An intelligent analysis method and system for heat conduction equations driven by deep learning

Abstract

The present invention discloses an intelligent analysis method and system for heat conduction equations driven by deep learning, including a heat conduction initialization unit, an equation constraint analysis unit, a graph neural network correction unit, a hot spot analysis unit, and a parameter update unit. A heat generation rate model is constructed based on the workload matrix and power matrix of functional nodes, and the diffusion coefficient tensor is initialized according to the thermal design information; through an encoder layer, a decoder layer, and a heat conduction differential constraint layer, a first heat distribution that satisfies the heat conduction equation constraints is generated; a graph neural network is used to process the topological structure of functional nodes, and a corrected heat distribution is obtained through a diffusion model, and a second heat distribution is corrected; the deviation degree between the second heat distribution and the heat conduction equation is analyzed in real time to identify potential hot spots; the neural network parameters are updated through an incremental learning mechanism. The present invention solves the problems that the numerical dissipation introduced by discretization and the sparse sensor data affect the calculation accuracy and calculation efficiency of the numerical solution of the heat conduction equation.

Description

Technical Field

[0001] The present invention relates to the technical field of neural network structures, and in particular to an intelligent analysis method and system for heat conduction equations driven by deep learning. Background Art

[0002] The numerical solution of the heat conduction equation in the field of engineering thermophysics has long relied on discretization methods, which face significant challenges in dealing with complex geometric topologies or transient non-linear problems. Traditional numerical frameworks require the pre-construction of high-quality computational grids, and their accuracy and computational efficiency are restricted by the selection of spatial discretization density and time step size. In particular, numerical oscillations and convergence problems are prone to occur in scenarios such as phase change heat transfer and porous media mass transfer coupling. In recent years, deep learning paradigms represented by Physics-Informed Neural Networks (PINNs) have provided a new path for equation solving. By embedding the governing equation into the loss function, they construct a meshless solution space representation in the continuous space-time domain, effectively avoiding the numerical dissipation problems introduced by traditional methods due to discretization.

[0003] Although existing physics-informed neural networks can incorporate heat conduction equation constraints, the accuracy of reconstructing the complete temperature distribution still needs to be improved when sensor data is sparse. Therefore, an intelligent analysis method and system for heat conduction equations driven by deep learning are proposed. Summary of the Invention

[0004] (I) Technical Problems to be Solved

[0005] Based on the above problems, the present invention provides an intelligent analysis method and system for heat conduction equations driven by deep learning, which solve the problems that numerical dissipation introduced by discretization and sparse sensor data affect the computational accuracy and computational efficiency of the numerical solution of heat conduction equations.

[0006] (II) Technical Solutions

[0007] Based on the above technical problems, the present invention provides an intelligent analysis method for heat conduction equations driven by deep learning, including:

[0008] S00. Collect sensor temperatures through a sensor array, obtain the workload matrix of functional nodes through a performance counter, obtain the power matrix of functional nodes through a power monitoring circuit, extract thermal design information, and establish a sensor position mapping matrix to record the coordinates of each sensor in the three-dimensional space of the chip;

[0009] S10. Construct a heat generation rate model based on the workload matrix and the power matrix of the functional nodes, obtain the heat generation rate of all coordinate points of the chip, and initialize the diffusion coefficient tensor according to the thermal design information;

[0010] S20. Process the time series of the sensor temperature, the heat generation rate, and the diffusion coefficient tensor using an encoder-decoder network, and generate a first heat distribution that satisfies the constraints of the heat conduction equation through an encoder layer, a decoder layer, and a heat conduction differential constraint layer.

[0011] S30. Process the functional node topology using a graph neural network, aggregate node features through stacked multi-scale graph convolutional layers and an attention mechanism to obtain a comprehensive node feature matrix, obtain a corrected heat distribution through a diffusion model, and add the first heat distribution and the corrected heat distribution to obtain a second heat distribution.

[0012] S40. Analyze the deviation of the second heat distribution from the heat conduction equation in real time to identify potential hotspots.

[0013] Further, in S10, constructing the heat generation rate model based on the workload matrix and the power matrix of the functional nodes includes: calculating the heat generation rate of each functional node according to the workload matrix and the power matrix, and expanding the discrete heat generation rate of each functional node into a continuous heat generation rate model through a radial basis function interpolation method to obtain the heat generation rate data of all coordinate points of the chip; the heat generation rate model is:

[0014]

[0015] where Q(x, y, z, t) represents the heat generation rate of the point (x, y, z) in the chip at time t, q ij represents the heat generation rate of the i-th functional node in the j-th time window, m represents the number of functional nodes, k represents the number of time windows, represents the spatial radial basis function, ψ() represents the time decay function, represents the central coordinate of the i-th functional node, t j represents the representative time of the j-th time window; ζ i is the energy-heat conversion efficiency coefficient of the i-th functional node, p ij represents the power consumption of the i-th functional node in the j-th time window, f(w ij ) represents the non-linear mapping function from workload to heat generation, which is obtained through pre-training with historical data.

[0016] Further, in S10, initializing the diffusion coefficient tensor according to the thermal design information includes: obtaining the thermal conductivity, density, and specific heat capacity according to the thermal design information, calculating the diffusion coefficients in the three main axis directions of x, y, and z, and initializing the diffusion coefficient tensor in the heat conduction equation according to the diffusion coefficients in the main axis directions; the diffusion coefficients in the main axis directions are:

[0017]

[0018] The diffusion coefficient tensor is as follows:

[0019]

[0020] where λ u (x, y, z), ρ(x, y, z), and c(x, y, z) represent the thermal conductivity in the direction of the principal axis u at the corresponding position, the density at the point (x, y, z), and the specific heat capacity, respectively; R(x, y, z) represents the local coordinate rotation matrix, and R T (x, y, z) is the transpose of R(x, y, z), and d x (x, y, z), d y (x, y, z), and d z (x, y, z) are the diffusion coefficients in the x, y, and z principal axis directions, respectively, and diag() represents constructing a diagonal matrix.

[0021] Furthermore, the S20 includes: the encoder layer receives the time series of the sensor temperature, the heat generation rate, and the diffusion coefficient tensor, extracts hidden features through a fully connected neural network, and the decoder layer uses transposed convolution to map the hidden features back to the three-dimensional spatial domain to generate a complete first heat distribution.

[0022] Furthermore, the S30 includes: based on the physical layout and functional node distribution of the chip, constructing a functional node topology structure, assigning feature vectors to each functional node, extracting a node feature matrix through a graph convolution layer containing multi-scale graph convolution kernels, fusing the results of multiple graph convolution layers with an attention mechanism to obtain a comprehensive node feature matrix, mapping the comprehensive node feature matrix to the chip heat distribution through a diffusion model to obtain a corrected heat distribution; adding the first heat distribution and the corrected heat distribution to obtain a second heat distribution;

[0023]

[0024] where ΔT(x, y, z, t) represents the corrected heat distribution, m represents the number of functional nodes, W i (x, y, z) represents the spatial weight function of the i-th functional node, which is designed based on Gaussian kernel functions in the x, y, and z directions, represents the final node feature vector of the i-th functional node extracted from the comprehensive node feature matrix, fnn() represents a feedforward neural network, and T (2) (x, y, z, t) represents the second heat distribution, and T (1) (x, y, z, t) represents the first heat distribution.

[0025] Further, the S40 includes: defining a local residual function by calculating the deviation of the second heat distribution from the heat conduction equation; calculating an anomaly score based on the local residual function and the second heat distribution, and determining that the point (x, y, z) at time t is a potential hot spot if the anomaly score S(x, y, z, t) is greater than the adaptive threshold λ(t); the formulas for the local residual function, the anomaly score, and the adaptive threshold are respectively:

[0026]

[0027] where R(x, y, z, t) represents the local residual at the point (x, y, z) at time t, T (2) (x, y, z, t) represents the second heat distribution, ρ and c respectively represent the density and specific heat capacity of the chip material, represents the partial derivative of temperature with respect to time, D represents the diffusion coefficient tensor, represents the gradient operator, Q(x, y, z, t) represents the heat generation rate; S(x, y, z, t) represents the anomaly score, μ R (t) and σ R (t) respectively represent the time-varying mean and standard deviation of the local residual, μ T (t) and σ T (t) respectively represent the time-varying mean and standard deviation of the heat distribution; λ0 and λ1 represent the base threshold parameters, t represents the current time, t last represents the time when the last anomaly was detected, τ adapt represents the time adaptation coefficient, and exp() represents the exponential function with the natural constant as the base.

[0028] Further, it further includes: S50, updating the parameters of the encoder-decoder network and the graph neural network through an incremental learning mechanism.

[0029] Further, the S50 includes: constructing an experience replay buffer, designing a knowledge distillation mechanism, comparing the prediction results of the current model with the prediction results of the historical model, and defining a knowledge distillation loss; estimating the importance of each parameter to the model performance through the Fisher information matrix, and introducing an elastic weight consolidation regularization term; during the training process, defining the total loss function of incremental learning to include the loss function of the current task, the knowledge distillation loss, and the regularization term; finally, designing an adaptive parameter update strategy, and selectively updating the parameters in the neural network according to the parameter importance and performance changes, and the update rule is:

[0030]

[0031] where θ new and θ old represent the parameters after and before the update, and η represents the learning rate. Represents the gradient of the total loss function L for incremental learning with respect to the parameter θ , s represents the parameter importance score, τ update represents the update threshold, and σ() represents the activation function.

[0032] The present invention also discloses an intelligent analysis system for heat conduction equations driven by deep learning, which runs the intelligent analysis method for heat conduction equations driven by deep learning, including: a heat conduction initialization unit, an equation constraint analysis unit, a graph neural network correction unit, a hot spot analysis unit, and a parameter update unit, which respectively run the S10, S20, S30, S40, and S50.

[0033] (III) Beneficial effects

[0034] The above technical solutions of the present invention have the following advantages:

[0035] (1) Based on the construction method of continuous heat source distribution using radial basis function interpolation, the present invention expands the heat generation rate of discrete functional nodes into a full-chip continuous function, combines the initialization of the diffusion coefficient tensor, and then expands the sparse sensor data into a three-dimensional field through an encoder-decoder network to reconstruct the full-chip heat distribution from the sparse sensor data. By introducing a heat conduction differential constraint layer, the spatio-temporal derivatives of the predicted heat distribution are calculated using automatic differentiation technology and forced to satisfy the partial differential equation of heat conduction. During training, the loss function fuses the data matching loss, physical constraint loss, and boundary condition loss, enabling the model to not only fit the limited observed data but also conform to the physical laws of heat conduction; it solves the accuracy problem of heat source modeling in the sparse sensor scenario, compensates for data deficiencies by combining physical constraints, significantly reduces the dependence on the number of sensors, solves the problem of efficient reconstruction of the full heat distribution with limited sensors, provides a high-precision basis for subsequent correction and hot spot identification, and thus is beneficial to improving the computational accuracy of the numerical solution of the heat conduction equation;

[0036] (2) Aiming at the non-uniform layout of the chip and the blind area covered by sensors, the present invention models the chip as a topological graph structure, combines a graph convolutional network to correct the first heat distribution, aggregates local and global heat conduction modes through a multi-scale graph convolutional network, and the diffusion model maps the node features to the chip temperature field to generate a second heat distribution; accurately characterizes the heat interaction relationship between functional nodes through graph structure modeling, and uses the topological perception ability of the graph convolutional network to correct the temperature distribution in the area not covered by sensors, effectively improving the physical consistency and spatial resolution of the full heat distribution reconstruction, and further improving the computational accuracy of the numerical solution of the heat conduction equation;

[0037] (3) By analyzing the deviation degree of the second heat distribution from the heat conduction equation, the present invention defines a local residual function, calculates an anomaly score by combining the statistical characteristics of the heat distribution; quantifies the difference between the theoretical prediction of the heat conduction equation and the measured heat distribution through the residual function, and the anomaly score combines the standardized value of the residual and the time-varying statistic of the heat distribution, and determines potential hot spots through an adaptive threshold; by combining physical laws and statistical analysis, the present invention accurately locates temperature anomalies in areas not covered by sensors, and the adaptive threshold can dynamically respond to changes in working conditions, significantly improving the sensitivity and reliability of hot spot identification, providing real-time early warning for chip thermal safety, thereby facilitating improving the calculation accuracy and calculation efficiency of the numerical solution of the heat conduction equation. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] The features and advantages of the present invention will be more clearly understood by referring to the accompanying drawings. The drawings are schematic and should not be construed as imposing any limitation on the present invention. In the drawings:

[0039] Figure 1 It is a schematic structural diagram of an intelligent analysis system for a heat conduction equation driven by deep learning according to an embodiment of the present invention;

[0040] Figure 2 It is a schematic flowchart of an intelligent analysis method for a heat conduction equation driven by deep learning according to an embodiment of the present invention;

[0041] Figure 3 It is a schematic connection diagram between fully connected layers in a decoder layer according to an embodiment of the present invention;

[0042] Figure 4 It is a schematic data flow diagram of an intelligent analysis method for a heat conduction equation driven by deep learning according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0043] The following will further describe in detail the specific embodiments of the present invention in conjunction with the accompanying drawings and embodiments. The following embodiments are used to illustrate the present invention but are not used to limit the scope of the present invention.

[0044] Embodiment 1 of the present invention is an intelligent analysis system for a heat conduction equation driven by deep learning, as Figure 1 shown, including: a heat conduction initialization unit, an equation constraint analysis unit, a graph neural network correction unit, a hot spot analysis unit, and a parameter update unit.

[0045] The heat conduction initialization unit constructs a heat generation rate model based on the workload matrix and power matrix of functional nodes, and initializes the diffusion coefficient tensor according to the thermal design information;

[0046] The equation constraint analysis unit processes the sensor temperature time series, heat generation rate, and diffusion coefficient tensor using an encoder-decoder network, and generates a first heat distribution that satisfies the heat conduction equation constraint through the encoder layer, decoder layer, and heat conduction differential constraint layer.

[0047] The graph neural network correction unit processes the functional node topology structure using a graph neural network, aggregates node features through stacked multi-scale graph convolutional layers and an attention mechanism to obtain a comprehensive node feature matrix, obtains a corrected heat distribution through a diffusion model, and obtains a second heat distribution based on the first heat distribution and the corrected heat distribution.

[0048] The hot spot analysis unit analyzes the deviation degree of the second heat distribution from the heat conduction equation in real time to identify potential hot spots.

[0049] The parameter update unit updates the parameters of the encoder-decoder network and the graph neural network through an incremental learning mechanism.

[0050] Embodiment 2 of the present invention is a deep learning-driven intelligent analysis method for the heat conduction equation, as Figures 2-3 shown, including:

[0051] S00. Collect sensor temperatures through a sensor array, obtain the workload matrix of functional nodes through a performance counter, obtain the power matrix of functional nodes through a power monitoring circuit, extract thermal design information, and establish a sensor position mapping matrix to record the coordinates of each sensor in the three-dimensional space of the chip.

[0052] Obtain sensor temperatures through a temperature sensor array distributed on the chip; collect the instruction execution status of each functional node of the chip through a performance counter to obtain the workload matrix W = {w ij}, where w ij represents the instruction execution frequency of the i-th functional node in the j-th time window; obtain the power matrix P = {p ij} through an integrated power monitoring circuit, where p ij represents the power consumption of the i-th functional node in the j-th time window; extract thermal design information from the chip design database, including the thermal conductivity, density, specific heat capacity of the chip material, and the heat transfer coefficient with the radiator; establish a sensor position mapping matrix to record the exact coordinates of each sensor in the three-dimensional space of the chip.

[0053] Synchronously collect multi-source data through the sensor array, performance counter, and power monitoring circuit, and combine the thermal design information to provide multi-dimensional input for heat distribution reconstruction, ensuring the accurate association between limited sensor data and the heat source distribution.

[0054] S10. Construct a heat generation rate model based on the workload matrix and the power matrix of the functional nodes, obtain the heat generation rates of all coordinate points of the chip, and initialize the diffusion coefficient tensor according to the thermal design information;

[0055] Constructing a heat generation rate model based on the workload matrix and the power matrix includes: calculating the heat generation rate of each functional node according to the workload matrix and the power matrix; expanding the discrete heat generation rate into a continuous heat generation rate model by the radial basis function interpolation method to obtain the heat generation rate data of all coordinate points of the chip;

[0056] The formula of the heat generation rate model is:

[0057]

[0058] where Q(x, y, z, t) represents the heat generation rate of the point (x, y, z) in the chip at time t, q ij represents the heat generation rate of the i-th functional node in the j-th time window, m represents the number of functional nodes, k represents the number of time windows, represents the spatial radial basis function, ψ() represents the time decay function, represents the central coordinate of the i-th functional node, t j represents the representative time of the j-th time window; ζ i is the energy - heat conversion efficiency coefficient of the i-th functional node, p ij represents the power consumption of the i-th functional node in the j-th time window, f(w ij ) represents the non-linear mapping function from workload to heat generation, which is obtained by pre-training with historical data. Table 1 gives an example of the heat generation rate calculated by obtaining the load and power consumption of each unit through the performance counter and the power monitoring circuit.

[0059] Table 1 Example of heat generation rate

[0060]

[0061] Initializing the diffusion coefficient tensor in the heat conduction equation according to the thermal design information includes: obtaining the thermal conductivity, density and specific heat capacity according to the thermal design information, calculating the diffusion coefficients in the three main axis directions of x, y and z; initializing the diffusion coefficient tensor in the heat conduction equation according to the diffusion coefficients in the main axis directions.

[0062] Diffusion coefficients in the main axis directions:

[0063] ;

[0064] Diffusion coefficient tensor:

[0065] ;

[0066] Among them, λ u (x, y, z), ρ(x, y, z) and c(x, y, z) respectively represent the thermal conductivity in the direction of the principal axis u at the corresponding position, the density at the point (x, y, z), and the specific heat capacity; R(x, y, z) represents the local coordinate rotation matrix, and R T (x, y, z) is the transpose of R(x, y, z), and d x (x, y, z), d y (x, y, z) and d z (x, y, z) are the diffusion coefficients in the three principal axis directions of x, y, and z respectively, and diag() represents constructing a diagonal matrix.

[0067] The method for constructing a continuous heat source distribution based on radial basis function interpolation in this embodiment expands the heat generation rate of discrete functional nodes into a continuous function of the entire chip, and combines the initialization of the diffusion coefficient tensor to solve the accuracy problem of heat source modeling in the sparse sensor scenario.

[0068] S20. Use an encoder-decoder network to process the sensor temperature time series, heat generation rate, and diffusion coefficient tensor, and generate a first heat distribution that satisfies the heat conduction equation constraint through an encoder layer, a decoder layer, and a heat conduction differential constraint layer;

[0069] The encoder layer receives the time series of the sensor temperature, the heat generation rate, and the diffusion coefficient tensor, and extracts hidden features through a fully connected neural network; specifically including: constructing the input data into an input feature vector, and obtaining hidden features after being processed by L e layers of fully connected layers. Each layer of fully connected layer multiplies the input feature vector by a weight matrix, adds a bias vector, and then performs a non-linear transformation through an activation function to obtain the output of each layer of fully connected layer; a residual connection mechanism is adopted between every two layers of fully connected layers. As Figure 3 shown, the output of the previous layer is directly added to the output of the current layer, and the result is used as the input feature vector of the next layer of fully connected layer until the output of the last layer of fully connected layer is the hidden feature.

[0070] The decoder layer uses transposed convolution to connect feature reshaping, transposed convolution layers, and linear activation in sequence, so as to map the hidden features back to the three-dimensional spatial domain and generate a complete first heat distribution. Specifically including: reshaping the hidden features output by the encoder into a three-dimensional feature map with low resolution, and performing upsampling through L d layers of transposed convolution layers to gradually increase the spatial resolution of the three-dimensional feature map to reach the target spatial resolution (corresponding to the physical size of the chip), and at the same time gradually reduce the number of channels to 1. Finally, the temperature value corresponding to each voxel of the three-dimensional feature map is output through a linear activation function to obtain the first heat distribution.

[0071] During the training process of the encoder-decoder network, a heat conduction differential constraint layer is introduced. The derivatives of the predicted heat distribution with respect to space and time are calculated through automatic differentiation technology, and the partial differential equation of heat conduction is forced to be satisfied. The loss function of the encoder-decoder network includes a data matching loss L data , a physical constraint loss L physics and a boundary condition loss L boundary , and the specific formulas are as follows:

[0072]

[0073] where N represents the number of temperature sensors, T (1) (x n ,y n ,z n ,t) represents the predicted temperature value at the position (x n ,y n ,z n ) of the nth temperature sensor, which is obtained from the first heat distribution obtained during the training process, and T measured,n represents the actual measured temperature value corresponding to the nth temperature sensor;

[0074]

[0075] where T (1) (x,y,z,t) represents the first heat distribution, ρ and c respectively represent the density and specific heat capacity of the chip material, represents the partial derivative of temperature with respect to time, D represents the diffusion coefficient tensor, represents the gradient operator, Q(x,y,z,t) represents the heat generation rate, represents the Euclidean norm on the computational domain Ω;

[0076]

[0077] where B(T) represents the boundary operator, including specifying the boundary temperature, specifying the boundary heat flux, or a mixed heat flux and temperature, g represents the heat conduction boundary condition, that is, the target value of the boundary operator, represents the boundary of the computational domain Ω.

[0078] In this embodiment, through the design of the loss function of the heat conduction constrained neural network, the model output is forced to conform to the heat conduction equation, compensating for the lack of physical laws caused by insufficient sensor data and improving the physical rationality of the reconstruction results.

[0079] S30. Process the functional node topology structure using a graph neural network, aggregate node features through stacked multi-scale graph convolutional layers and an attention mechanism to obtain a comprehensive node feature matrix, obtain a corrected heat distribution through a diffusion model, and add the first heat distribution and the corrected heat distribution to obtain a second heat distribution;

[0080] Based on the physical layout and functional node distribution of the chip, construct a functional node topology structure G=(V, E, A), where the vertex set V includes m functional nodes, the edge set E represents the heat conduction paths between functional nodes, and the adjacency matrix A represents the strength of the topological relationship between functional nodes; assign a feature vector to each functional node , where, represents the average temperature of the i-th functional node region extracted from the first heat distribution, represents the average heat generation rate, h i represents the sub-vector composed of the position and regional geometric features of the functional node;

[0081] The element in the adjacency matrix A

[0082]

[0083] where, d ij represents the Euclidean distance between the i-th and j-th functional nodes in the horizontal plane, z i and z j respectively represent the vertical coordinates of the i-th and j-th functional nodes, σ d and σ z represent scaling parameters, and exp() represents the exponential function with the natural constant as the base;

[0084] Extract the node feature matrix through a graph convolutional layer containing multi-scale graph convolutional kernels, and combine the attention mechanism to fuse the results of multiple graph convolutional layers to obtain a comprehensive node feature matrix, specifically including: each graph convolutional layer contains H parallel graph convolutional kernels of different scales, and each kernel focuses on nodes in different ranges; in each graph convolutional layer, the node updates its own features by aggregating the feature information from its neighbors, and performs attention-weighted fusion on the updated node feature matrices of H scales; finally, perform final fusion on the outputs of all graph convolutional layers through a multi-head attention mechanism to obtain a comprehensive node feature matrix.

[0085] Map the comprehensive node feature matrix to the chip heat distribution through a diffusion model to obtain a corrected heat distribution; specifically:

[0086]

[0087] where, ΔT(x, y, z, t) represents the corrected heat distribution, m represents the number of functional nodes, W i(x, y, z) represents the spatial weight function of the i-th functional node, which is designed based on Gaussian kernel functions in the three directions of x, y, and z. represents the final node feature vector of the i-th functional node extracted from the comprehensive node feature matrix. fnn() represents a feedforward neural network, such as a multi-layer perceptron, which is used to implement mapping to the corrected temperature value of this node;

[0088] The second heat distribution is obtained by adding the first heat distribution and the corrected heat distribution:

[0089]

[0090] where, T (2) (x, y, z, t) represents the second heat distribution, T (1) (x, y, z, t) represents the first heat distribution, and ΔT(x, y, z, t) represents the corrected heat distribution;

[0091] In this embodiment, through topological graph structure modeling and multi-scale graph convolutional network, the topological relationship between functional nodes is used to correct the temperature distribution in the sensor blind area, enhancing the spatial integrity of the full heat distribution reconstruction. The comparison of the heat distribution before and after correction in the key position area on the chip is shown in Table 2 specifically.

[0092] Table 2 Comparison of heat distribution before and after correction

[0093]

[0094] S40. Analyze the deviation degree between the second heat distribution and the heat conduction equation in real time to identify potential hot spots;

[0095] By calculating the deviation degree of the second heat distribution from the heat conduction equation, a local residual function is defined; according to the local residual function and the second heat distribution, an anomaly score is calculated. If the anomaly score S(x, y, z, t) is greater than the adaptive threshold λ(t), then the point (x, y, z) at time t is determined to be a potential hot spot.

[0096] Based on the residual function and anomaly score algorithm, combined with the dynamic threshold to determine hot spots, realizing the accurate positioning of temperature anomalies in the uncovered area and reducing the risk of false negatives.

[0097] Among them, the formulas for the local residual function and the anomaly score are:

[0098]

[0099] Among them, R(x, y, z, t) represents the local residual at the point (x, y, z) at time t, T (2) (x, y, z, t) represents the second heat distribution, and ρ and c respectively represent the density and specific heat capacity of the chip material. represents the partial derivative of temperature with respect to time, D represents the diffusion coefficient tensor, represents the gradient operator, and Q(x, y, z, t) represents the heat generation rate;

[0100] where S(x, y, z, t) represents the anomaly score, μ R (t) and σ R (t) represent the time-varying mean and standard deviation of the local residuals respectively, and μ T (t) and σ T (t) represent the time-varying mean and standard deviation of the heat distribution respectively.

[0101] The formula for the adaptive threshold λ(t) is:

[0102]

[0103] where λ0 and λ1 represent the base threshold parameters, t represents the current time, tlast represents the time when the last anomaly was detected, τadapt represents the time adaptation coefficient, and exp() represents the exponential function with the natural constant as the base.

[0104] This embodiment tightly combines physical laws (heat conduction equation) with statistical analysis (normalized residuals and heat distribution). The residual function not only reflects temperature anomalies but also reveals whether the anomalies conform to the heat conduction law. For example, high residuals may be caused by material defects or sudden changes in heat sources. The normalization process eliminates the difference in data dimensions under different working conditions, and the adaptive threshold can dynamically adjust the sensitivity.

[0105] Generate the initial heat distribution from sparse data through an encoder-decoder network, correct topology-related errors by combining with a graph neural network, and finally identify potential hotspots through residual analysis. This embodiment breaks through the dependence of traditional methods on dense sensors and high computing power, uses physical constraints and topological modeling to make up for data sparsity, and realizes efficient and high-precision reconstruction from local observations to global heat distribution. It provides an intelligent solution for chip thermal management with low hardware cost and high real-time performance, and significantly improves the ability of heat dissipation design optimization and fault warning.

[0106] S50. Update the parameters of the encoder-decoder network and the graph neural network through an incremental learning mechanism.

[0107] Construct an experience replay buffer, design a knowledge distillation mechanism, compare the prediction results of the current model with those of the historical model, and define the knowledge distillation loss; estimate the importance of each parameter for the model performance through the Fisher information matrix, and introduce the Elastic Weight Consolidation (EWC) regularization term; during the training process, define the total loss function for incremental learning, including the loss function of the current task, the knowledge distillation loss, and the regularization term; finally, design an adaptive parameter update strategy, and selectively update the parameters in the neural network according to the parameter importance and performance changes. The update rule is

[0108] ;

[0109] where θnew and θold represent the parameters after and before the update, η represents the learning rate, represents the gradient of the total loss function L for incremental learning with respect to the parameter θ , s represents the parameter importance score, τupdate represents the update threshold, and σ() represents the activation function. The schematic diagram of the data flow in this embodiment is as Figure 4 shown.

[0110] Finally, it should be noted that the above analysis method can be converted into software program instructions, which can be implemented either by using an analysis system including a processor and a memory or by computer instructions stored in a non-transitory computer-readable storage medium. The above integrated unit implemented in the form of a software functional unit can be stored in a computer-readable storage medium. The above software functional unit stored in a storage medium includes several instructions for causing a computer device (which can be a personal computer, a server, or a network device, etc.) or a processor to execute some steps of the methods described in various embodiments of the present invention. The aforementioned storage medium includes: various media such as a USB flash drive, a mobile hard disk, a Read-Only Memory (ROM), a Random Access Memory (RAM), a magnetic disk, or an optical disc that can store program codes.

[0111] In summary, through the above-mentioned intelligent analysis method and system for heat conduction equations driven by deep learning, the following beneficial effects are achieved:

[0112] (1)The continuous heat source distribution construction method based on radial basis function interpolation in the present invention expands the heat generation rate of discrete functional nodes into a continuous function across the entire chip. Combining the initialization of the diffusion coefficient tensor, and then expanding the sparse sensor data into a three-dimensional field through an encoder-decoder network, reconstructing the full-chip heat distribution from the sparse sensor data, introducing a heat conduction differential constraint layer, calculating the spatio-temporal derivatives of the predicted heat distribution through automatic differentiation technology, and forcing it to satisfy the partial differential equation of heat conduction. During training, the loss function fuses the data matching loss, physical constraint loss, and boundary condition loss, enabling the model to not only fit the limited observed data but also conform to the physical laws of heat conduction; it solves the accuracy problem of heat source modeling in the sparse sensor scenario, and combines physical constraints to make up for insufficient data, significantly reducing the dependence on the number of sensors, solving the problem of efficient reconstruction of the full heat distribution with limited sensors, providing a high-precision basis for subsequent correction and hot spot identification, and thus being conducive to improving the computational accuracy of the numerical solution of the heat conduction equation;

[0113] (2)Aiming at the non-uniform layout of the chip and the blind area covered by sensors, the present invention models the chip as a topological graph structure, combines a graph convolutional network to correct the first heat distribution, aggregates local and global heat conduction modes through a multi-scale graph convolutional network, and the diffusion model maps the node features to the chip temperature field to generate the second heat distribution; accurately characterizing the heat interaction relationship between functional nodes through graph structure modeling, and using the topological perception ability of the graph convolutional network to correct the temperature distribution in the area not covered by sensors, effectively improving the physical consistency and spatial resolution of the full heat distribution reconstruction, and further improving the computational accuracy of the numerical solution of the heat conduction equation;

[0114] (3)By analyzing the deviation degree between the second heat distribution and the heat conduction equation, the present invention defines a local residual function, and calculates the anomaly score in combination with the statistical characteristics of the heat distribution; quantifying the difference between the theoretical prediction of the heat conduction equation and the measured heat distribution through the residual function, the anomaly score fuses the normalized value of the residual and the time-varying statistic of the heat distribution, and determines potential hot spots through an adaptive threshold; by combining physical laws and statistical analysis, the present invention accurately locates the temperature anomalies in the area not covered by sensors, and the adaptive threshold can dynamically respond to changes in working conditions, significantly improving the sensitivity and reliability of hot spot identification, providing real-time early warning for chip thermal safety, and thus being conducive to improving the computational accuracy and computational efficiency of the numerical solution of the heat conduction equation.

[0115] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the embodiments of the present invention are described in conjunction with the accompanying drawings, those skilled in the art can make various modifications and variations without departing from the spirit and scope of the present invention, and such modifications and variations all fall within the scope defined by the appended claims.

Claims

1. An intelligent analysis method for heat conduction equations driven by deep learning, characterized in that, Including: S00: Collect the sensor temperature through a sensor array, obtain the workload matrix of the functional nodes through a performance counter, obtain the power matrix of the functional nodes through a power monitoring circuit, extract the thermal design information, and establish a sensor position mapping matrix to record the coordinates of each sensor in the three-dimensional space of the chip; S10: Construct a heat generation rate model based on the workload matrix and the power matrix of the functional nodes, obtain the heat generation rate of all coordinate points on the chip, and initialize the diffusion coefficient tensor according to the thermal design information; S20: Use an encoder-decoder network to process the time series of the sensor temperature, the heat generation rate, and the diffusion coefficient tensor. Through the encoder layer, decoder layer, and heat conduction differential constraint layer, generate a first heat distribution that satisfies the heat conduction equation constraint; S30: Use a graph neural network to process the functional node topology structure. Through the stacked multi-scale graph convolutional layers and the attention mechanism, aggregate the node features to obtain a comprehensive node feature matrix. Obtain a corrected heat distribution through a diffusion model, and add the first heat distribution and the corrected heat distribution to obtain a second heat distribution; S40: Analyze the deviation degree of the second heat distribution from the heat conduction equation in real time to identify potential hot spots.

2. The intelligent analysis method for heat conduction equation driven by deep learning according to claim 1, characterized in that In S10, the constructing a heat generation rate model based on the workload matrix and the power matrix of the functional nodes includes: calculating the heat generation rate of each functional node according to the workload matrix and the power matrix, and expanding the discrete heat generation rate of each functional node into a continuous heat generation rate model through a radial basis function interpolation method to obtain the heat generation rate data of all coordinate points on the chip; the heat generation rate model is: Among them, Q(x, y, z, t) represents the heat generation rate of the point (x, y, z) in the chip at time t, q ij represents the heat generation rate of the i-th functional node in the j-th time window, m represents the number of functional nodes, k represents the number of time windows, represents the spatial radial basis function, ψ() represents the time decay function, represents the central coordinates of the i-th functional node, t j represents the representative time of the j-th time window; ζ i is the energy-heat conversion efficiency coefficient of the i-th functional node, p ij represents the power consumption of the i-th functional node in the j-th time window, f(w ij ) represents the non-linear mapping function from workload to heat generation, which is obtained by pre-training with historical data.

3. The intelligent analysis method of the heat conduction equation driven by deep learning according to claim 1, characterized in that, In S10, the initializing the diffusion coefficient tensor according to the thermal design information includes: obtaining the thermal conductivity, density, and specific heat capacity according to the thermal design information, calculating the diffusion coefficients in the x, y, and z principal axis directions, and initializing the diffusion coefficient tensor in the heat conduction equation according to the diffusion coefficients in the principal axis directions; the diffusion coefficients in the principal axis directions are: The diffusion coefficient tensor is as follows: Among them, λ u (x, y, z), ρ(x, y, z) and c(x, y, z) represent the thermal conductivity in the direction of the principal axis u at the corresponding position, the density at the point (x, y, z), and the specific heat capacity, respectively; R(x, y, z) represents the local coordinate rotation matrix, and R T (x, y, z) is the transpose of R(x, y, z), and d x (x, y, z), d y (x, y, z) and d z (x, y, z) are the diffusion coefficients in the three principal axis directions of x, y, and z respectively, and diag() represents constructing a diagonal matrix.

4. The intelligent analysis method for the heat conduction equation driven by deep learning according to claim 1, wherein, The S20 includes: The encoder layer receives the time series of the sensor temperature, the heat generation rate, and the diffusion coefficient tensor, extracts hidden features through a fully connected neural network, and the decoder layer uses a transposed convolution to map the hidden features back to the three-dimensional spatial domain to generate a complete first heat distribution.

5. The intelligent analysis method for heat conduction equation driven by deep learning according to claim 1, characterized in that The S30 includes: Based on the physical layout and functional node distribution of the chip, construct a functional node topology structure, assign a feature vector to each functional node, extract a node feature matrix through a graph convolutional layer containing a multi-scale graph convolutional kernel, combine the attention mechanism to fuse the results of multiple graph convolutional layers to obtain a comprehensive node feature matrix, map the comprehensive node feature matrix to the chip heat distribution through a diffusion model to obtain a corrected heat distribution; add the first heat distribution and the corrected heat distribution to obtain a second heat distribution; Among them, ΔT(x, y, z, t) represents the corrected heat distribution, m represents the number of functional nodes, and W i (x, y, z) represents the spatial weight function of the i-th functional node, which is designed based on the Gaussian kernel functions in the three directions of x, y, and z. represents the final node feature vector of the i-th functional node extracted from the comprehensive node feature matrix, fnn() represents the feedforward neural network, and T (2) (x, y, z, t) represents the second heat distribution, and T (1) (x, y, z, t) represents the first heat distribution.

6. The intelligent analysis method of the heat conduction equation driven by deep learning according to claim 1, wherein The S40 includes: defining a local residual function by calculating the deviation degree of the second heat distribution from the heat conduction equation; calculating an anomaly score according to the local residual function and the second heat distribution, and determining that the point (x, y, z) at time t is a potential hot spot if the anomaly score S(x, y, z, t) is greater than the adaptive threshold λ(t); the formulas for the local residual function, the anomaly score, and the adaptive threshold are respectively: Among them, R(x, y, z, t) represents the local residual at the point (x, y, z) at time t, T (2) (x, y, z, t) represents the second heat distribution, ρ and c respectively represent the density and specific heat capacity of the chip material, represents the partial derivative of temperature with respect to time, D represents the diffusion coefficient tensor, represents the gradient operator, Q(x, y, z, t) represents the heat generation rate; S(x, y, z, t) represents the anomaly score, μ R (t) and σ R (t) respectively represent the time-varying mean and standard deviation of the local residual, μ T (t) and σ T (t) respectively represent the time-varying mean and standard deviation of the heat distribution; λ0 and λ1 represent the base threshold parameters, t represents the current time, t last represents the time of the last detected anomaly, τ adapt represents the time adaptation coefficient, exp() represents the exponential function with the natural constant as the base.

7. The intelligent analysis method for heat conduction equation driven by deep learning according to claim 1, characterized in that It further includes: S50, updating the parameters of the encoder-decoder network and the graph neural network through an incremental learning mechanism.

8. The intelligent analysis method for heat conduction equation driven by deep learning according to claim 7, characterized in that, The S50 includes: constructing an experience replay buffer, designing a knowledge distillation mechanism, comparing the prediction results of the current model with those of the historical model, and defining a knowledge distillation loss; estimating the importance of each parameter to the model performance through the Fisher information matrix, and introducing an elastic weight consolidation regularization term; during the training process, defining the total loss function of incremental learning to include the loss function of the current task, the knowledge distillation loss, and the regularization term; finally, designing an adaptive parameter update strategy, and selectively updating the parameters in the neural network according to the parameter importance and performance change, and the update rule is: Among them, θ new and θ old represent the parameters before and after the update, η represents the learning rate, represents the gradient of the total loss function L of incremental learning with respect to the parameter θ , s represents the parameter importance score, τ update represents the update threshold, and σ() represents the activation function.

9. An intelligent analysis system for heat conduction equations driven by deep learning, characterized in that, Running the intelligent analysis method for the heat conduction equation driven by deep learning according to any one of claims 7-8, including: a heat conduction initialization unit, an equation constraint analysis unit, a graph neural network correction unit, a hot spot analysis unit, and a parameter update unit, respectively running the S10, S20, S30, S40, and S50.

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