EDA false violation identification method based on ai discrimination and uncertainty quantification

Abstract

The present application relates to a kind of EDA false violation identification method based on AI discrimination and uncertainty quantification, belong to EDA technical field.The present application will convert EDA violation sample uncertainty quantification into large-scale sparse precision matrix inverse diagonal element solving problem, rearrange precision matrix by nesting subdivision ordering, construct the double-layer hierarchical decomposition framework of outer BBD and inner BBD, execute Cholesky decomposition and Schur supplement update to global lower triangular factor matrix in parallel for each inner layer submatrix, extract multi-level subfactor matrix and divide adaptive parallel unit, distribute to multi-core processor independent solving the inverse diagonal element of each submatrix, finally reconstruct global precision matrix inverse diagonal element vector as the uncertainty quantification index of violation sample, according to which false violation screening and risk classification are carried out.The present application does not need to generate complete matrix inverse explicitly, has whole-process parallel computing capability and multi-level computing result reuse mechanism, and can be adapted to large-scale industrial scene.

Description

Technical Field

[0001] This invention belongs to the field of integrated circuit electronic design automation (EDA) technology, specifically relating to an EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification. Background Technology

[0002] In the integrated circuit chip design process, physical verification is a crucial step in ensuring that the chip design meets the foundry's manufacturing requirements. Design rule checking (DRC), as the core method of physical verification, is used to detect areas in the layout design that violate manufacturing rules. However, in practical engineering applications, the violation reports output by EDA tools often contain a large number of false violations—that is, false alarms that, while formally triggering the alarm conditions of design rule checking, do not actually affect chip manufacturing yield or functional correctness. As integrated circuit process nodes continue to evolve towards 7nm and below, chip design complexity increases dramatically, and the number of violation samples generated in a single physical verification can reach tens of thousands or even hundreds of thousands, of which false violations account for a considerable proportion. How to efficiently and accurately distinguish between genuine design violations and false violations from massive violation samples has become a bottleneck problem restricting the automation level of EDA physical verification.

[0003] In recent years, artificial intelligence (AI) technology has been widely applied in the field of EDA (Electronic Design Automation) rule violation prediction and detection. However, traditional AI models only output classification or regression results, lacking the ability to quantitatively evaluate the reliability of prediction results. In industrial applications, quantifying the uncertainty of model prediction results is the core foundation for achieving human-machine collaborative decision-making, intelligent screening, and anomaly filtering. Intelligent systems with uncertainty assessment capabilities can accurately screen low-confidence samples, samples with ambiguous boundaries, and suspected anomaly samples, thereby significantly reducing the cost of manual review. Currently, the mainstream technical routes for machine learning uncertainty assessment include: model output confidence analysis, multi-model ensemble learning, Bayesian neural network approximate inference, Monte Carlo random sampling, and graph structure association propagation analysis. Among them, graph structure analysis, by fully exploring the feature similarity, spatial correlation, and rule constraint relationships between samples, constructs discrete samples into an associated topological structure. Compared with traditional unstructured sample analysis methods, it can more accurately represent the global association characteristics of samples, especially suitable for industrial data with strong correlation and strong clustering, such as EDA violation samples.

[0004] Within the graph structure modeling framework, the industry-standard modeling approach is to abstract individual EDA violation samples as nodes in a topological graph, and to abstract the feature similarity and rule correlation between samples as topological edges, thus constructing a violation association topological graph. Based on this topological graph, a weighted association weight matrix can be generated, and then the degree matrix and the standard graph Laplacian matrix can be solved. To eliminate the interference of singular values ​​in the matrix and improve numerical stability, a common practice is to introduce regularization coefficients to construct a stable precision matrix. From a probabilistic statistical modeling perspective, this precision matrix corresponds to the Gaussian precision matrix of the graph model, and its inverse matrix is ​​the covariance matrix of the sample nodes. The diagonal elements of the covariance matrix correspond to the marginal variance of a single sample node, which can directly quantify the uncertainty of the AI ​​model's judgment result for the corresponding sample. Specifically, if the marginal variance of a sample node is small, it indicates that the sample has a high degree of consistency with the features of surrounding samples and strong neighborhood support, and the AI ​​judgment result is stable and reliable; if the marginal variance is large, it indicates that the sample features are fuzzy, it is at the category boundary, and the neighborhood association is sparse, the AI ​​judgment result is unreliable, and it needs to be included in the scope of key manual review.

[0005] Although the aforementioned theoretical framework has gained widespread acceptance in academic research, existing technical solutions still have many shortcomings in practical deployments for large-scale EDA industrial scenarios. First, the computational cost of solving the inverse diagonal elements of a large-scale sparse precision matrix is ​​extremely high. For the precision matrix constructed from large-scale violation samples in EDA, its dimension increases linearly with the number of samples. Traditional solutions that directly solve the complete inverse matrix will incur O(N) computational costs. 3First, the computational complexity is at the level of 1000x1000 and consumes massive amounts of memory resources. If a unit vector iterative solution to linear equations is used, there is a large amount of repetitive matrix decomposition and iterative calculation, resulting in serious waste of computing power and making it unsuitable for industrial application scenarios with hundreds of thousands of samples. Second, the uncertainty quantification indicators lack global structure and interpretability. Most existing AI uncertainty assessment schemes rely on empirical confidence thresholds as evaluation criteria, which can only reflect the local output features of the model and cannot relate to the global topological relationships of samples. Traditional techniques cannot quantify the neighborhood support strength and global correlation stability of samples, resulting in highly subjective and poorly interpretable judgment results, which is difficult to meet the stringent requirements of EDA industrial scenarios for accurate and traceable detection results. Third, numerical stability and parallel computing efficiency are difficult to balance. Mainstream iterative solution algorithms are highly susceptible to the influence of matrix condition number, regularization parameters, and preprocessing accuracy, and their convergence is unstable in sparse and non-uniform EDA violation sample matrices, which can easily lead to computational bias. While the traditional Cholesky direct decomposition algorithm boasts excellent numerical stability, the inversion of the resulting triangular matrix suffers from strong data serial dependency, a massive number of filler elements, and an inability to fully utilize multi-core parallel computing power, resulting in extremely low computational efficiency. Fourth, the multi-task repetitive computation incurs significant overhead and low resource utilization. The EDA violation detection process includes multiple related tasks such as false violation screening, risk level ranking, review priority allocation, and boundary sample mining, all of which share the same batch of sample topology graphs and precision matrices. Traditional techniques require repeating the entire process of matrix sorting, decomposition, and solution in each round of task inference, making it impossible to reuse previous computation results. This leads to excessive redundant computation and high inference latency in the overall detection process. Summary of the Invention

[0006] The purpose of this invention is to address the aforementioned problems of existing machine learning uncertainty assessment techniques in large-scale graph structure data processing, and to provide an EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification. This invention can improve the efficiency and intelligence level of AI uncertainty assessment and EDA pseudo-violation intelligent identification in large-scale graph structures while ensuring industrial-grade numerical stability.

[0007] To achieve the above objectives, the present invention adopts the following technical solution: an EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification, comprising:

[0008] Obtain violation sample data generated by EDA detection, construct a violation association topology graph based on the violation sample data, and generate a symmetric sparse positive definite accuracy matrix. ; By permutation matrix to the precision matrix Perform row and column rearrangement to distribute non-zero elements in a clustered manner, resulting in the rearranged precision matrix. ;

[0009] For the rearranged precision matrix Perform global single-layer diagonal boundary block partitioning to divide all sample variables into K independent local variable clusters and 1 global coupled variable cluster, and construct a global single-layer BBD block matrix;

[0010] The global local diagonal blocks in the global single-layer BBD block matrix are split into inner diagonal boundary blocks. Each local cluster sample is further divided into M inner sub-local clusters and 1 inner local coupled cluster, thus constructing an inner BBD block matrix and forming a two-layer BBD hierarchical architecture that combines outer BBD and inner BBD.

[0011] Parallel Cholesky decomposition is performed on each inner submatrix in the global local diagonal block. The inner coupling blocks in the inner submatrix are iteratively updated based on the Schur complement principle. The updated inner coupling blocks are then subjected to Cholesky decomposition again to obtain the lower triangular factor matrix of the inner coupling blocks.

[0012] Based on the results of all inner-layer hierarchical decompositions, the rearranged precision matrix is ​​constructed. The block-based Cholesky decomposition architecture is used to obtain the global lower triangular factor matrix; all global correlation factor matrices are solved in parallel based on the block matrix multiplication equivalence constraint, and the precision matrix after rearrangement is then refined based on the Schur complement principle. The global coupling block in the process is updated, and Cholesky decomposition is performed on the updated global coupling block.

[0013] Based on the outer global cluster index and the inner sub-cluster index, extract mutually independent multi-level sub-factor matrices from the global lower triangular factor matrix.

[0014] Each sub-factor matrix is ​​adaptively partitioned into parallel units, and each sub-factor matrix is ​​decomposed into multiple completely decoupled parallel sub-computation units;

[0015] All parallel sub-computation units are distributed to multi-core processors, and each parallel sub-computation unit independently performs the solution of the inverse diagonal elements of the local positive definite matrix, thereby obtaining the inverse diagonal elements of the local positive definite matrix corresponding to each parallel sub-computation unit;

[0016] Based on the index mapping relationship formed by matrix rearrangement, double-layer BBD hierarchical structure and parallel unit partitioning, the inverse diagonal element of the global precision matrix is ​​reconstructed. The inverse diagonal element of the global precision matrix is ​​used as the AI ​​discrimination uncertainty quantification index for each violation sample, so as to perform false violation screening and risk classification based on the uncertainty quantification index.

[0017] Furthermore, the step of altering the precision matrix using a permutation matrix... Perform row and column rearrangement, including:

[0018] Let the permutation matrix corresponding to the rearrangement process be . The rearranged precision matrix is ​​then expressed as:

[0019]

[0020] in, This indicates the total number of violation samples. Represents a symmetric sparse positive definite precision matrix. This represents the precision matrix after rearrangement. Indicates the transpose; the precision matrix after rearrangement. It retains the symmetric positive definite property of the original matrix, and the non-zero elements exhibit clustered distribution characteristics.

[0021] Furthermore, the rearranged precision matrix Perform global single-layer diagonal boundary block partitioning to obtain the global single-layer BBD block matrix, the expression of which is:

[0022]

[0023] in, This represents the local correlation matrix of the k-th global local diagonal block in the global single-layer BBD block matrix, corresponding to the k-th independent violation sample cluster. , Indicates the number of diagonal blocks in both the global and local areas. This represents the number of samples in the k-th local cluster. This represents a globally coupled block, corresponding to the global coupling sample node association matrix outside of all local clusters. Indicates the number of globally coupled samples; This represents the outer correlation matrix between the k-th local cluster and the global coupled cluster, used to characterize the topological relationship between local samples and global coupled samples;

[0024] The global single-layer BBD block matrix satisfies the dimension conservation constraint. ,in This indicates the total number of violation samples.

[0025] Further, the step of performing inner-layer diagonal boundary block splitting on each global local diagonal block in the global single-layer BBD block matrix to obtain the inner-layer BBD block matrix includes:

[0026] For any k-th global local diagonal block Nested partitioning sort is used to complete local index rearrangement and construct a local permutation matrix. The rearranged local optimization matrix is ​​obtained. ;

[0027] The rearranged local optimization matrix Perform inner diagonal boundary block splitting to obtain the inner BBD block matrix, the expression of which is:

[0028]

[0029] in, This represents the m-th inner diagonal block within the k-th global local diagonal block, corresponding to the inner independent subsample cluster association matrix. , Indicates the number of inner diagonal pieces. This represents the number of samples in the m-th inner sub-local cluster within the k-th global local diagonal block; This represents the inner local coupling block within the k-th global-local diagonal block, corresponding to the coupling sample correlation matrix of each inner sub-local cluster. This represents the number of samples in the inner local coupling cluster within the k-th global-local diagonal block; The association matrix represents the relationship between the m-th inner sub-local cluster and the inner local coupled cluster within the k-th global local diagonal block, and is used to characterize the topological relationship between the inner sub-samples and the local coupled samples.

[0030] outer layer correlation matrix Applying the corresponding local permutation yields the rearranged outer correlation matrix. .

[0031] Further, the parallel Cholesky decomposition is performed on each inner submatrix in the global local diagonal block, the inner coupling blocks in the inner submatrix are iteratively updated based on the Schur complement principle, and the Cholesky decomposition is performed again on the updated inner coupling blocks, including:

[0032] For any inner sub-cluster within the k-th global local diagonal block, construct the inner sub-matrix:

[0033]

[0034] inner submatrix Perform Cholesky decomposition:

[0035]

[0036] in, for The lower triangular factor matrix obtained by decomposition;

[0037] from Extract the inner layer coupling block The corresponding associated row segments are denoted as the associated submatrix. ;

[0038] After all M inner diagonal blocks within the k-th global local diagonal block have undergone Cholesky decomposition, the inner coupling blocks are decomposed according to the following formula. Update:

[0039]

[0040] For the updated Perform Cholesky decomposition again: The lower triangular factor matrix of the inner coupling block is obtained. .

[0041] Furthermore, the construction of the rearranged precision matrix The block-based Cholesky decomposition framework yields the global lower triangular factor matrix, whose expression is:

[0042]

[0043] in, Indicates the first The lower triangular factor matrix of each global and local diagonal block. Indicates the first The correlation factor matrix of each global local diagonal block and global coupled block. This is the lower triangular factor matrix of the global coupling block;

[0044] Based on the equivalence constraint of block matrix multiplication, establish the equation for solving the correlation factor:

[0045]

[0046] The equations for solving the correlation factors are transformed into a system of lower triangular linear equations. ,in All global correlation factor matrices are solved synchronously using a multi-core parallel architecture. ;

[0047] Based on the Schur complement principle, the global coupling block is calculated using the following formula. Update:

[0048]

[0049] For the updated Perform Cholesky decomposition: .

[0050] Furthermore, the adaptive parallel unit partitioning of each sub-factor matrix includes:

[0051] Based on the outer global cluster index and the inner sub-cluster index, a multi-level sub-factor matrix is ​​extracted hierarchically from the global lower triangular factor matrix; let the first... The first global local diagonal block The sub-factor matrix corresponding to each inner subdivision block is: ;set up Any element is Define column dependency sets respectively. and row dependency set ,in, Used for determination The Middle The non-zero dependency index of the column element. Used for determination The Middle The non-zero dependency index of the row element in the previous row;

[0052] Based on adaptively adjustable adaptive scale threshold A greedy grouping strategy is used to... The matrix index set is divided to obtain multiple independent index subsets. ,in Indicates the first The first global local diagonal block, the first The first inner subdivision block The serial number of each parallel sub-computation unit;

[0053] Based on each set of independent index subsets To each Fragment extraction is performed to generate fully decoupled parallel sub-computation units. This is used for solving the inverse diagonal elements later.

[0054] Furthermore, each parallel sub-computation unit independently performs the solution of the inverse diagonal elements of the local positive definite matrix, including:

[0055] Record No. The first global local diagonal block, the first The first inner subdivision block The local Cholesky lower triangular factor matrix corresponding to each parallel sub-computation unit is: Its associated local positive definite matrix satisfies the decomposition relation: Define the inverse matrix of this local positive definite matrix. The objective matrix of the diagonal elements of the inverse matrix to be solved is a locally positive definite matrix. inverse matrix Local Cholesky lower triangular factor matrix The core computational basis for solving the diagonal elements of this inverse matrix;

[0056] Along local index Perform a reverse recursive solution from back to front; for local end indices. The corresponding column pivot has no non-zero dependencies, and the diagonal elements of the corresponding inverse matrix are directly calculated from the reciprocal of the square of the Cholesky pivot, using the following formula:

[0057]

[0058] Define the index of the current column. The set of non-zero dependency row indices below the principal element: Extract the corresponding matrix elements from this set to form a column vector. ;like Then, the current diagonal element is recursively calculated using the elements of the already solved lower local inverse matrix:

[0059]

[0060] If there are no non-zero related elements below the principal element, i.e. The above formula degenerates into its simplest form:

[0061]

[0062] Each parallel sub-computation unit only stores the intermediate quantities of the local inverse matrix and the diagonal element results necessary for the reverse recursion process, without explicitly assembling or outputting the complete local positive definite inverse matrix.

[0063] Furthermore, the step of screening for false violations and classifying risks based on the uncertainty quantification index includes:

[0064] If the marginal variance of a violation sample node is less than a preset threshold, the AI ​​judgment result of the sample is determined to be stable and reliable, and it is classified as a true violation or a low-risk category.

[0065] If the marginal variance of a violation sample node is greater than or equal to a preset threshold, the sample is judged to have fuzzy features and low reliability of the judgment result, and is classified as a false violation or a high-risk category, and is subject to manual review.

[0066] The i-th element in the inverse diagonal element vector of the global precision matrix The marginal variance corresponding to the i-th EDA violation sample is the AI-based uncertainty quantification index.

[0067] The present invention also provides an AI-based uncertainty quantification parallel solution system for EDA pseudo-violation identification, including a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the above-mentioned method.

[0068] Compared with the prior art, the present invention has the following beneficial effects:

[0069] Compared to existing machine learning uncertainty assessment techniques and EDA violation sample identification schemes, this invention, through a novel algorithm architecture and technical logic, possesses the following core technical advantages:

[0070] 1. The uncertainty index has strong interpretability. This invention abandons the traditional evaluation methods of model confidence and empirical thresholds. Based on the graph probability statistical model, it uses the inverse diagonal elements of the matrix to represent the marginal variance of the samples, accurately quantifying the global neighborhood support strength, discrimination stability and boundary ambiguity of EDA violation samples. The index has strict mathematical theoretical support, and its interpretability and traceability are far superior to traditional empirical evaluation indicators.

[0071] 2. Significantly reduces the computational overhead of solving large-scale matrices. This invention eliminates the need to explicitly generate the complete matrix inverse, and only solves the core diagonal metadata, thus avoiding the massive storage and computational overhead of traditional complete inverse calculations. At the same time, through dual-layer BBD layered decoupling, it eliminates the problem of repetitive calculations in column-by-column iterative solutions, significantly reducing the computational complexity of large-scale EDA sample scenarios.

[0072] 3. Adaptable to ultra-large-scale industrial sample scenarios. Through improved nested partitioning sorting and double-layer hierarchical splitting, the growth of filler elements in the matrix decomposition process is effectively suppressed, and the ultra-high-dimensional global matrix is ​​decomposed into multi-level independent sub-blocks. This breaks through the matrix dimension limitation of traditional algorithms and can efficiently adapt to uncertainty assessment scenarios with hundreds of thousands of EDA violation samples.

[0073] 4. Excellent numerical calculation stability and consistency. This invention is based on a symmetric positive definite accuracy matrix and the standard Cholesky direct decomposition algorithm. It has no iterative convergence process and no random calculation deviation, avoiding the defects of traditional iterative algorithms that are affected by matrix condition number. The calculation results are stable and reproducible, fully meeting the stringent requirements of EDA industrial inspection for accuracy and consistency.

[0074] 5. Completely overcomes the serial computing bottleneck of triangular matrix inversion. Addressing the technical pain point of strong serial dependence in traditional triangular matrix inversion, this invention decomposes a single serial computing task into a large number of independent subtasks through element dependency analysis, adaptive greedy grouping, and multi-level decoupling and partitioning. This achieves full-process multi-core parallel computing, significantly improving processor resource utilization and overall inference speed.

[0075] 6. Supports efficient reuse of multiple tasks and reduces redundant calculations. This invention enables multi-level reuse of matrix sorting, hierarchical splitting, Cholesky factor and calculation unit partitioning results. For multi-task scenarios such as EDA false violation screening, risk ranking, review grading and boundary sample mining, it eliminates the need for repeated full-process calculations, significantly improving the overall efficiency of industrial inspection.

[0076] 7. Improve the intelligence level of EDA false violation identification. Based on quantified uncertainty indicators, it can automatically filter false violations and suspected risk samples with ambiguous boundaries and insufficient neighborhood support, realize intelligent sorting of manual review priorities and accurate filtering of false violations, reduce manual intervention costs, and improve the intelligence and automation of EDA physical verification.

[0077] In summary, this invention overcomes the shortcomings of existing technologies from multiple dimensions of algorithm architecture and engineering implementation. While ensuring industrial-grade numerical stability, it significantly improves the efficiency of large-scale graph structure AI uncertainty assessment and EDA pseudo-violation intelligent identification, and has extremely high industrial application value and general scalability. Attached Figure Description

[0078] Figure 1 This is a schematic diagram of the disordered distribution of the original sparse precision matrix in an embodiment of the present invention.

[0079] Figure 2 This is a schematic diagram of the sparse precision matrix clustering distribution after nested partitioning and rearrangement in an embodiment of the present invention.

[0080] Figure 3 This is a schematic diagram of the process for solving the inverse diagonal elements of a matrix in a two-layer BBD parallel solution embodiment of the present invention. Detailed Implementation

[0081] The present invention will be further described below with reference to the accompanying drawings and embodiments.

[0082] It should be noted that the following detailed descriptions are exemplary and intended to provide further explanation of this application. Unless otherwise specified, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains.

[0083] It should be noted that the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the exemplary embodiments according to this application. As used herein, the singular form is intended to include the plural form as well, unless the context clearly indicates otherwise. Furthermore, it should be understood that when the terms "comprising" and / or "including" are used in this specification, they indicate the presence of features, steps, operations, devices, components, and / or combinations thereof.

[0084] This embodiment provides a method for identifying false violations in EDA based on AI discrimination and uncertainty quantification, including the following steps:

[0085] S1. Obtain violation sample data generated by EDA detection, construct a violation association topology graph based on the violation sample data, and generate a symmetric sparse positive definite accuracy matrix. ; By permutation matrix to the precision matrix Perform row and column rearrangement to distribute non-zero elements in a clustered manner, resulting in the rearranged precision matrix. ;

[0086] S2. The rearranged precision matrix Perform global single-layer diagonal boundary (BBD) partitioning, dividing all sample variables into K independent local variable clusters and 1 global coupled variable cluster, and constructing a global single-layer BBD partitioning matrix;

[0087] S3. Perform inner-layer diagonal boundary block splitting on each global local diagonal block in the global single-layer BBD block matrix, further dividing each local cluster sample into M inner-layer sub-local clusters and 1 inner-layer local coupled cluster, and constructing an inner-layer BBD block matrix to form a two-layer BBD hierarchical architecture that combines outer-layer BBD and inner-layer BBD.

[0088] S4. Perform parallel Cholesky decomposition on each inner submatrix in the global local diagonal block, iteratively update the inner coupling block in the inner submatrix based on the Schur complement principle, and perform Cholesky decomposition again on the updated inner coupling block to obtain the lower triangular factor matrix of the inner coupling block.

[0089] S5. Based on the results of all inner-layer hierarchical decompositions, construct the rearranged precision matrix. The block-based Cholesky decomposition architecture is used to obtain the global lower triangular factor matrix; all global correlation factor matrices are solved in parallel based on the block matrix multiplication equivalence constraint, and the precision matrix after rearrangement is then refined based on the Schur complement principle. The global coupling block in the process is updated, and Cholesky decomposition is performed on the updated global coupling block.

[0090] S6. Extract mutually independent multi-level sub-factor matrices from the global lower triangular factor matrix according to the outer global cluster index and the inner sub-cluster index.

[0091] S7. Perform adaptive parallel unit partitioning on each sub-factor matrix, decomposing each sub-factor matrix into multiple completely decoupled parallel sub-computation units;

[0092] S8. Distribute all parallel sub-computation units to a multi-core processor. Each parallel sub-computation unit independently performs the solution of the inverse diagonal elements of the local positive definite matrix, and obtains the inverse diagonal elements of the local positive definite matrix corresponding to each parallel sub-computation unit.

[0093] S9. Based on the index mapping relationship formed by matrix rearrangement, double-layer BBD layering and parallel unit partitioning, reconstruct the inverse diagonal element of the global precision matrix, and use the inverse diagonal element of the global precision matrix as the AI ​​discrimination uncertainty quantification index for each violation sample, so as to perform false violation screening and risk classification based on the uncertainty quantification index.

[0094] The following section provides a further explanation of the relevant technical aspects involved in this method.

[0095] I. Sparse Matrix Sorting and Rearrangement Preprocessing

[0096] This invention constructs a symmetric sparse positive definite accuracy matrix using EDA violation samples. As the core processing object, The original precision matrix represents the total number of violation samples. Non-zero elements are randomly distributed, with a shape like Figure 1 As shown. To address the problems of excessive padding elements, numerical offset, and poor parallelism in traditional matrix decomposition, this step employs an improved nested partitioning and sorting algorithm to globally rearrange the rows and columns of the matrix. This breaks the disordered coupling structure of the original matrix, optimizes the distribution of non-zero elements, and lays a structural foundation for reducing padding and improving parallelism in subsequent block decomposition. Let the permutation matrix corresponding to the rearrangement process be... The rearranged precision matrix can then be expressed as:

[0097]

[0098] in, This indicates the total number of violation samples. Represents a symmetric sparse positive definite precision matrix. This represents the precision matrix after rearrangement. Indicates the transpose; the precision matrix after rearrangement. It retains the symmetric positive definite property of the original matrix, and the non-zero elements exhibit clustered distribution characteristics.

[0099] After the above symmetric permutation process, the rearranged precision matrix The original matrix retains its core properties of being symmetric and positive definite, and its non-zero elements exhibit clustered distribution characteristics. The rearranged matrix has the following form: Figure 2 As shown, this arrangement allows for the centralization of locally related elements and the independence of globally coupled elements, adapting to the subsequent requirements for layered and segmented decomposition of the two-layer BBD.

[0100] II. Construction of a Global Single-Layer BBD Structure

[0101] Based on the sparse matrix after rearrangement preprocessing Based on the characteristic coupling strength and topological clustering association properties of the violation samples, global single-layer block diagonal boundary partitioning is performed. This step will involve all... dimensional sample variables adaptively partitioned into A set of independent local variable clusters and a set of globally coupled variable clusters completely decouple and separate the local related structure from the global coupled structure, avoiding the high computational overhead of solving the global matrix as a whole. The standard expression of the global single-layer BBD block matrix obtained by this invention is:

[0102]

[0103] in, This represents the local correlation matrix of the k-th global local diagonal block in the global single-layer BBD block matrix, corresponding to the k-th independent violation sample cluster. Indicates the number of diagonal blocks in both the global and local areas. This represents the number of samples in the k-th local cluster. This represents a globally coupled block, corresponding to the global coupling sample node association matrix outside of all local clusters. Indicates the number of globally coupled samples; The outer correlation matrix represents the relationship between the k-th local cluster and the globally coupled cluster, used to characterize the topological relationship between local samples and globally coupled samples; the overall block structure strictly satisfies the dimension conservation constraint. To ensure that the blocks are divided without omissions or overlaps, among which This represents the total number of violation samples. Through the above global single-layer BBD block processing, the high-dimensional global sparse matrix is ​​decomposed into a structured form of multiple independent local sub-blocks + a single global coupled block. The local diagonal blocks are not coupled to each other, which can support subsequent parallel computing and significantly reduce the dimensionality of a single matrix operation.

[0104] III. Construction of the Inner BBD Layered Structure

[0105] To further refine the fine-grained coupling relationships of the matrix and maximize the potential of parallel computing, this invention refines each global local diagonal block in the global single-layer BBD structure. Perform recursive hierarchical optimization to construct the inner BBD structure, forming a two-layer hierarchical architecture of "global outer BBD + local inner BBD". First, for any k-th global local diagonal block... A lightweight nested partitioning sort is used to complete the local index rearrangement and construct the local permutation matrix. The rearranged local optimization matrix is:

[0106]

[0107] Secondly, the local optimization matrix after rearrangement optimization Perform inner-layer BBD fine-grained block splitting, further dividing individual local cluster samples into... The inner-layer sub-local clusters of Group 1 are coupled with the inner-layer local clusters of Group 1 to obtain the inner-layer BBD block matrix. The expression of the inner-layer BBD block matrix is ​​as follows:

[0108]

[0109] in, This represents the m-th inner diagonal block within the k-th global local diagonal block, corresponding to the inner independent subsample cluster association matrix. Indicates the number of inner diagonal pieces. This represents the number of samples in the m-th inner sub-local cluster within the k-th global local diagonal block; This represents the inner local coupling block within the k-th global-local diagonal block, corresponding to the coupling sample correlation matrix of each inner sub-local cluster. This represents the number of samples in the inner local coupling cluster within the k-th global-local diagonal block; Let represent the association matrix between the m-th inner-layer sub-local cluster and the inner-layer local coupling cluster within the k-th global-local diagonal block, used to characterize the topological association between inner-layer sub-samples and locally coupled samples; the inner-layer block structure of a single global-local diagonal block strictly satisfies the dimension conservation constraint. This ensures that the inner layer sample dimensions are completely and without redundancy. Finally, the outer layer correlation matrix... Simultaneously apply the corresponding local permutations to obtain the rearranged and optimized outer correlation matrix. This ensures that the inner local index and the global index are fully aligned and that the data mapping is consistent, eliminating index misalignment issues. At this point, the complete two-layer BBD hierarchical architecture is built, achieving multi-level fine-grained decoupling of matrix coupling relationships.

[0110] IV. Parallel Decomposition of Inner Submatrices

[0111] Based on the constructed two-layer BBD hierarchical matrix structure, parallel Cholesky decomposition is performed on each inner layer through refined block division. Leveraging the symmetric positive definite property of the original matrix, the uniqueness and numerical stability of the decomposition results are guaranteed. This step uses the inner submatrix of a single global-local diagonal block as an independent parallel computation unit. The decomposition process of each global-local diagonal block has no data dependency and can be executed synchronously on multiple cores in parallel.

[0112] First, for any inner sub-cluster within the k-th global local diagonal block, construct the inner sub-matrix, defined as:

[0113]

[0114] Due to the original precision matrix Given a symmetric positive definite matrix, the inner submatrices after hierarchical partitioning are... It also satisfies the symmetric positive definite condition, allowing for a uniquely invertible Cholesky decomposition. For the inner submatrices... Perform Cholesky decomposition of the standard:

[0115]

[0116] In the formula, for The lower triangular Cholesky factor matrix obtained from decomposition. From Extract the inner layer coupling block The corresponding associated row segments are denoted as the associated submatrix. This is used for subsequent Schur complement updates. After all M inner diagonal blocks within the k-th global local diagonal block have completed Cholesky decomposition and correlation matrix extraction, the inner coupling blocks are updated according to the Schur complement principle. Perform iterative updates to eliminate coupling interference in inner sub-blocks. The update formula is:

[0117]

[0118] For the updated Perform Cholesky decomposition again: The lower triangular factor matrix of the inner coupling block is obtained. .

[0119] After the inner coupling block is updated, the updated... Perform the Cholesky decomposition again to obtain the lower triangular factor matrix of the inner coupling block. :

[0120]

[0121] The inner decomposition, update, and secondary decomposition processes of each global and local diagonal block are independent of each other, with no data interaction or serial dependency, and can be executed in full parallel, which greatly improves the computational efficiency and resource utilization of the local decomposition stage.

[0122] V. Construction and Update of Global Factor Matrix

[0123] Based on the results of all inner-layer decompositions completed in the previous step, the global matrix structure is integrated to construct the rearranged complete precision matrix. The block-based Cholesky decomposition architecture yields the global lower triangular factor matrix, completing the decoupled modeling of the global matrix. The expression for the optimized global lower triangular factor matrix of this invention is as follows:

[0124]

[0125] in, Indicates the first The lower triangular factor matrix of each global and local diagonal block. Indicates the first The correlation factor matrix of each global local diagonal block and global coupled block. Let be the lower triangular factor matrix of the global coupling block; denoted as . The overall result satisfies the standard Cholesky decomposition constraints:

[0126]

[0127] Based on the equivalence constraint of block matrix multiplication, establish the equation for solving the correlation factor:

[0128]

[0129] The equations for solving the correlation factors are transformed into a system of lower triangular linear equations, which facilitates parallel solving.

[0130]

[0131] Among them, the variables to be solved Due to differences The corresponding linear equation system has no cross-data dependencies and can be solved synchronously using a multi-core parallel architecture to obtain all global correlation factor matrices in batches. .

[0132] After all correlation factors have been solved, based on the Schur complement principle, the global coupling block is... The coupling interference elimination update is performed, and the update formula is:

[0133]

[0134] For the updated global coupling block Performing the final Cholesky decomposition yields the global coupling factor matrix:

[0135]

[0136] Thus, the complete global lower triangular factor matrix adapted to the two-layer BBD structure is now complete. Once completed, the matrix structure and hierarchical splitting logic correspond one-to-one, providing a complete foundation for the subsequent parallel solution of sparse triangular equations and the extraction of inverse diagonal elements.

[0137] VI. Extraction of Hierarchical Sub-Factor Matrix

[0138] Based on the global lower triangular factor matrix constructed in the previous step Based on the hierarchical division rules of the two-layer BBD layered architecture, according to the outer global cluster sequence number and inner sub-cluster sequence number The global lower triangular factor matrix is ​​decomposed and extracted into independent multi-level sub-factor matrices, which serve as the basic computational units for subsequent parallel inversion, thus completely decomposing global data dependencies.

[0139] VII. Adaptive Parallel Unit Partitioning

[0140] Let the first In the nth global local block The sub-factor matrix corresponding to each inner subdivision block is: ;set up Any element is Define column dependency sets respectively. and row dependency set ,in, Used for determination The Middle The non-zero dependency index of the column element. Used for determination The Middle The non-zero dependency index of the row element's line.

[0141] Based on adaptively adjustable adaptive scale threshold A greedy grouping strategy is used to... The matrix index set is divided to obtain multiple independent index subsets. ,in Indicates the first The first global local block, the first The first inner subdivision block The serial number of each parallel sub-computation unit.

[0142] Based on each set of independent index subsets To each Fragment extraction is performed to generate fully decoupled parallel sub-computation units. This is used for solving the inverse diagonal elements later.

[0143] 8. Multi-core parallel diagonal element solving

[0144] All decoupled sub-computation units obtained in the previous step are distributed in batches to multi-core processors. Each computation unit independently performs the sparse lower triangular matrix inversion operation. Only the core diagonal metadata is retained throughout the process, and redundant off-diagonal metadata results are discarded, minimizing memory usage and data transfer overhead, and achieving lightweight and high-speed solution.

[0145] Record No. The first global local block, the first The first inner subdivision block The local Cholesky lower triangular factor matrix corresponding to each parallel sub-computation unit is: Its associated local positive definite matrix satisfies the decomposition relation: Define the inverse matrix of this local positive definite matrix. The objective matrix of the diagonal elements of the inverse matrix to be solved is a locally positive definite matrix. inverse matrix Local Cholesky lower triangular factor matrix The core computational basis for solving the diagonal elements of this inverse matrix;

[0146] Along local index Perform a reverse recursive solution from back to front; for local end indices. The corresponding column pivot has no non-zero dependencies, and the diagonal elements of the corresponding inverse matrix are directly calculated from the reciprocal of the square of the Cholesky pivot, using the following formula:

[0147]

[0148] Define the index of the current column. The set of non-zero dependency row indices below the principal element: Extract the corresponding matrix elements from this set to form a column vector. ;like Then, the current diagonal element is recursively calculated using the elements of the already solved lower local inverse matrix:

[0149]

[0150] If there are no non-zero related elements below the principal element, i.e. The above formula degenerates into its simplest form:

[0151]

[0152] Each parallel sub-computation unit only stores the intermediate quantities of the local inverse matrix and the diagonal element results required for the reverse recursion process, without explicitly assembling and outputting the complete local positive definite inverse matrix, thereby reducing storage overhead.

[0153] IX. Global Diagonal Element Reconstruction and Calibration

[0154] Based on the multiple sets of local inverse diagonal element results obtained in the previous step, and combined with the index mapping relationship of matrix rearrangement and hierarchical partitioning, the reconstruction and precise calibration of the global precision matrix inverse diagonal elements are completed, resulting in the final uncertainty quantification index. Let the first... The original index set corresponding to each parallel sub-computation unit is: The local diagonal element vectors obtained by solving are: Initialize the global empty diagonal element vector Complete global data backfilling according to the one-to-one index mapping relationship:

[0155]

[0156] After data backfilling, the diagonal elements of the inverse matrix of the precision matrix with vector The values ​​of the i-th element in the model correspond one-to-one. This value also represents the marginal variance of the i-th EDA violation sample, and can be used as a quantitative indicator of the uncertainty of AI judgment in the final model.

[0157] If the marginal variance of a violation sample node is less than a preset threshold, the AI ​​judgment result for that sample is considered stable and reliable, and it is classified as a true violation or a low-risk category. If the marginal variance of a violation sample node is greater than or equal to a preset threshold, the sample is considered to have ambiguous features and low credibility of the judgment result, and it is classified as a false violation or a high-risk category, requiring manual review.

[0158] At this point, the complete solution process for the inverse diagonal elements of a large-scale sparse precision matrix is ​​finished. The overall process architecture is as follows: Figure 3 As shown. It is important to note that this invention features a multi-level computation result reuse mechanism, which can significantly reduce redundant computational overhead in multi-task scenarios: within the same EDA detection and diagnosis cycle, if the topological structure of the violation sample remains unchanged, i.e., the accuracy matrix... If the non-zero sparse structure remains unchanged, then the matrix nesting sorting result, the two-layer BBD hierarchical splitting structure, and the adaptive parallel unit partitioning result can be completely reused; if the sample features and associations are not updated, i.e., the matrix If the numerical values ​​remain completely unchanged, the core calculation results such as the hierarchical Cholesky factor matrix and sub-factor matrix can be directly reused without repeating the entire process of decomposition and solution. This mechanism can be adapted to parallel inference of multiple tasks such as false violation screening, risk classification, review ranking, and boundary sample mining, significantly improving the detection efficiency in industrial scenarios.

[0159] This embodiment also provides an AI-based uncertainty quantification parallel solution system for EDA pseudo-violation identification, including a memory, a processor, and computer program instructions stored in the memory and executable by the processor. When the processor executes the computer program instructions, it can implement the above-described method.

[0160] This embodiment also provides a computer-readable storage medium storing computer program instructions thereon, characterized in that the above-described method is implemented when the computer program instructions are executed by a processor.

[0161] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0162] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0163] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0164] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0165] The above description is merely a preferred embodiment of the present invention and is not intended to limit the invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. An EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification, characterized in that, include: Obtaining EDA detection generated exception sample data, constructing exception correlation topology graph based on the exception sample data, and generating a symmetric sparse positive definite precision matrix ; the precision matrix is replaced by a permutation matrix Row and column rearrangement is performed to make non-zero elements cluster distribution, and a rearranged precision matrix is obtained ; on the rearranged precision matrix A global single-layer diagonal boundary block partition is performed, all sample variables are divided into K independent local variable clusters and 1 global coupled variable cluster, and a global single-layer BBD block matrix is constructed. The global local diagonal blocks in the global single-layer BBD block matrix are split into inner diagonal boundary blocks. Each local cluster sample is further divided into M inner sub-local clusters and 1 inner local coupled cluster, thus constructing an inner BBD block matrix and forming a two-layer BBD hierarchical architecture that combines outer BBD and inner BBD. Parallel Cholesky decomposition is performed on each inner submatrix in the global local diagonal block. The inner coupling blocks in the inner submatrix are iteratively updated based on the Schur complement principle. The updated inner coupling blocks are then subjected to Cholesky decomposition again to obtain the lower triangular factor matrix of the inner coupling blocks. Based on the results of all inner-layer hierarchical decompositions, the rearranged precision matrix is ​​constructed. The block-based Cholesky decomposition framework yields the global lower triangular factor matrix; All global correlation factor matrices are solved in parallel based on the block matrix multiplication equivalence constraint, and the rearranged precision matrix is ​​then refined based on the Schur complement principle. The global coupling block in the process is updated, and Cholesky decomposition is performed on the updated global coupling block. Based on the outer global cluster index and the inner sub-cluster index, extract mutually independent multi-level sub-factor matrices from the global lower triangular factor matrix. Each sub-factor matrix is ​​adaptively partitioned into parallel units, and each sub-factor matrix is ​​decomposed into multiple completely decoupled parallel sub-computation units; All parallel sub-computation units are distributed to multi-core processors, and each parallel sub-computation unit independently performs the solution of the inverse diagonal elements of the local positive definite matrix, thereby obtaining the inverse diagonal elements of the local positive definite matrix corresponding to each parallel sub-computation unit; Based on the index mapping relationship formed by matrix rearrangement, double-layer BBD hierarchical structure and parallel unit partitioning, the inverse diagonal element of the global precision matrix is ​​reconstructed. The inverse diagonal element of the global precision matrix is ​​used as the AI ​​discrimination uncertainty quantification index for each violation sample, so as to perform false violation screening and risk classification based on the uncertainty quantification index.

2. The EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification according to claim 1, characterized in that, The precision matrix is ​​obtained by permutation matrix Perform row and column rearrangement, including: Let the permutation matrix corresponding to the rearrangement process be . The rearranged precision matrix is ​​then expressed as: in, This indicates the total number of violation samples. Represents a symmetric sparse positive definite precision matrix. This represents the precision matrix after rearrangement. Indicates the transpose; the precision matrix after rearrangement. It retains the symmetric positive definite property of the original matrix, and the non-zero elements exhibit clustered distribution characteristics.

3. The EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification according to claim 1, characterized in that, The rearranged precision matrix Perform global single-layer diagonal boundary block partitioning to obtain the global single-layer BBD block matrix, the expression of which is: in, This represents the local correlation matrix of the k-th global local diagonal block in the global single-layer BBD block matrix, corresponding to the k-th independent violation sample cluster. , Indicates the number of diagonal blocks in both the global and local areas. This represents the number of samples in the k-th local cluster. This represents a globally coupled block, corresponding to the global coupling sample node association matrix outside of all local clusters. Indicates the number of globally coupled samples; This represents the outer correlation matrix between the k-th local cluster and the global coupled cluster, used to characterize the topological relationship between local samples and global coupled samples; The global single-layer BBD block matrix satisfies the dimension conservation constraint. ,in This indicates the total number of violation samples.

4. The EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification according to claim 1, characterized in that, The process of performing inner-layer diagonal boundary block splitting on each global local diagonal block in the global single-layer BBD block matrix to obtain the inner-layer BBD block matrix includes: For any k-th global local diagonal block Nested partitioning sort is used to complete local index rearrangement and construct a local permutation matrix. The rearranged local optimization matrix is ​​obtained. ; The rearranged local optimization matrix Perform inner diagonal boundary block splitting to obtain the inner BBD block matrix, the expression of which is: in, This represents the m-th inner diagonal block within the k-th global local diagonal block, corresponding to the inner independent subsample cluster association matrix. , Indicates the number of inner diagonal pieces. This represents the number of samples in the m-th inner sub-local cluster within the k-th global local diagonal block; This represents the inner local coupling block within the k-th global-local diagonal block, corresponding to the coupling sample correlation matrix of each inner sub-local cluster. This represents the number of samples in the inner local coupling cluster within the k-th global-local diagonal block; The association matrix represents the relationship between the m-th inner sub-local cluster and the inner local coupled cluster within the k-th global local diagonal block, and is used to characterize the topological relationship between the inner sub-samples and the local coupled samples. outer layer correlation matrix Applying the corresponding local permutation yields the rearranged outer correlation matrix. .

5. The EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification according to claim 1, characterized in that, The process of performing parallel Cholesky decomposition on each inner submatrix in the global local diagonal block, iteratively updating the inner coupling blocks in the inner submatrix based on the Schur complement principle, and performing Cholesky decomposition again on the updated inner coupling blocks includes: For any inner sub-cluster within the k-th global local diagonal block, construct the inner sub-matrix: inner submatrix Perform Cholesky decomposition: in, for The lower triangular factor matrix obtained by decomposition; from Extract the inner layer coupling block The corresponding associated row segments are denoted as the associated submatrix. ; After all M inner diagonal blocks within the k-th global local diagonal block have undergone Cholesky decomposition, the inner coupling blocks are decomposed according to the following formula. Update: For the updated Perform Cholesky decomposition again: The lower triangular factor matrix of the inner coupling block is obtained. .

6. The EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification according to claim 1, characterized in that, The construction of the rearranged precision matrix The block-based Cholesky decomposition framework yields the global lower triangular factor matrix, whose expression is: in, Indicates the first The lower triangular factor matrix of each global and local diagonal block. Indicates the first The correlation factor matrix of each global local diagonal block and global coupled block. This is the lower triangular factor matrix of the global coupling block; Based on the equivalence constraint of block matrix multiplication, establish the equation for solving the correlation factor: The equations for solving the correlation factors are transformed into a system of lower triangular linear equations. ,in All global correlation factor matrices are solved synchronously using a multi-core parallel architecture. ; Based on the Schur complement principle, the global coupling block is calculated using the following formula. Update: For the updated Perform Cholesky decomposition: .

7. The EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification according to claim 1, characterized in that, The adaptive parallel unit partitioning of each sub-factor matrix includes: Based on the outer global cluster index and the inner sub-cluster index, a multi-level sub-factor matrix is ​​extracted hierarchically from the global lower triangular factor matrix; let the first... The first global local diagonal block The sub-factor matrix corresponding to each inner subdivision block is: ;set up Any element is Define column dependency sets respectively. and row dependency set ,in, Used for determination The Middle The non-zero dependency index of the column element. Used for determination The Middle The non-zero dependency index of the row element in the previous row; Based on adaptively adjustable adaptive scale threshold A greedy grouping strategy is used to... The matrix index set is divided to obtain multiple independent index subsets. ,in Indicates the first The first global local diagonal block, the first The first inner subdivision block The serial number of each parallel sub-computation unit; Based on each set of independent index subsets To each Fragment extraction is performed to generate fully decoupled parallel sub-computation units. This is used for solving the inverse diagonal elements later.

8. The EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification according to claim 7, characterized in that, Each parallel sub-computation unit independently performs the solution of the inverse diagonal elements of the local positive definite matrix, including: Record No. The first global local diagonal block, the first The first inner subdivision block The local Cholesky lower triangular factor matrix corresponding to each parallel sub-computation unit is: Its associated local positive definite matrix satisfies the decomposition relation: Define the inverse matrix of this local positive definite matrix. The objective matrix of the diagonal elements of the inverse matrix to be solved is a locally positive definite matrix. inverse matrix Local Cholesky lower triangular factor matrix The core computational basis for solving the diagonal elements of this inverse matrix; Along local index Perform a reverse recursive solution from back to front; for local end indices. The corresponding column pivot has no non-zero dependencies, and the diagonal elements of the corresponding inverse matrix are directly calculated from the reciprocal of the square of the Cholesky pivot, using the following formula: Define the index of the current column. The set of non-zero dependency row indices below the principal element: Extract the corresponding matrix elements from this set to form a column vector. ;like Then, the current diagonal element is recursively calculated using the elements of the already solved lower local inverse matrix: If there are no non-zero related elements below the principal element, i.e. The above formula degenerates into its simplest form: Each parallel sub-computation unit only stores the intermediate quantities of the local inverse matrix and the diagonal element results necessary for the reverse recursion process, without explicitly assembling or outputting the complete local positive definite inverse matrix.

9. The EDA pseudo-violation identification method based on AI discrimination and uncertainty quantification according to claim 1, characterized in that, The process of screening for false violations and classifying risks based on the uncertainty quantification index includes: If the marginal variance of a violation sample node is less than a preset threshold, the AI ​​judgment result of the sample is determined to be stable and reliable, and it is classified as a true violation or a low-risk category. If the marginal variance of a violation sample node is greater than or equal to a preset threshold, the sample is judged to have fuzzy features and low reliability of the judgment result, and is classified as a false violation or a high-risk category, and is subject to manual review. The i-th element in the inverse diagonal element vector of the global precision matrix The marginal variance corresponding to the i-th EDA violation sample is the AI-based uncertainty quantification index.

10. A parallel solution system for AI-based uncertainty quantization in EDA pseudo-violation identification, characterized in that, It includes a memory, a processor, and computer program instructions stored in the memory and executable by the processor, wherein when the processor executes the computer program instructions, it can implement the method as described in any one of claims 1-9.

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