Graph neural network congestion prediction method based on Stener tree two-end connection

Abstract

The invention discloses a graph neural network congestion prediction method based on Stener tree two-end connection, relates to artificial intelligence, and provides the scheme for overcoming the defects in the prior art. The method comprises the following steps of: respectively constructing a GSgent structure and a hypergraph structure through Stepner tree topological information, establishing and obtaining an STGSG model based on a GNN model, and performing binary classification on overflow congestion at a GCell of a global wiring device by utilizing the STGSG model. The method has the advantages that a multi-terminal network composed of input and output ports sharing public signals is refined into a plurality of two-terminal networks by introducing a Stepner tree structure, the congestion probability of each wiring unit can be calculated more accurately, and therefore the accuracy of congestion classification is improved.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence, and in particular, to a graph neural network congestion prediction method based on Steiner tree two-terminal connection. Background Art

[0002] In the process of physical design, the main tasks include placement and routing. Both of these tasks are NP-complete problems and need to find the optimal solution under the constraints of design rules. In addition to wire length, optimization objectives such as routability are also crucial considerations in placement and routing problems. Especially in the field of very large scale integration (VLSI), the global router (GR) simplifies the minimum routing unit to a GCell. Each GCell corresponds to a certain routing capacity. After routing by the routing algorithm, each GCell will obtain the corresponding routing quantity, and exceeding the routing capacity will cause overflow (OF). When optimizing and iterating the routing, the global router usually relies on specific congestion information for rip-up and reroute (RRR), as Figure 1 shown, which will undoubtedly prolong the running time. Predicting the congestion area before the routing stage and incorporating corresponding optimization measures into the routing algorithm can reduce the number of routing iterations, thereby improving the overall quality of results (QoR).

[0003] In the prior art, although some machine learning-based methods have been proposed for congestion prediction, most of these methods are based on convolutional neural networks (CNNs) or traditional graph neural networks (GNNS). When dealing with complex VLSI layouts, there are problems such as insufficient utilization of topological structure information of long-distance routing networks and low prediction accuracy. For example, CNN-based methods need to expand the receptive field through multiple layers of convolution to obtain long-distance routing information, but this way is prone to information loss and overfitting. And traditional GNN methods are prone to be affected by the over-smoothing problem when dealing with large-scale VLSI layouts, resulting in a decrease in the distinguishability of node features.

[0004] In the physical design of very large scale integration (VLSI), congestion prediction in the pre-routing stage is a key link for optimizing the layout and reducing the number of iterations. The prior art is mainly divided into three categories: traditional empirical models, prediction methods based on convolutional neural networks (CNNs), and topological modeling methods based on graph neural networks (GNNS), but all have significant defects.

[0005] 1) Limitations of Traditional Empirical Models

[0006] Typical methods such as RUDY (Rectangular Uniform wire Density) estimate the routing requirements of GCell by statistically analyzing pin distributions. However, they rely on empirically designed formulas (such as the proportional relationship between wire length and BBox area), making it difficult to accurately capture the topological features of complex circuits. For example, RUDY uses the entire bounding box (BBox) of a multi-terminal network (GNet) as the unit for calculating routing probabilities, resulting in a uniform distribution of probabilities within the box and ignoring the actual routing distribution differences of different two-terminal connections (GSegments) after Steiner tree decomposition (such as a significant reduction in probability in areas far from pins). This coarse-grained prediction makes the congestion heatmap output by the model have blurred boundaries and limited classification accuracy.

[0007] 2) Efficiency of CNN models and receptive field issues

[0008] CNN-based models (such as RouteNet, RPOS) extract local geometric features through convolutional operations. However, they need to stack multiple layers to expand the receptive field, resulting in a sharp increase in computational complexity. Moreover, their ability to capture long-distance topological relationships (such as interconnections across logic clusters) is insufficient. In addition, it is difficult for CNN to directly model the topological structure of circuit netlists, leading to a relatively high misjudgment rate for large areas with low pin densities. By using GNN, routing units can be modeled as graph nodes to optimize these processes.

[0009] 3) Over-smoothing and insufficient topological modeling of GNN models

[0010] Recently proposed related GNN models (such as LHNN, CongestionNet) model specific circuit topology units as graph structures. CongestionNet only uses pins as graph nodes and does not incorporate the geometric features of the two-dimensional congestion map. LHNN combines GCell and GNet as graph nodes for message passing. However, assigning routing probabilities based on multi-terminal networks (GNet) as units leads to the following problems:

[0011] Blurred prediction boundaries: The global BBox of GNet has a wide coverage range, and low-probability regions inside it are mislabeled as high-probability, resulting in unclear classification boundaries (such as misjudgments of sparse regions by GNet-based models in Figure 2 ).

[0012] Over-smoothing phenomenon: The message passing mechanism of traditional GNNs is prone to losing local features after multiple layers of stacking and requires complex skip connection structures to mitigate.

[0013] Dataset Limitations: In existing datasets, such as the datasets based on ISPD 2011 and DAC 2012 used by LHNN, the congestion rate distribution is single, making it difficult to prove the generalization ability of the model. Therefore, a dataset with a more dispersed scale distribution and containing Steiner Tree information was established through the open-source physical design software OpenROAD. Summary of the Invention

[0014] The object of the present invention is to provide a congestion prediction method for a graph neural network based on two-terminal connection of Steiner trees to solve the problems existing in the above-mentioned prior art.

[0015] In the congestion prediction method for a graph neural network based on two-terminal connection of Steiner trees in the present invention, a GSgment structure and a hypergraph structure are respectively constructed through the Steiner tree topology information, and an STGSG model is established based on the GNN model. The STGSG model is used to perform binary classification on the overflow congestion at the GCell of the global router.

[0016] The process includes the following steps:

[0017] Use a number of open-source real-world based netlists and perform placement and routing operations using physical design backend process tools; when constructing the Steiner tree in global routing, decompose a multi-terminal netlist sharing the same signal into several GSgments, and extract the physical positions of the standard cells of the netlist, the Steiner tree structure, and the information of the GSgments as initial data; perform feature extraction on the initial data through preprocessing to obtain specific graph node input features; extract the horizontal and vertical overflows of the GCell of the global routing result; the preprocessed node features are used as the input of the STGSG model, and the output of the STGSG model is the binary classification result regarding the overflow corresponding to the GCell, which is used for supervised training and evaluation with the overflow label to predict the GCell overflow after routing before routing.

[0018] The congestion prediction method for a graph neural network based on two-terminal connection of Steiner trees in the present invention has the advantage that by introducing the Steiner tree structure, a multi-terminal network composed of input and output ports sharing a common signal is refined into several two-terminal networks, which can calculate the congestion probability of each routing unit more accurately, thereby improving the accuracy of congestion prediction. Brief Description of the Drawings

[0019] Figure 1 It is a schematic structural diagram of a global router in the prior art.

[0020] Figure 2 It is a schematic diagram comparing the effects of GNet and GSegmen.

[0021] Figure 3It is a schematic diagram of the overall process of the method described in the present invention.

[0022] Figure 4 It is a schematic diagram of the structure of the STGSG model described in the present invention; where Figure 4 (a) is the STGSG model architecture, Figure 4 (b) is the HMP module structure, Figure 4 (c) is the graph convolution process.

[0023] Figure 5 It is a visualization schematic diagram of the classification result. Detailed implementation manner

[0024] For the graph neural network congestion prediction method based on Steiner tree two-terminal connection described in the present invention, a GSegment structure and a hypergraph structure are respectively constructed through the Steiner tree topology information, and an STGSG model (Steiner Tree Grid Segment GNN) is established based on the GNN model. The STGSG model is used to perform binary classification on the overflow congestion at the GCell of the global router.

[0025] The overall construction process is as Figure 3 shown. Fourteen open-source real-world netlists are used, and the physical design backend process tool OpenROAD is used for placement and routing operations. By modifying the OpenROAD source code, when constructing the Steiner tree in global routing, the multi-terminal net GNet sharing the same signal is decomposed into several GSegments, and the physical positions of the standard cells in the netlist, the Steiner tree structure, and the GSegment information are extracted as the initial data. Feature extraction is performed on the initial data through preprocessing to obtain specific graph node input features. The horizontal and vertical overflows of the GCell in the global routing result are extracted, where 1 represents overflow and 0 represents no overflow otherwise. To prevent the problem of label imbalance, the congestion overflow data of the horizontal and vertical channels are processed into one channel through a logical "or" operation. The preprocessed node features are used as the input of the STGSG model, and the output of the STGSG model is the binary classification result regarding overflow corresponding to the GCell, which is supervised and trained with the overflow label and evaluated, realizing the prediction of the GCell overflow after routing before routing, so as to optimize the detailed routing structure and reduce the overall routing iteration times.

[0026] The graph structure in the present invention is a kind of graph structure including two node types GCell and GSegment, and three edge types A CC 、A CS 、A SCHypergraph. GCell node: Represents the basic unit of global routing, corresponding to each grid cell in the 2D layout diagram, and is used to characterize the local routing resource capacity and congestion characteristics. GSegment node: A two-terminal connection segment (Pin-to-Pin or Pin-to-Steiner node) generated based on the Steiner tree, whose bounding box BBox is the refined routing probability prediction range. Compared with the broad bounding box of the traditional GNet, it significantly improves the prediction accuracy. A CC : The adjacency relationship between GCells, which characterizes the spatial adjacency in the 2D layout. Each GCell is only connected to other GCells in the adjacent layer. A CS : The connection from a GCell to all GSegments within the bounding box of the GSegment to which it belongs, and is used to transfer local routing demand information. A SC : The connection from a GSegment to all GCells within its bounding box, and is used to back-propagate topological features to the GCell subgraph. The number of edges from GCell to GSegment is equal to the number of edges from GSegment to GCell.

[0027] The GSegment node has 5 node features. They are the width, height, area of the bounding box corresponding to the GSegment, the number of nodes within the bounding box, and a flag bit indicating whether the GSegment is a connection related to the top-level pin. The first 4 features specify the basic features of the GSegment, and the last flag bit is used to distinguish the top-level topological connections. Because it is found through experiments that the connections related to the top level often have longer connections, which increases the complexity of routing probability prediction and decreases the accuracy.

[0028] For the GCell node, a 7-dimensional feature vector is used as the input feature related to congestion at the geometric level. These include the horizontal / vertical routing capacity Capacity and the number of pins within each GCell node. The remaining four are the routing probabilities obtained through raw data preprocessing: the horizontal and vertical network densities NetDensity based on RUDY and the pin density PinDensity. After obtaining a 2D feature, it is converted into the corresponding feature of the graph node GCell.

[0029] The STGSG model consists of a feature embedding module FE and a hypergraph message passing module HMP, as shown in Figure 4 (a). The overall structure adopts a U-Net-like encoder-decoder structure with skip connections. Skip connections are introduced between the encoder and the decoder to fuse shallow local features and deep global features, and to improve the model's perception ability of long-distance routing topologies.

[0030] The feature embedding module FE first projects the GCell node and GSegment node features into a high-dimensional design space to enhance the model's ability to express local geometric features. The matrix transformation is performed using a multi-layer perceptron MLP. For GCell features, a separate graph convolution is executed.

[0031] The specific structure of the hypergraph message passing module HMP is as Figure 4 (b) shown. Besides obtaining geometric information from the 2D congestion map using A CC , message passing is also performed in the circuit topology at the GSegment level using A CS and A SC . Using a GNN to perform message passing between the GSegment subgraph and GCell can extract the features of the circuit topology. Especially for longer segments, compared with CNN, it can achieve a jump in the receptive field. The MLP layer is used for initial dimension conversion. The features from the GCell subgraph are first transmitted to the GSegment through A CS , connected and transformed with the initial GSegment features, and then transmitted back to the GCell subgraph through A SC . Finally, they are connected with the initial GCell features on the GCell subgraph and convolved. The formula is as follows:

[0032] V s,out = f s2 (f s1 (V s,in )|G cs (f c1 (V c,in ))) (1)

[0033] V c,out = G cc (f c2 (f c1 (V c，in )||G sc (V s,out ))) (2)

[0034] In the formula, f c1 / f s1 represents the multi-layer perceptron transformation operation on the GCell and GSegment subgraphs, f c2 / f s2 represents the linear transformation operation, ‖ represents the concatenation operation, Figure 4 (b) G represents the message passing and aggregation method in the graph convolution process. STGSG adopts a unified method, as Figure 4 (c) shown. Based on the GraphSAGE model, four aggregators are used for convolution to extract features from the surrounding GCell nodes.

[0035] Experimental tests and comparisons are carried out based on the dataset:

[0036] To obtain the netlist distribution containing Steiner tree information, the open-source physical design tool OpenROAD is used to run the entire process of obtaining the original data and OF tags. Real-world benchmarks come from OpenROAD and OpenCores, and the open-source PDK Nangate45 is used. When running the global router FastRoute of OpenROAD, to prevent the situation of no congestion or label imbalance, its optimization iteration is restricted, allowing overflows to occur, and the number of routing layers is set to 1 - 5. All benchmarks maintain an aspect ratio of 1. Information on the relevant benchmarks of the dataset is as follows:

[0037] TABLE I

[0038] DATASET STATISTICS

[0039]

[0040] Where #GS represents the number of GSgments, #GC represents the number of GCells, #ecs,sc represents the number of edges between GCell and GSegment, and #ecc represents the number of edges between GCell and GCell. The congestion rate CR represents the percentage of overflowing GCells among all GCells. Here, a logical OR operation is applied to the horizontal and vertical OF tags. In this dataset, to prevent errors caused by the bounding boxes of super-large two-terminal nets, connections with segment bounding boxes exceeding 0.25% of the total two-dimensional layout area are removed. Compared with the dataset used in LHNN, the dataset shows a more diverse circuit scale and congestion rate distribution, indicating that the model training difficulty of the present invention has increased, but it is more in line with the actual situation and can better illustrate the generalization ability of the model.

[0041] The experiments were carried out on a Linux server equipped with an NVIDIA RTX 3090 GPU and an AMD EPYC 7713 64-core CPU. The PyTorch and DGL graph learning frameworks are used to implement STGSG. Adam is used as the optimizer, with a learning rate and weight decay of 0.0001. Binary cross-entropy BCE is selected as the loss function for the overflow binary classification task.

[0042] To solve the problem of unbalanced overflow labels, the logical OR operation is used to combine the horizontal and vertical channel overflow labels into a single channel. In the experiment, the dataset is divided into a training set and a test set at a ratio of 10:4. Mini-batch training is adopted with a batch size of 7. In binary classification problems, according to the predictability of the prediction results and the ground truth, the prediction results are divided into four groups: true positive TP, true negative TN, false positive FP, and false negative FN. TP / TN are the correctly predicted positive / negative samples, and FN / FP are the incorrectly predicted positive / negative samples. Based on these four groups, the following five metrics are used to evaluate the performance of the model in the experiment. For this binary classification task, three evaluation metrics are used: accuracy ACC, F1-score, and false positive rate FPR.

[0043] The relevant calculation formulas are as follows:

[0044]

[0045] Model performance: The model of the present invention is evaluated under 10 random seeds, and the mean and variance of the evaluation metrics are reported. Table 2 shows the results of STGSG on the three classification metrics for all benchmarks.

[0046] TABLE II

[0047] STGSG MODEL EVALUATION RESULTS FOR ALL BENCHMARKS

[0048]

[0049] In the test set, the model reaches 94.54%, 77.42%, and 3.49% on these three metrics respectively. Circuits with congestion and larger scales usually exhibit better prediction performance. The model correctly captures the internal distribution pattern, and even the circuit wbqspiflash with a scale of thousands also obtains a higher F1-score. Due to the small size of the test set and the particularly good results of aes_cipher, the performance of the test set exceeds that of the training set.

[0050] Model Comparison: For comprehensive evaluation, the model of the present invention was compared with U-Net, GraphSAGE, and LHNN. For the U-Net model, two experiments were conducted respectively based on GNet and GSegment. In the model based on GNet, the input is 2D image data with 5 channels. Different from Vc, it uses 2 fewer channels of PinDensity data and replaces the NetDensity based on GSegment with NetDensity based on GNet in the horizontal and vertical channels. The model based on GSegment uses the same 7 GCell subgraph input features as STGSG. U-Net adopts 8 convolutional layers with a maximum hidden channel size of 512. GraphSAGE performs message passing based on the GCell subgraph using the adjacency matrix Acc, uses 4 graph convolutional layers, with a mean aggregator and a hidden dimension both of 256. For LHNN, the original node features are used and the hidden dimension is set to 64 to ensure a fair comparison in terms of GPU memory usage and running speed.

[0051] TABLE III

[0052] COMPARISON WITH U-NET, GRAPHSAGE AND LHNN MODELS

[0053]

[0054] As can be seen from Table 3, compared with other models, the model of the present invention has improvements of 5.47%, 15.65%, and 3.27% respectively in terms of the evaluation metrics ACC, F1, and FPR compared with the model predicting the routing probability based on GNet. The relative percentage optimizations are 6.13%, 25.28%, and 48.78% respectively. This shows the efficiency of the routing prediction proposed based on GSegment. In addition, it is found that the U-Net model carrying GSegment information can obtain good classification results without a hypergraph structure.

[0055] Test Set Visualization: Three benchmarks, namely aes cipher, picorv32a, and wbqspiflash, were selected from the test set and Figure 5Visualization of the LHNN and STGSG models was carried out. It can be observed that both LHNN and STGSG can make relatively accurate predictions for the overall OF congestion clusters. However, it was found that for the classification of the OF cluster at the red-circle marked A similar to the aes cipher, LHNN predicted the entire interior of the congestion cluster as congested, while STGSG did not. This is because LHNN makes routing predictions based on the large-area bounding boxes of GNet. Similarly, this shortcoming also led to the entire interior at the marked C of wbqspiflash being classified as congested, which greatly reduced the classification prediction performance. For relatively sparse regions that do not form OF clusters like the marked B of aes_cipher, LHNN could not classify them correctly, but STGSG could.

[0056] Ablation experiments: To verify the effectiveness of different components in the model of the present invention, ablation experiments were conducted on various combinations of input node features. Table 4 shows the F1 scores on the test set under different settings. The experiments revealed several key findings:

[0057] 1) The feature NetDensity of Vc based on GSegment has a quite significant positive impact on the classification performance of the model. The experiments showed that when NetDensity was removed, the F1 score dropped sharply to 50.9%.

[0058] 2) In the smaller circuit wbqspiflash, the low F1 score without NetDensity was particularly obvious, and its F1 score was zero, which indicates the importance of NetDensity for model generalization.

[0059] 3) A very high F1 score can be obtained only by using NetDensity, which indicates that GSegment has strong prediction ability in congestion prediction.

[0060] TABLE IV

[0061] ABLATION STUDIES OF STGSG

[0062]

[0063] In summary, the congestion prediction method of the graph neural network based on the two-terminal connection of the Steiner tree described in the present invention refines a multi-terminal network composed of input and output ports sharing a common signal into several two-terminal networks by introducing the Steiner tree structure, and can calculate the congestion probability of each routing unit more accurately, thereby improving the accuracy of congestion prediction.

[0064] 1. Fine-grained routing probability prediction: In the traditional global routing process, GNet is usually treated as a whole, which leads to inaccurate prediction of routing probability. In the present invention, by constructing a Steiner tree, a multi-terminal network is divided into several two-terminal networks GSegment, and the routing probability is predicted based on these two-terminal networks, so as to more accurately reflect the demand situation of routing resources. For example, Figure 2 shows the comparison between GNet and GSegment. It can be seen that the routing probability within the bounding box of GSegment is significantly higher than that in the external area. This fine-grained prediction method can better capture the routing hotspots.

[0065] 2. Utilizing the message passing mechanism of graph neural network: The present invention utilizes the message passing mechanism of the graph neural network GNN to perform information transmission and feature extraction on the topological structure of GSegment, rather than just performing convolution through convolutional kernels on the geometric structure. By designing a specific graph structure and message passing method, the topological information of the circuit can be effectively utilized to further improve the prediction performance. For example, in Figure 2 through the division of GSegment, the connection relationship between different routing units and the difference in routing probability can be seen more clearly, thus providing more accurate input information for the message passing of GNN.

[0066] 3. Improving prediction efficiency: In the prediction process of the method of the present invention, through fine-grained routing probability calculation and message passing of the graph neural network, congestion prediction can be completed in a short time, significantly improving the prediction efficiency.

[0067] For those skilled in the art, according to the technical solutions and concepts described above, various corresponding changes and deformations can be made, and all these changes and deformations should fall within the protection scope of the claims of the present invention.

Claims

1. A congestion prediction method for graph neural network based on Steiner tree two-end connection, characterized in that: The GSgment structure and the hypergraph structure are constructed respectively through the Steiner tree topology information, and the STGSG model is established based on the GNN model, and the STGSG model is used to perform binary classification on the GCell overflow congestion of the global router; The process includes the following steps: Several open source netlists based on the real world are used, and physical design back-end flow tools are used for layout and routing operations; when constructing a Steiner tree during global routing, multi-terminal nets sharing the same signal are decomposed into several GSGments, and the physical position of the standard cells in the netlist, the Steiner tree structure, and the GSGment information are extracted as initial data; the initial data is subjected to feature extraction through preprocessing to obtain specific graph node input features; the horizontal and vertical overflows of the GCell of the global routing result are extracted; the preprocessed node features are used as the input of the STGSG model, and the output of the STGSG model is the binary classification result of the overflow corresponding to the GCell, which is supervised training and evaluation with the overflow label to predict the GCell overflow after routing before routing.

2. According to claim 1, a congestion prediction method of a graph neural network based on a Steiner tree two-end connection is characterized in that: The congestion overflow data of the horizontal and vertical channels are processed into one channel through a logical "OR" operation.

3. According to claim 1, a congestion prediction method of a graph neural network based on a Steiner tree two-end connection is characterized in that: The node types of the hypergraph include GCell and GSegment; the edge types include A CC , A CS , A SC .

4. According to claim 3, a congestion prediction method of a graph neural network based on a Steiner tree two-end connection is characterized in that: The GCell represents a global wiring basic unit, corresponding to each grid unit in the two-dimensional layout diagram, and is used to characterize the local wiring resource capacity and congestion characteristics; The GSegment is a two-terminal connection segment generated based on the Steiner tree, and the bounding box is the refined wiring probability prediction range.

5. According to claim 4, a congestion prediction method of a graph neural network based on a Steiner tree two-end connection is characterized in that: The A CC It is the adjacency relationship between GCells, representing the spatial adjacency in a two-dimensional layout. Each GCell is only connected to the GCell in the adjacent layer. The A CS It is the connection between GCell and all GSegments within the bounding box of the GSegment to which it belongs, and is used to convey local wiring requirement information; The A SC It is the connection between GSegment and all GCells within its bounding box, used to return topological features to the GCell subgraph.

6. According to claim 5, a congestion prediction method of a graph neural network based on a Steiner tree two-end connection is characterized in that: The number of edges from GCell to GSgement is equal to the number of edges from GSegment to GCell.

7. According to claim 6, a congestion prediction method of a graph neural network based on a Steiner tree two-end connection is characterized in that: The GSegment has 5 node features; They are the width, height, area, number of nodes in the bounding box corresponding to the GSegment, and a flag indicating whether the GSegment is a top-level pin-related connection; the width, height, area, and number of nodes in the bounding box are the basic characteristics of the GSegment, and the flag is used to distinguish the topological connection of the top-level signal.

8. According to claim 1, a congestion prediction method of a graph neural network based on a Steiner tree two-end connection is characterized in that: The STGSG model consists of a feature embedding module and a hypergraph message passing module, and adopts a U-Net-like encoder-decoder structure with skip connections; The feature embedding module FE first projects the GCell node and GSegment node features into a high-dimensional design space to enhance the model's ability to express local geometric features. The matrix transformation is performed using a multi-layer perceptron MLP. For the GCell features, a separate graph convolution is performed. The hypergraph message passing module uses A CC Get geometry information from a 2D congestion map using A CS and A SC Perform message passing in the circuit topology at the GSegment level; Features from the GCell subgraph are first passed through A CS Transferred to GSegment, concatenated and transformed with the original GSegment features, and then transmitted through A SC Transmitted back to the GCell subgraph; finally connected with the initial GCell feature on the GCell subgraph and convolved; the formula is as follows: V s,out =f s2 (f s1 (V s，in )||G cs (f c1 (V cin ))) (1) V cout =G cc (f c2 (f c1 (V c，in )||G sc (V s，out ))) (2) In the formula, f c1 represents the multilayer perceptron transformation operation on the GCell subgraph; f c2 represents the linear transformation operation on the GCell subgraph; f c2 represents the multilayer perceptron transformation operation on the GCell subgraph; f c2 represents the linear transformation operation on the GCell subgraph; ‖ represents the concatenation operation.

Images