector fitting method, which serves as the global label data for the corresponding graph structure. The processed graph data and label data together constitute the final training dataset and test dataset.

[0016] S4. Training the graph neural network model: Construct a graph neural network regression model consisting of multiple graph convolutional layers, a detection port node feature extraction and aggregation layer, and a fully connected layer; input the training dataset obtained in step S3 into the model, and perform layer-level regression training with the transfer function coefficient vector as the learning target until the model converges;

[0017] S5. Impedance Prediction: The performance of the model trained in step S4 is verified using the test dataset obtained in step S3. After verification, the power transmission network to be predicted under unknown environment and process parameter combinations can be processed by the methods described in steps S2 and S3 and then input into the model to directly output the prediction result of its secondary upper envelope impedance.

[0018] Furthermore, step S1 involves extracting the secondary upper envelope, specifically including: based on the primary upper envelope, combining the position and amplitude information of the resonant peak in the original impedance frequency response curve, by setting the peak detection threshold and minimum spacing parameter, and selectively sampling from the original curve and the primary upper envelope to generate a conservative design boundary line that maintains high accuracy at key frequency points and is always located above the original curve.

[0019] Furthermore, the vector fitting method used in step S3 specifically involves: in order to uniformly process power transmission networks with different structures, the number of poles in the denominator of the transfer function is pre-set to a fixed value N, and then the coefficient vector containing the coefficients of the numerator and denominator is obtained by the vector fitting algorithm, which serves as the global label data.

[0020] Furthermore, the graph convolutional layer in step S4 operates based on a message passing mechanism and uses the edge attribute resistance R defined in S2 as weights to aggregate the feature information of a node and its neighboring nodes, thereby embedding the physical connection characteristics and loss information of the circuit during the feature update process.

[0021] Furthermore, the operation of the graph convolutional layer is defined by the following formula:

[0022]

[0023] In the formula, This represents the feature vector of node i in the l-th layer. For edge attributes, Let be the set of neighbors of node i, and AGGREGATE be the feature aggregation function. Weights are set based on edge impedance for weighted aggregation. and For trainable parameters, It is a non-linear activation function.

[0024] Furthermore, in step S4, the layer-level regression training uses the mean absolute percentage error as the loss function, and minimizes this loss function using the gradient descent algorithm to update the weight coefficients of the graph neural network model.

[0025] Furthermore, the formula for calculating the mean absolute percentage error is as follows:

[0026]

[0027] In the formula, The Euclidean norm of a vector is denoted as . .

[0028] Furthermore, the calculation formula for the gradient descent algorithm is as follows:

[0029]

[0030] In the formula, This indicates that the value to the right of the symbol updates the value to the left. Indicates the learning rate. The loss function is the mean absolute percentage error (MAPE).

[0031] Furthermore, the position coordinates of the node in step S2 include the horizontal and vertical coordinates of the basic unit on the two-dimensional plane, and the distance from the current detection port is the Euclidean distance from the center point of the basic unit to the detection port.

[0032] Furthermore, the power delivery network is a heterogeneous power delivery network composed of an interposer layer and multiple core layers under a 2.5D or 3D integrated packaging structure.

[0033] Second, the present invention also provides an electronic device, including a memory and a processor, wherein the memory stores a computer program, and the processor, when executing the computer program, controls the electronic device to perform the method described above.

[0034] Compared with existing technologies, the beneficial effects of this invention are as follows: it includes impedance simulation data acquisition and secondary upper envelope extraction; it performs United cell discretization and graph structure modeling of the PDN structure; it divides the training set and test set; it trains the model on the training set using a regression model based on a graph neural network; it then validates the trained model on the test set; finally, it can use the trained model to quickly predict the impedance secondary upper envelope under unknown topology and port conditions; it has cross-structure generalization ability and versatility, and can predict the impedance envelope trend of complex PDNs with high accuracy (correlation coefficient with the original data reaches 0.97). At the same time, it achieves a performance acceleration of more than 100 times compared with traditional full-wave electromagnetic simulation methods, which is of great value for System-Technology Co-Optimization (STCO) and rapid assessment of high-speed and high-reliability power integrity in advanced packaging and chiplet integration. [Attached Image Description]

[0036] Figure 1 This is a flowchart of a fast impedance prediction method based on graph neural networks.

[0037] Figure 2 It is a schematic diagram that uses the standard cell modeling method to transform the power transmission network into a graph data structure.

[0038] Figure 3 This is an example structure diagram of a graph neural network learning model based on an embodiment.

[0039] [Specific Implementation Methods]

[0040] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the following will be combined with the present invention.

[0041] The accompanying drawings in the embodiments clearly and completely describe the technical solutions in the embodiments of the present invention. Based on

[0042] The embodiments in this invention were obtained by those skilled in the art without inventive effort.

[0043] All other embodiments thereof are within the scope of protection of this invention.

[0044] A fast prediction method for the impedance envelope of a power transmission network based on graph structure learning includes the following steps:

[0045] S1. Based on the target PDN structure, construct training and test datasets using EDA simulation tools, extract impedance curves detected at specified ports at different frequencies, and generate corresponding "secondary upper envelopes". Use amplitude vector fitting to generate the coefficients of the corresponding rational functions as label data. The extraction method of the "secondary upper envelope" includes: based on the primary upper envelope, combining the position and amplitude information of the resonant peak, selectively sampling from both the original impedance data and the primary upper envelope to ensure that the envelope maintains high accuracy and trend consistency at key frequency points.

[0046] S2. Discretize the PDN and divide the intermediate layer power transmission network and chiplet layer power transmission network into multiple Unitedcells. Each Unitedcell is a node in the graph structure and has five attributes: inductance L, capacitance C, position coordinates (including horizontal and vertical coordinates on the plane), and distance from the detection port. The edges between nodes represent electrical connection relationships, and the edge attributes include resistance R.

[0047] S3. Normalize the graph data structure by normalizing the different attributes of nodes and edges and converting them into feature vectors.

[0048] S4. Construct a regression model based on a graph neural network and train the model using the training dataset;

[0049] The model training process includes:

[0050] Treating the power delivery networks of the interposer and chiplet layers as linear time-invariant systems, the transfer function (i.e., the impedance of the entire system as seen from the output port) of a linear time-invariant system can be expressed in the following mathematical form:

[0051]

[0052] The above equation is an impedance expression in the complex domain. Let... The amplitude-frequency variation curve can then be obtained. The specific shape of the amplitude-frequency curve is determined by a coefficient. Strict control is required. The zeros in the denominator of the transfer function are the system's poles. The distribution of these poles in the complex plane significantly influences the shape of the amplitude-frequency response curve and the location of the resonance peaks. Using vector fitting to analyze the "secondary upper envelope," and considering different numbers of resonance peaks, the number of poles selected is 20. And fit the polynomial of each simulation curve to form a label vector. The dimension of the output layer of a neural network is... ;

[0053] The predicted performance values ​​of the standard unit are obtained by forward propagating the training dataset data x along the graph neural network-based machine learning model. , where g is the forward pass function of a machine learning model based on a graph neural network;

[0054] Then, the mean absolute percentage error (MAPE) is used to calculate the predicted performance values ​​of the standard unit. Compared with the true performance value of the standard unit The relative error between them, the mean absolute percentage error (MAPE), is calculated using the following formula:

[0055]

[0056] In the formula, The Euclidean norm of a vector is denoted as . .

[0057] Finally, the weight coefficients of the graph neural network-based machine learning model are updated using the gradient descent algorithm in reverse feedback until the error converges. The formula for calculating the gradient descent algorithm is as follows:

[0058]

[0059] In the formula, This indicates that the value to the right of the symbol updates the value to the left. Indicates the learning rate. The loss function is the mean absolute percentage error (MAPE).

[0060] S5. Test the trained graph neural network-based machine learning model on the test dataset. Use the graph neural network-based machine learning model to quickly characterize the accuracy of impedance prediction under unknown environments and chiplet combinations.

[0061] The graph neural network model employs an architecture combining multi-layer graph convolutional layers and fully connected layers, effectively aggregating node and edge information to achieve layer-level regression prediction. Specifically, the graph convolutional layers iteratively update the features of nodes and their neighborhoods through a message-passing mechanism. Each graph convolutional operation can be represented as:

[0062]

[0063] in, This represents the feature vector of node i in the l-th layer. For edge attributes, Let be the set of neighbors of node i, and AGGREGATE be the feature aggregation function. Weights are set based on edge impedance for weighted aggregation. and For trainable parameters, It is a non-linear activation function.

[0064] By employing multi-layer graph convolution, the model progressively captures topological dependencies from local to global levels. Subsequently, global pooling aggregates the features of all nodes in the graph into a global representation vector, which is then input into a fully connected layer for regression prediction, outputting the impedance envelope values ​​corresponding to each frequency point. This structure not only fully leverages the graph structure characteristics of PDN but also possesses end-to-end prediction capabilities, making it suitable for network topologies of varying sizes and complexities.

[0065] The United cell, as the basic unit for discretized modeling of PDN, encompasses local electrical characteristics and spatial information, specifically including inductance (L), capacitance (C), cell center coordinates (x, y), and Euclidean distance (d) from the impedance detection port. Each United cell represents a local functional block in the PDN, with its electrical parameters L and C characterizing the frequency response of that region, while the spatial coordinates and distance information are used to construct the positional relationship between the detection port and the cell, providing the model with physical spatial awareness. When constructing the graph structure, if there is an electrical connection between two United cells, a corresponding edge is established, with the edge attribute including connection resistance (R) to describe path loss. By discretizing the continuous PDN structure into a United cell network, the electrical behavior characteristics of the original network are preserved, and it is transformed into a non-Euclidean data structure suitable for graph neural network processing, laying the foundation for efficient learning of impedance characteristics.

[0066] Impedance envelope predictions can be directly used to guide power integrity design, and their conservative nature helps improve system robustness. Specifically, the "secondary upper envelope" preserves the overall trend of the original impedance curve while highlighting key resonant points and smoothing unnecessary fluctuations, forming an envelope trajectory that always lies above the original curve. This envelope, as a design boundary condition, ensures that the system design still has sufficient noise margin and stability margin even under simulation-uncovered process fluctuations, temperature changes, or dynamic load scenarios. For example, in decoupling capacitor optimization, power plane partitioning, and package stack-up design, using the envelope as an impedance constraint can effectively avoid voltage drops or noise exceedances caused by local resonances, thereby improving the overall power supply quality and product yield.

[0067] Example

[0068] This embodiment uses a 2.5D integrated system containing 6 chiplets as an application scenario to quickly predict the impedance secondary upper envelope of its power delivery network (PDN).

[0069] Figure 1This is a flowchart of a fast impedance prediction method based on graph neural networks. (Example) Figure 1 As shown, it includes: generating training and testing datasets; constructing a graph data structure; training the model; and testing the model; specifically, it includes the following steps:

[0070] S1. Simulation and Envelope Data Preparation. For the power transmission network consisting of the target intermediate layer and chiplet layer, the raw impedance curve data of multiple different detection ports within a specified frequency band (0.1GHz-10GHz) is first obtained using a circuit simulation tool (ngspice). Then, for each simulated impedance-frequency curve, its "secondary upper envelope" is extracted. This envelope extraction is not simply smoothing; instead, it combines the position and amplitude information of the resonant peak for intelligent sampling to ensure data simplification while preserving key trends.

[0071] S2. Amplitude Vector Fitting and Label Data Generation. To construct label data suitable for machine learning models, each extracted "quadratic upper envelope" is further considered as the frequency response result of a linear time-invariant (LTI) system. The transfer function (i.e., impedance function) of this system can be expressed in rational fractional form in the complex frequency domain s:

[0072]

[0073] Among them, coefficient and The unique pole and zero distribution of the system is determined, thus defining the amplitude-frequency curve (taking...). The shape of the envelope is described. This invention employs a vector fitting method to fit the "secondary upper envelope" to determine the coefficients of the rational fraction. In specific implementations, to uniformly handle different PDN structures, the number of poles is fixed at 20 (i.e., denominator order n=20, numerator order m=19). Through amplitude vector fitting, each envelope is transformed into a 39-dimensional coefficient vector. This vector serves as the true label for training the model. This transforms the curve prediction problem into a high-dimensional coefficient regression problem, which helps the model learn the intrinsic system characteristics of the impedance curve more accurately.

[0074] S3. Based on standard cell theory, the continuous PDN structure is discretized. The power / ground planes of the interposer and chiplet layers are divided into multiple United cells, each serving as a node in the graph structure. Each node contains five attributes: local equivalent inductance L, equivalent capacitance C, the two-dimensional coordinates (x, y) of its center position, and the Euclidean distance d from the cell to the current excitation port. If two United cells are physically adjacent and connected by a conductor, an edge is established between them, with the edge attribute being the connection resistance R. Finally, the entire PDN is transformed into a property graph G=(V,E), where V is the set of nodes and E is the set of edges.

[0075] S4. For all graph structure data constructed in step S3, normalize the node and edge attributes to eliminate dimensional differences and accelerate model convergence. Subsequently, randomly divide the entire dataset into training, validation, and test sets to ensure that various PDN topologies are evenly distributed in the sets.

[0076] S5. Construct a machine learning model based on a graph neural network and train the model using the training set data. The forward propagation direction of the machine learning model based on the graph neural network includes a regression network composed of several graph convolutional layers and fully connected layers; training the model using the training set data refers to obtaining the prediction of the power transmission network impedance by propagating the training set data x along the forward path of the machine learning model based on the graph neural network. The g function is the forward transfer function of the model; then, the mean absolute percentage error (MAPE) is used to calculate the predicted performance values ​​of the standard cells. Compared with the true value The formula for calculating the relative error and the mean absolute percentage error is:

[0077]

[0078] In the formula, The Euclidean norm of a vector is denoted as . Finally, the weight coefficients of the graph neural network-based machine learning model are updated using the gradient descent algorithm in reverse feedback until the error converges. The formula for calculating the gradient descent algorithm is as follows:

[0079]

[0080] In the formula, This indicates that the value to the right of the symbol updates the value to the left. Indicates the learning rate. The loss function is the mean absolute percentage error (MAPE).

[0081] S6. Model Validation and Application

[0082] Specifically, the fast impedance prediction method based on graph neural networks uses a circuit for predicting impedance that is a PDN impedance prediction method under 2.5D / 3D integrated chip manufacturing process, which includes a power transport network combining an intermediate layer PDN and a chiplet layer PDN.

[0083] Specifically, the power, model, and other characteristics of a chiplet are included in the node attributes of its equivalent PDN; the process and electrical parameters of the interposer are also included in the node attributes of its PDN.

[0084] Taking the ROCKET-64 architecture as an example, it contains 6 small cores, one on-chip network, one memory controller, and four composite units that integrate dual ROCKET cores and cache. The intermediate layer is discretized and modeled as an 11×11 global network, and each core sample is a 3×3 local network.

[0085] Generating training and testing datasets: Based on varying power consumption, area, placement, and global decoupling capacitor placement of the small chip, the circuit netlist file was input into ngspice simulations. The simulation frequency was set from 0.1 GHz to 20 GHz, outputting simulation data showing different impedance variations with frequency. In addition to the ROCKET-64 architecture, several other different architectures were included, ultimately generating a dataset of 220,000 possible cases. This simulation data will serve as data labels for subsequent machine learning training and testing.

[0086] Extracting the "Secondary Upper Envelope": Due to the complexity of the original simulation data and the excessive number of small and concentrated peaks, it has little significance in practical use or data fitting. Therefore, the envelope method is used to smooth the data to the greatest extent while retaining the main resonance peaks. This reduces the complexity of subsequent neural network tasks and allows for the design of a more robust impedance prediction strategy, as the envelope data is always slightly larger than the original data. The smoothing effect of the primary envelope is not good, so the envelope is extracted again to form the secondary upper envelope. In the actual extraction process, some fine modifications were made to the extraction code to retain the trend of the original data to the greatest extent and accurately fit the position of the resonance peaks. For example, sampling was performed simultaneously from the primary envelope and the original data to better match the trend of the original data; parameters such as peak detection threshold and minimum peak detection spacing were set to ensure that only the most important resonance peaks are retained.

[0087] Rational function fitting: The magnitude vector fitting method is used to fit "quadratic upper envelope data" using rational functions. By iteratively estimating the phase, the magnitude vector fitting method transforms the difficult magnitude fitting problem into a series of mature complex number fitting problems, thereby finding the optimal model. The target model for magnitude vector fitting is a transfer function with N poles, which can usually be expressed in partial fractional form (pole-residue form):

[0088]

[0089] In the formula, For the nth pole, Let d be the residue corresponding to the nth pole, d be the DC term, and e be the proportional term.

[0090] By observing the data, we can set the highest degree of the denominator of the rational function to 20 (i.e., the linear time-invariant system has 20 poles), and the degree of the numerator to the degree of the denominator minus 2, i.e., 18. Each "quadratic upper envelope data" is transformed into a vector composed of coefficients with a dimension of 20+18+1+1=40 (the two 1s are constant terms in the numerator and denominator), and stored as label data in a pkl file.

[0091] Constructing graph data structures: such as Figure 2 As shown, the power transmission network can be modeled as a directed isomorphic graph according to the following rules: nodes are divided into middle-level nodes and chiplet layer nodes, and edges are divided into four categories: intermediate layer-intermediate layer; chiplet layer-chiplet layer; intermediate layer-chiplet layer; and chiplet layer-intermediate layer. Intermediate layer nodes and chiplet layer nodes share five attributes: two electrical parameters (inductance L and capacitance C), position coordinates (horizontal and vertical coordinates), and distance from the detection port. Therefore, although they belong to different structures, they can be unified in the graph data structure, without the need for further subdivision into heterogeneous graphs. Edge attributes include direction and resistance R, both of which jointly affect the aggregation of neural network information. The graph data structure is extracted and stored in a JSON file.

[0092] Constructing Node Feature Vectors: To facilitate information aggregation and neural network computation, the five node attributes mentioned above are sequentially concatenated to form a five-dimensional feature vector. For the capacitance parameter, since its values ​​are in the range of 1e-9 to 1e-12, the natural logarithm is used for computational convenience. Then, the min-max normalization method is used to normalize all parameters. Note that different attributes are normalized separately.

[0093] Model training: After completing all data analysis and processing preparations, machine learning training is performed using a graph neural network-based model architecture. Figure 3 This is an example structure diagram of a graph neural network learning model used in this embodiment. For example... Figure 3 As shown, the machine learning model based on graph neural networks consists of 8 layers. The first layer projects the original node feature dimensions to 64 dimensions, the second layer flattens the 64 dimensions to 128 dimensions, and the third to seventh layers are all fully connected layers with a dimension of 128. The ReLU activation function is sampled between layers, the batch training set size is set to 256, the loss function is sampled as Mean Absolute Percentage Error (MAPE), and the gradient descent algorithm is used to train the network. The total number of iterations is 5000, the initial learning rate is set to 0.001, and the learning rate is halved after every 500 iterations.

[0094] Model Testing: Five models were trained on the training dataset for different combinations of parameters and processes for the interposer and chiplet layers. The models were then tested using the test dataset. The test results are shown in the table below.

[0095]

[0096] Test results show that this fast impedance prediction method based on graph neural networks can predict impedance in the 0.1GHz to 20GHz frequency range with high accuracy under new environments, processes and chiplet combinations, while achieving a performance speedup of more than 100 times compared to traditional SPICE simulation methods.

[0097] Those skilled in the art will understand that all or part of the steps of the above embodiments can be implemented by hardware or by a program instructing related hardware. The program can be stored in a computer-readable storage medium, such as a magnetic disk, optical disk, read-only memory (ROM), or random access memory (RAM).

[0098] The above description is only a preferred embodiment of the present invention. It should be noted that those skilled in the art can make several improvements and additions without departing from the principle of the present invention, and these improvements and additions should also be considered within the scope of protection of the present invention.

Claims

1. A fast prediction method for the impedance envelope of a power transmission network based on graph structure learning, used to avoid time-consuming electromagnetic simulation and achieve rapid evaluation in complex environments, characterized in that... Includes the following steps: S1. Data Preparation and Feature Extraction: Based on the standard cell theory, the power transmission network (PDN) of the intermediate layer and the core layer is discretized into multiple basic cells; within the range of different environmental and process parameters, the original impedance frequency response data of multiple detection ports under different conditions are obtained using simulation tools. For each piece of raw data, a quadratic upper envelope that can retain the main resonance peak and smooth the secondary fluctuations is extracted to form the initial dataset; S2. Graph Structure Modeling and Attribute Definition: Using standard cell theory, the power transmission network in step S1 is discretized and modeled as a combination of connections of different United cells, and abstracted into a graph data structure. Each basic cell is a node in the graph, and five attributes are defined for each node, including inductance L, capacitance C, position coordinates, and distance from the current detection port. The electrical connection relationship between United cells is used as an edge, and a resistance R attribute is defined for each edge. S3. Feature Engineering and Label Generation: The graph data structure defined in step S2 is normalized to generate node feature vectors. At the same time, each of the quadratic upper envelope lines extracted in step S1 is fitted into a transfer function coefficient vector of a linear time-invariant system using a vector fitting method, which serves as the global label data for the corresponding graph structure. The processed graph data and label data together constitute the final training dataset and test dataset. S4. Training the graph neural network model: Construct a graph neural network regression model consisting of multiple graph convolutional layers, a detection port node feature extraction and aggregation layer, and a fully connected layer; input the training dataset obtained in step S3 into the model, and perform layer-level regression training with the transfer function coefficient vector as the learning target until the model converges; S5. Impedance Prediction: The performance of the model trained in step S4 is verified using the test dataset obtained in step S3. After verification, the power transmission network to be predicted under unknown environment and process parameter combinations can be processed by the methods described in steps S2 and S3 and then input into the model to directly output the prediction result of its secondary upper envelope impedance.

2. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 1, characterized in that, The extraction of the secondary upper envelope in step S1 specifically includes: based on the primary upper envelope, combining the position and amplitude information of the resonant peak in the original impedance frequency response curve, by setting the peak detection threshold and minimum spacing parameter, selectively sampling from the original curve and the primary upper envelope to generate a conservative design boundary line that maintains high accuracy at key frequency points and is always located above the original curve.

3. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 1 or 2, characterized in that, The vector fitting method used in step S3 specifically involves: in order to uniformly process power transmission networks with different structures, the number of poles in the denominator of the transfer function is preset to a fixed value N, and then the coefficient vector containing the coefficients of the numerator and denominator is obtained by the vector fitting algorithm, which serves as the global label data.

4. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 1, characterized in that, The graph convolutional layer in step S4 operates based on a message passing mechanism and uses the edge attribute resistance R defined in S2 as weights to aggregate the feature information of a node and its neighboring nodes, thereby embedding the physical connection characteristics and loss information of the circuit during the feature update process.

5. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 4, characterized in that, The operation of the graph convolutional layer is defined by the following formula: In the formula, This represents the feature vector of node i in the l-th layer. For edge attributes, Let be the set of neighbors of node i, and AGGREGATE be the feature aggregation function. Weights are set based on edge impedance for weighted aggregation. and For trainable parameters, It is a non-linear activation function.

6. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 1, characterized in that, In step S4, layer-level regression training is performed, and the loss function used is the mean absolute percentage error. This loss function is minimized by the gradient descent algorithm to update the weight coefficients of the graph neural network model.

7. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 6, characterized in that, The formula for calculating the mean absolute percentage error is: In the formula, The Euclidean norm of a vector is denoted as . .

8. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 6, characterized in that, The calculation formula for the gradient descent algorithm is as follows: In the formula, This indicates that the value to the right of the symbol updates the value to the left. Indicates the learning rate. The loss function is the mean absolute percentage error (MAPE).

9. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 1, characterized in that, The position coordinates of the node in step S2 include the horizontal and vertical coordinates of the basic unit on the two-dimensional plane, and the distance from the current detection port is the Euclidean distance from the center point of the basic unit to the detection port.

10. The fast prediction method for the impedance envelope of a power transmission network based on graph structure learning according to claim 1, characterized in that, The power delivery network is a heterogeneous power delivery network composed of an interposer layer and multiple core layers under a 2.5D or 3D integrated packaging structure.

11. An electronic device comprising a memory and a processor, wherein the memory stores a computer program, characterized in that, When the processor executes the computer program, it controls the electronic device to perform the method as described in any one of claims 1 to 10.

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