A neural network-based TSV three-dimensional SiP packaging thermal field distribution prediction method and system

Abstract

The application discloses a TSV three-dimensional SiP packaging thermal field distribution prediction method and system based on a neural network, and belongs to the field of electronic design automation.The method comprises the following steps: acquiring real-time power consumption distribution data of a TSV three-dimensional SiP packaging structure to be predicted; calculating a global linear temperature field of the packaging structure at a current time based on a pre-constructed reduced-order model; constructing an equivalent thermal resistance tensor of the packaging structure; inputting the global linear temperature field and the equivalent thermal resistance tensor into a pre-trained residual prediction neural network; and superimposing the global linear temperature field and a thermal residual field to obtain the final three-dimensional thermal field distribution of the packaging structure.The application effectively solves the nonlinear prediction problem caused by the decrease of thermal conductivity of silicon semiconductor material at high temperature.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of electronic design automation, and in particular to a neural network-based TSV three-dimensional SiP package thermal field distribution prediction method and system. BACKGROUND

[0002] With the slowing down of Moore's law, three-dimensional integrated circuits (3D-IC) and system-in-package (SiP) technologies have become a key way to improve system performance, reduce power consumption and reduce size by vertically stacking chips. In 3D-IC, through-silicon via (TSV) is the core technology for vertical interconnection between layers. However, the high-density stacking of power devices and the introduction of TSV structure result in a sharp increase in the internal heat flux of the package and the thermal field distribution becomes extremely complex. Excessive temperature can seriously affect the performance, reliability and life of the chip, so accurate and real-time thermal field prediction of the package structure is a prerequisite for dynamic thermal management (DTM).

[0003] Currently, there are mainly two methods for thermal simulation of 3D packages:

[0004] Traditional finite element analysis (FEM) or computational fluid dynamics (CFD) methods: such as using commercial software such as ANSYS Icepak, Flotherm, etc. This method is based on physical principles and has high accuracy, but the computational complexity is extremely high (usually exponentially or quadratically increasing with the number of grids). For a complex 3D package containing millions of grids, a transient thermal simulation may take several hours or even days, which is completely unable to meet the needs of online real-time thermal management (millisecond-level response).

[0005] Pure data-driven deep learning methods: use convolutional neural networks (CNN) and other models to directly learn the mapping relationship between power and temperature. This method has fast inference speed, but has significant drawbacks: lack of physical interpretability, it is a "black box" model; poor generalization ability, when the input power distribution or geometric structure changes slightly, the prediction error increases dramatically; and its prediction results often do not satisfy the law of conservation of energy, and are prone to "pseudo hot spots" that violate common sense.

[0006] Therefore, there is an urgent need for a thermal field prediction method that can maintain the accuracy and interpretability of physical methods, have the inference speed of deep learning methods, and properly handle the anisotropic thermal conduction and material thermal nonlinearity problems brought about by TSV microstructure. SUMMARY

[0007] One of the purposes of the present application is to provide a neural network-based TSV three-dimensional SiP package thermal field distribution prediction method to solve the problems of excessive calculation time, lack of physical interpretability, and difficulty in handling complex microstructure thermal characteristics in the prior art.

[0008] This invention is achieved through the following technical solution: a method for predicting the thermal field distribution of a TSV three-dimensional SiP package based on a neural network, comprising the following steps: acquiring real-time power consumption distribution data of the TSV three-dimensional SiP package structure to be predicted; calculating the global linear temperature field of the package structure at the current moment based on a pre-built reduced-order model; constructing an equivalent thermal resistance tensor of the package structure, wherein the equivalent thermal resistance tensor is calculated based on the volume ratio of different materials within the voxel of the package structure and a thermal resistance model, and is used to characterize the heat conduction characteristics in different directions; inputting the global linear temperature field and the equivalent thermal resistance tensor into a pre-trained residual prediction neural network, and using the temperature-sensing gating mechanism in the neural network to adaptively adjust the feature response, thereby predicting the thermal residual field caused by material nonlinearity and local microstructure; and superimposing the global linear temperature field and the thermal residual field to obtain the final three-dimensional thermal field distribution of the package structure.

[0009] Furthermore, the reduced-order model is constructed by projecting the high-dimensional physical space onto a low-dimensional subspace using the three-dimensional transient heat conduction partial differential equations and the techniques of eigenorthogonal decomposition and Galerkin projection.

[0010] Furthermore, the three-dimensional transient heat conduction partial differential equation can be expressed by the following equation:

[0011]

[0012] After discretization using the finite volume method (FVM), the following is obtained:

[0013]

[0014] in, For Nabla operators; The symbol is for partial differentials; Represents three-dimensional spatial coordinates ; The spatiotemporal temperature field distribution; It is the volumetric heat capacity, which typically exhibits a nonlinear relationship with temperature. The thermal conductivity tensor is a parameter that is spatially determined by the material distribution and numerically affected by temperature. Influence; Let be the volumetric power density. In the discretized equations, for Temperature vector of each grid node ( (Typically reaching millions) and They are respectively The global thermal capacity matrix and thermal conductivity matrix of the dimensionality represent the thermal inertia and thermal resistance characteristics of the system. This refers to the input power vectors of each functional module of the chip; is a power distribution mapping matrix used to accurately map the module-level power to specific grid nodes.

[0015] Further, the pre-trained residual prediction neural network model is trained by using a composite loss function comprising a data-driven loss term and a physical constraint loss term; the physical constraint loss function comprises a data-driven loss term and a physical residual regularization term; wherein the physical residual regularization term is used to constrain the final temperature field output by the network to satisfy the energy conservation law defined by the three-dimensional transient heat conduction partial differential equation.

[0016] Further, the step of calculating the global linear temperature field of the packaging structure at the current time comprises: constructing a reduced-order differential equation set in the low-dimensional subspace based on the real-time power consumption distribution data; solving the reduced-order differential equation set by using an implicit time integration format to obtain low-dimensional modal coefficients; and performing linear reconstruction by using the low-dimensional modal coefficients and the pre-extracted orthogonal basis functions to map back to the physical space to obtain the global linear temperature field.

[0017] Further, the mapping process and the final reduced-order differential equation set can be represented by the following formula:

[0018] wherein, , and are pre-computed micro-matrices, is a pre-computed dimensional micro-matrix, is the reduced input matrix, so the above formula can be simplified as: wherein, is a low-dimensional time coefficient vector comprising elements, and the dimension of the low-dimensional time coefficient vector is much smaller than the original dimension .

[0019] Further, the linear reconstruction, mapping back to the physical space to obtain the global linear temperature field can be represented by the following formula: ,

[0020] wherein, is a time step; is a modal coefficient vector of the next time step to be solved; is the input power of the next time step; is the reconstructed global linear temperature field, is the coefficient of the th mode obtained by solving the reduced-order differential equation; is the th spatial basis function.

[0021] Furthermore, the process of constructing the reduced-order model includes: establishing a three-dimensional thermal finite element model of the encapsulation structure, obtaining a temperature field snapshot matrix through transient thermal simulation; performing singular value decomposition on the snapshot matrix, extracting the first k modes whose energy proportion exceeds a preset threshold as orthogonal basis functions; and using the orthogonal basis functions, projecting the system matrix of the original high-dimensional heat conduction equation to a k-dimensional subspace through Galerkin projection to generate a reduced-order system matrix.

[0022] Furthermore, the singular value decomposition of the snapshot matrix can be expressed by the following formula:

[0023] , ,in, This is a snapshot matrix that compiles temperature vectors at different times; This is the result of singular value decomposition; For the truncated form from the front A basis function matrix consisting of principal modes. The matrix retains only the first few lines. The mode with the highest energy; the selection criterion is usually based on the energy criterion, i.e. This ensures that the vast majority of physical information is preserved; For the first Singular values ​​of each mode, For the first The singular values ​​of the i-th mode represent the i-th mode. and Energy of each mode; The number of modes retained after truncation ( The selection criterion is that the cumulative energy percentage exceeds 99%. For the reason before The projection basis matrix consists of several principal modes; subsequently, the original high-dimensional equation is projected onto this low-dimensional subspace using Galerkin projection, by left-multiplying both sides of the original equation by the transpose of the basis function matrix. This compresses high-dimensional matrices into miniature matrices.

[0024] Furthermore, the residual prediction neural network adopts a 3D-ResNet network architecture; the temperature-sensing gating mechanism in the residual prediction neural network is used to adaptively adjust the feature response, specifically including: setting a critical temperature threshold for material thermal nonlinearity; determining whether the local temperature in the global linear temperature field exceeds the critical temperature threshold; if it exceeds, activating the gating mechanism to amplify the feature response of the neural network in the corresponding region to compensate for the additional temperature rise caused by the decrease in the thermal conductivity of the material at high temperatures.

[0025] Further, in calculating the physical residual regular term, a weight given to a TSV silicon hole region in the packaging structure is greater than a weight of a non-TSV region, so as to strengthen the constraint on the local hotspot region physical consistency.

[0026] Further, the thermal field distribution prediction method further comprises: transmitting the obtained final three-dimensional thermal field distribution to a dynamic thermal management controller; and the dynamic thermal management controller performs task scheduling or working frequency adjustment on the microprocessor chip in the packaging structure according to the thermal field distribution.

[0027] Another aspect of the present application provides a neural network-based TSV three-dimensional SiP packaging thermal field distribution prediction system, comprising a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the neural network-based TSV three-dimensional SiP packaging thermal field distribution prediction method as described above when executing the program.

[0028] Compared with the prior art, the present application has the following advantages and beneficial effects:

[0029] 1. The present application adopts a hybrid architecture of reduced order model (ROM) + residual neural network, first uses the reduced order model to project the high-dimensional heat conduction equation set of the million-level grid to a subspace with extremely low dimension, realizes the avalanche-like reduction of the calculation complexity, and can quickly capture the global heat flow trend; then, only a lightweight neural network is used to predict the local nonlinear residual, and this divide-and-conquer strategy enables the present application to maintain the high precision comparable to the commercial FEM software (such as ANSYS) while improving the inference speed, realizes fast response, and provides real-time and accurate thermal field data support for the online dynamic thermal management (DTM) and task scheduling of three-dimensional chips.

[0030] 2. The present application abandons the blind learning mode of the pure data-driven model, and instead introduces an equivalent thermal resistance tensor as a physical coding feature, constructs a vertical parallel model and a horizontal series model, explicitly injects the physical properties of the TSV microstructure into the neural network, so that the neural network does not need to guess the influence of the structure with a large amount of training data, but directly infers based on the input physical tensor, which not only significantly improves the representation ability of the model for complex heterogeneous structures, but also greatly improves the generalization ability of the model under different TSV densities and different packaging processes.

[0031] 3、The application integrates a temperature perception gating mechanism in the neural network, which acts as an intelligent nonlinear switch, when the local area temperature exceeds the material linear threshold, the feature response weight of the area is automatically activated and amplified, forcing the network output higher temperature rise residual, through this adaptive compensation mechanism, ensures that the model can maintain high prediction accuracy in the full temperature range from low temperature standby to high temperature full load, effectively solves the problem of inaccurate prediction of thermal runaway risk at high temperature.

[0032] 4、The application introduces a physical constraint loss term based on the heat conduction partial differential equation in model training, forcing the predicted thermal field distribution to meet the heat flow continuity principle, not only eliminating the pseudo hot spot phenomenon, ensuring the physical consistency of the result, but also significantly reducing the dependence of the model on a large amount of high-precision label data, so that even with fewer simulation samples for training, a robust model can be trained. BRIEF DESCRIPTION OF DRAWINGS

[0033] The drawings described herein are used to provide further understanding of the embodiments of the application, constitute a part of the application, and do not constitute a limitation on the embodiments of the application. In the drawings:

[0034] Figure 1 The method flowchart provided for embodiment 1 of the application.

[0035] Figure 2 The schematic diagram of the three-dimensional TSV packaging structure physical model provided for embodiment 1 of the application.

[0036] Figure 3 The modal energy truncation schematic diagram provided for embodiment 1 of the application.

[0037] Figure 4 The two-dimensional slice diagram provided for embodiment 1 of the application.

[0038] Figure 5 The full-order physical model and reduced-order model transient response comparison diagram provided for embodiment 1 of the application.

[0039] Figure 6 The schematic diagram of the basic linear field provided for embodiment 1 of the application.

[0040] Figure 7 The anisotropic equivalent thermal conductivity change relationship diagram provided for embodiment 1 of the application.

[0041] Figure 8 The response curve diagram of the temperature perception gating mechanism provided for embodiment 1 of the application.

[0042] Figure 9 The loss function convergence curve diagram provided for embodiment 1 of the application. DETAILED DESCRIPTION

[0043] For the purposes of making the objects, technical solutions, and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are some but not all of the embodiments of the present application. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0044] Embodiment 1

[0045] The embodiment discloses a neural network-based TSV three-dimensional SiP packaging thermal field distribution prediction method, which aims to solve the problem that traditional finite element simulation (FEM) calculation is too time-consuming and cannot meet the online real-time thermal management requirements, and overcome the defects of pure data-driven models, such as lack of physical interpretability and poor generalization ability.

[0046] The embodiment takes a typical dual-chip stacked (3D-IC) packaging structure as an object for illustration, which includes an upper high-performance microprocessor chip (MPU) and a lower dynamic random access memory chip (DRAM); both chips have a size of 10 mm x 10 mm and are vertically interconnected through a 10x10 array of through-silicon vias (TSVs). The embodiment details how to apply the method of the present application to achieve online, real-time, and high-precision thermal field prediction for the packaging structure.

[0047] Figure 1 The overall method flowchart in the embodiment is shown, and it can be seen from the figure that the embodiment includes the following steps:

[0048] Step 1: First, during the product design and simulation stage, an order-reduction model is constructed offline to represent the thermodynamic characteristics of the specific 3D-IC packaging structure, a high-efficiency, low-dimensional thermal modal basis function library is generated, and a corresponding system matrix is established.

[0049] A complete three-dimensional thermal model of the 3D-IC packaging is established using a commercial finite element analysis software (such as ANSYS Icepak), which accurately defines the geometric dimensions, spatial layout, and material properties of each component, such as the silicon substrates (thermal conductivity K si ≈ 150 W / m·K) of the MPU and DRAM chips, the TSV copper pillars (K cu ≈ 400 W / m·K), the silicon dioxide dielectric layer (K sio2 ≈ 1.4 W / m·K) around the TSV, and the micro-bumps and BGA at the bottom, and the entire model is divided into about 1 million tetrahedral mesh elements. Figure 2A schematic diagram of a three-dimensional TSV package structure physical model is shown, which is a three-dimensional package unit for building a physical control equation. The central columnar TSV (copper, high thermal conductivity area) is surrounded by the surrounding medium layer (low thermal conductivity area) and the underlying silicon substrate. This geometric and material heterogeneity is the main reason for the complexity of the traditional model calculation and the physical basis for building the anisotropic thermal resistance tensor subsequently.

[0050] Step 2: Then, the physical basis describing the heat flow evolution of the dual-chip package structure is established. For the complex distribution of the silicon substrate, copper TSV and silicon dioxide medium layer in the MPU and DRAM stacked structure, a three-dimensional transient heat conduction partial differential equation is defined.

[0051] Specifically, by establishing a physical benchmark model describing the transient heat conduction mechanism of the three-dimensional package structure, and by constructing a low-dimensional characteristic subspace through the reduction technique, the high-dimensional physical problem is converted into a discrete form suitable for numerical calculation.

[0052] Specifically, in order to predict the thermal distribution in the chip package structure, the basic physical law controlling the flow and storage of thermal energy must be defined. For the three-dimensional transient heat conduction problem, the core is to balance the storage rate of thermal energy, the diffusion of heat flow and the generation of internal heat source. By introducing a three-dimensional transient heat conduction partial differential equation, the benchmark state of different material properties varying with space and temperature in the physical field is defined. Considering the strong spatial non-uniformity between silicon, copper and medium layer in the TSV package, as well as the nonlinear characteristics of the decrease of material thermal conductivity at high temperature, in this embodiment, a control equation containing volume heat capacity, thermal conductivity tensor and volume power density is constructed.

[0053] Exemplarily, in this embodiment, the three-dimensional transient heat conduction partial differential equation can be expressed by the following formula:

[0054]

[0055] After being discretized by the finite volume method (FVM), the following is obtained:

[0056]

[0057] Wherein, is the Nabla operator; is the partial differential symbol; represents the three-dimensional space coordinates ; is the space-time temperature field distribution; is the volume heat capacity, which usually shows nonlinearity with temperature; is the thermal conductivity tensor, which is determined by the material distribution (silicon, copper or medium) in space and is affected by temperature in numerical value; ​ Let be the volumetric power density. In the discretized equations, for Temperature vector of each grid node ( (Typically reaching millions) To represent this N The rate of temperature change of each node over time; and They are respectively The global thermal capacity matrix and thermal conductivity matrix of the dimensionality represent the thermal inertia and thermal resistance characteristics of the system. This refers to the input power vectors of each functional module of the chip; This is a power distribution mapping matrix used to accurately map module-level power to specific grid nodes.

[0058] Step 3: After dividing the continuous physical space into a grid using the finite volume method, the partial differential equations are transformed into a system of high-dimensional ordinary differential equations. However, considering the excessive computational cost of directly solving the system of equations with millions of nodes, this embodiment employs intrinsic orthogonal decomposition (POD) and Galerkin projection to construct a reduced-order model, thereby reducing the order of the discretized partial differential equations.

[0059] Specifically, the main characteristic modes of thermal field evolution are extracted through intrinsic orthogonal decomposition. This is achieved by collecting snapshots of the transient temperature field and performing singular value decomposition to extract the most energy-concentrated frontier modes. one mode ( As orthogonal basis functions, in this embodiment, the energy percentage of the first few atoms can be selected to be greater than 99%. The system is truncated using several modes as basis functions, and the original high-dimensional matrix is ​​projected onto this low-dimensional subspace using Galerkin projection, thus obtaining a set of reduced-order differential equations with minimal computational cost. During online execution, the global linear temperature field distribution can be quickly reconstructed simply by solving for the low-dimensional coefficients using an implicit time integration scheme and mapping them back to the physical space. Figure 3 The diagram illustrates the modal energy truncation of this embodiment. The diagram shows the curve of the cumulative energy percentage as the number of modes increases after singular value decomposition of the transient heat flux snapshot matrix. It can be seen from the figure that the curve rises rapidly in the initial stage. Only the first 30 modes (k=30) are needed to cover 99% of the energy characteristics of the original data. In other words, the scheme in this embodiment successfully and safely projects physical equations with millions of degrees of freedom into a very low-dimensional subspace with almost no loss of accuracy.

[0060] For example, in this embodiment, the snapshot matrix decomposition and basis function selection can be expressed by the following formula:

[0061]

[0062]

[0063] where, is the snapshot matrix which collects the temperature vector at different time instants; is the result of singular value decomposition; is the truncated basis function matrix composed of the first principal modes, which only retains the first modes with the largest energy (e.g. ), is the first principal mode with the largest energy (or eigenvalue / singular value) in the system, is the second principal mode with the second largest energy; is the retained k th principal mode, which is the truncation point, and the modes ranked after k are discarded, k The selection criterion of is usually based on the energy criterion, i.e. , to ensure that most of the physical information is retained; is the singular value of the th mode, is the singular value of the th mode, representing the energy of the th and th modes; is the number of retained modes after truncation ( ), whose selection criterion is that the cumulative energy ratio exceeds 99%; is the projection basis matrix composed of the first principal modes.

[0064] Subsequently, the original high-dimensional equation is projected into this low-dimensional subspace using Galerkin projection, and the high-dimensional matrix is compressed into a micro-matrix by left multiplying the transpose of the basis function matrix on both sides of the original equation .

[0065] Exemplarily, in the present embodiment, the projection process and the final reduced-order model can be represented by the following formula:

[0066]

[0067] where, , and are pre-computed micro-matrices, is the pre-computed -dimensional micro-matrix, is the reduced-order input matrix, so the above formula can be simplified as:

[0068]

[0069] wherein, is a low-dimensional time coefficient vector containing elements, whose dimension is much smaller than the original dimension , which realizes the avalanche reduction of computational complexity from to , making it possible to perform millisecond-level inference on resource-constrained hardware, laying the foundation for online real-time prediction; is the derivative (i.e., the rate of change) of the low-dimensional time coefficient vector with respect to time t , which represents the evolution speed of the reduced-order system state over time.

[0070] After the above simplification process, in the online running phase, only the low-dimensional equation needs to be solved, and in order to ensure numerical stability, implicit Euler format can be used for time integration, and basis functions can be used to reconstruct the global linear temperature field in the physical space. Figure 4 The two-dimensional slice diagram of the first k basis functions in the embodiment is shown. Mode 1 (left), representing the global average temperature rise trend (low-frequency main part); mode 2 (middle), representing the temperature gradient on the left and right sides; mode 30 (right), representing high-frequency local hot spot details; that is, when the algorithm is running online, it is essentially calculating the weighted combination of these fixed shapes, so as to instantly obtain the basic temperature distribution.

[0071] Exemplarily, in the online prediction and reconstruction process in the embodiment, the following formula can be used:

[0072]

[0073]

[0074] wherein, is the time step; is the next time modal coefficient vector to be solved; is the input power at the next time; is the reconstructed basic linear field, is the coefficient of the first modal obtained by solving the reduced-order differential equation; is the first spatial basis function.

[0075] Figure 5The full-order physical model and the reduced-order model transient response comparison chart in the embodiment is shown, which shows the effect and limitation of the reduced-order model in the step. As can be seen from the true value (FOM) and the ROM predicted value in the figure, although the linear ROM successfully captures the general trend of temperature rise, there are obvious errors in the red filled area (high temperature area and oscillation details), that is, it is not enough to rely on ROM alone, and a neural network must be introduced for nonlinear correction. Figure 6 The schematic diagram of the final reconstructed basic linear field in the embodiment is shown. As can be seen from the figure, the surface is smooth and continuous, and clearly reflects the overall trend of heat diffusion from the high-power area to the surrounding area. Although it does not yet contain the microscopic details of the TSV, the calculation time is greatly reduced, and an accurate physical baseline is provided for subsequent refinement.

[0076] Step 4: In the previous step, the reconstructed basic linear field is finally obtained, which captures the main diffusion trend of the heat flow. However, due to the linear superposition, it is difficult to accurately reflect the blocking or accelerating effect of the complex microstructure of the TSV area on the heat flow, as well as the local thermal bridge effect and the nonlinearity of the material. Therefore, in the embodiment, an equivalent thermal resistance tensor (ETRT) is introduced to physically encode the geometric structure; according to the volume ratio of copper (high thermal conductivity) and medium (low thermal conductivity) in each voxel, the equivalent thermal conductivity in different directions is calculated by using parallel and series thermal resistance models respectively, thereby explicitly describing the physical fact that heat flow is easy to flow in the Z-axis direction, but is blocked in the XY plane.

[0077] Specifically, for each voxel in the package, instead of considering it as a single material, according to the volume ratio of copper (TSV) and medium (dielectric) inside it, Specifically, for each voxel in the package, instead of considering it as a single material, according to the volume ratio of copper (TSV) and medium (dielectric) inside it,

[0078] Further, in order to deal with the nonlinearity problem of the thermal conductivity of the material changing with temperature, the embodiment introduces a temperature-aware gating mechanism. By setting a critical temperature threshold, when the basic linear temperature exceeds the threshold, the gating unit is activated to amplify the feature response, so that the network can adaptively predict higher temperature rise residuals.

[0079] Specifically, in the embodiment, the equivalent thermal resistance tensor and the anisotropy calculation of the TSV unit can be as follows:

[0080]

[0081] For the TSV area (assuming the copper ratio is 50%), the equivalent thermal resistance tensor can be calculated as follows: ), the Z-axis direction behaves as a high thermal conductive path (parallel thermal resistance model), while the X / Y-axis direction behaves as a thermal resistance barrier (series thermal resistance model), and the specific model can be shown as follows:

[0082]

[0083]

[0084] is the Z-axis thermal conductivity, and a parallel model (weighted sum) is adopted, which reflects the low resistance characteristics of the current / thermal flow along the TSV high thermal conductive path; is the horizontal direction thermal conductivity, and a series model (reciprocal sum) is adopted, which reflects the thermal resistance barrier effect when the thermal flow transversely passes through the low thermal conductive medium layer; is the volume fraction of copper in the voxel; are the thermal conductivities of copper and medium, respectively. Figure 7 The anisotropic equivalent thermal conductivity variation relationship based on the TSV volume fraction in the embodiment is shown in the figure, which shows the relationship between the equivalent thermal conductivity and the TSV volume fraction. It can be seen from the figure that the Z-axis (parallel model) thermal conductivity linearly increases with the copper content, showing high thermal conductivity; while the XY-axis (series model) thermal conductivity is limited by the medium layer and always maintains at a low level. This anisotropy difference of up to two orders of magnitude is the key prior knowledge input to the neural network.

[0085] Then, in order to correct the linear error brought by the reduced order model and the deviation caused by the change of material thermal conductivity with temperature (thermal nonlinearity), a lightweight 3D-ResNet neural network is constructed in the embodiment to predict the residual error. In particular, a temperature perception gating mechanism is introduced, which takes the linear predicted temperature as input. When the temperature exceeds the nonlinear critical point of the material, the neural network feature response is adaptively amplified, so as to accurately compensate the additional temperature rise at high temperature. Finally, the linear field and the residual field predicted by the neural network are added to obtain the final temperature field.

[0086] Exemplarily, the input construction, gating mechanism and residual output of the neural network in the embodiment are shown as follows:

[0087]

[0088]

[0089]

[0090]

[0091] wherein, is the basic linear field and the equivalent thermal resistance tensor The concatenated input tensor; This refers to the thermal nonlinear critical temperature of a material (e.g., the thermal conductivity of silicon changes significantly above 80°C). This represents the Sigmoid activation function; when the predicted temperature exceeds... At that time, gating weight Increasing and amplifying the characteristic response forces the network to predict higher temperature rise residuals to compensate for errors caused by material nonlinearity. Hadamard product operation, gating mechanism dynamically adjusts convolution features The intensity. This is the final synthesized temperature field. Finally, the linear prediction result is added to the residual of the neural network prediction to obtain the final accurate thermal field distribution. For example, in this embodiment, the final thermal field synthesis formula is as follows: .

[0092] Figure 8 The response curve of the temperature-sensing gating mechanism in this embodiment is shown, illustrating the change of gating weights with the temperature of the basic linear field. When the temperature is below the critical value (set to 80°C in this embodiment), the weights are low, and the model mainly relies on linear prediction. When the temperature exceeds the threshold and enters the nonlinear correction region, the Sigmoid function is activated, the weights rise rapidly, and the neural network focuses on compensating for the deviation caused by the high-temperature nonlinearity of the material.

[0093] Meanwhile, to ensure that the trained neural network conforms to the law of conservation of energy and does not produce predictions that violate physical principles, this embodiment can also use a physical constraint loss function as the optimization objective. This objective function not only includes the data-driven mean square error but also introduces a regularization term based on the residuals of partial differential equations, thereby forcing the network to learn the nature of heat conduction, enabling it to output results that satisfy energy conservation even when training data is lacking.

[0094] For example, in this embodiment, the total loss function is defined as follows:

[0095]

[0096] in, Mean squared error loss is used to measure the difference between the predicted value and the true value (simulation data).

[0097]

[0098] and For physical residual loss, local thermal equilibrium constraints based on steady-state assumptions:

[0099]

[0100] In the above formula, denotes the square of L2 norm (Euclidean norm), which represents the square of the size of the error or residual. In the training process of the neural network, this square of L2 norm is used to quantify the degree of deviation between the predicted value and the target value (or physical constraint). Figure 9 The loss function convergence curve in the physical constraint training process of the embodiment is shown, which shows the downward trend of the total loss, data error and physical residual in the training process. The convergence of the physical residual loss indicates that the temperature field predicted by the network not only fits the data, but also strictly obeys the law of conservation of energy, proving that the model has physical interpretability and good generalization ability. It should be noted that, the gradient of can be calculated by automatic differentiation or Sobel operator. In the summation process, higher weights can also be given to the TSV area to strengthen the constraint of physical consistency in the local hot spot area. By minimizing the comprehensive loss function, the model can achieve high-precision fitting and strict physical conservation at the same time. In the training process, the predicted is substituted into the above equation to verify whether it satisfies the law of conservation of energy, especially in the TSV dense area. This loss term can force the residual learned by the neural network to comply with the heat flow continuity principle, preventing the occurrence of pseudo hot spots or cold spots that violate the physical law. Finally, the output fine temperature field is transmitted to the dynamic thermal management controller for guiding the task scheduling and frequency adjustment of the MPU.

[0101] The above specific embodiments further illustrate the purpose, technical solutions and beneficial effects of the present application. It should be understood that the above description is only a specific embodiment of the present application and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for predicting the thermal field distribution of a TSV three-dimensional SiP package based on a neural network, characterized in that, The thermal field distribution prediction method includes: Acquire real-time power distribution data of the TSV 3D SiP package structure to be predicted; Based on a pre-built reduced-order model, the global linear temperature field of the encapsulation structure at the current moment is calculated; The equivalent thermal resistance tensor of the encapsulation structure is constructed. The equivalent thermal resistance tensor is calculated based on the volume ratio of different materials in the voxel of the encapsulation structure and the thermal resistance model. It is used to characterize the heat conduction characteristics in different directions. The global linear temperature field and the equivalent thermal resistance tensor are input into a pre-trained residual prediction neural network. The feature response is adaptively adjusted using the temperature-sensing gating mechanism in the neural network to predict the thermal residual field caused by material nonlinearity and local microstructure. The global linear temperature field is superimposed with the thermal residual field to obtain the final three-dimensional thermal field distribution of the packaging structure.

2. The method for predicting the thermal field distribution of TSV three-dimensional SiP packaging based on neural networks according to claim 1, characterized in that, The reduced-order model is constructed by projecting the high-dimensional physical space onto a low-dimensional subspace using the three-dimensional transient heat conduction partial differential equation, employing eigenorthogonal decomposition and Galerkin projection techniques.

3. The method for predicting the thermal field distribution of TSV three-dimensional SiP packaging based on neural networks according to claim 1, characterized in that, The pre-trained residual prediction neural network model is trained using a composite loss function that includes a data-driven loss term and a physical constraint loss term. The physical constraint loss function includes a data-driven loss term and a physical residual regularization term; The physical residual regularization term is used to constrain the final temperature field output by the network to satisfy the energy conservation law defined by the three-dimensional transient heat conduction partial differential equation.

4. The method for predicting the thermal field distribution of TSV three-dimensional SiP packaging based on neural networks according to claim 1 or 2, characterized in that, The steps for calculating the global linear temperature field of the packaging structure at the current moment specifically include: Based on the real-time power consumption distribution data, a reduced-order differential equation system is constructed in the low-dimensional subspace; The reduced-order differential equations are solved using an implicit time integration scheme to obtain low-dimensional modal coefficients. The low-dimensional modal coefficients are linearly reconstructed using pre-extracted orthogonal basis functions and mapped back to the physical space to obtain the global linear temperature field.

5. The method for predicting the thermal field distribution of TSV three-dimensional SiP packaging based on neural networks according to claim 1, characterized in that, The process of constructing the reduced-order model includes: A three-dimensional thermal finite element model of the encapsulation structure was established, and the temperature field snapshot matrix was obtained through transient thermal simulation. Singular value decomposition is performed on the snapshot matrix, and the top k modes whose energy percentage exceeds a preset threshold are extracted as orthogonal basis functions; Using the orthogonal basis functions, the system matrix of the original high-dimensional heat conduction equation is projected to a k-dimensional subspace through Galerkin projection, generating a reduced-order system matrix.

6. The method for predicting the thermal field distribution of TSV three-dimensional SiP packaging based on neural networks according to claim 1, characterized in that, The step of constructing the equivalent thermal resistance tensor of the packaging structure specifically includes: For each voxel after the discretization of the packaging structure, determine the volume ratio of its internal metal material to dielectric material; The equivalent thermal conductivity of the voxel in the plane perpendicular to the stacking direction is calculated based on the parallel thermal resistance model, and the equivalent thermal conductivity of the voxel in the stacking direction is calculated based on the series thermal resistance model. The equivalent thermal resistance tensor with anisotropic characteristics is constructed based on the equivalent thermal conductivity in different directions.

7. The method for predicting the thermal field distribution of TSV three-dimensional SiP packaging based on neural networks according to claim 3, characterized in that, The residual prediction neural network adopts a 3D-ResNet network architecture; The feature response is adaptively adjusted using the temperature-sensing gating mechanism in the residual prediction neural network, specifically including: Set the critical temperature threshold for the thermal nonlinearity of the material; Determine whether the local temperature in the global linear temperature field exceeds the critical temperature threshold. If the threshold is exceeded, the gating mechanism is activated to amplify the characteristic response of the neural network in the corresponding region to compensate for the additional temperature rise caused by the decrease in the thermal conductivity of the material at high temperatures.

8. The method for predicting the thermal field distribution of TSV three-dimensional SiP packaging based on neural networks according to claim 3, characterized in that, When calculating the physical residual regularization term, the weight assigned to the TSV (Through Silicon Via) region in the packaging structure is greater than the weight assigned to the non-TSV region, so as to strengthen the constraint on the physical consistency of local hot spot regions.

9. The method for predicting the thermal field distribution of TSV three-dimensional SiP packaging based on neural networks according to claim 1, characterized in that, The thermal field distribution prediction method also includes: The obtained final three-dimensional thermal field distribution is transmitted to the dynamic thermal management controller; The dynamic thermal management controller performs task scheduling or operating frequency adjustment for the microprocessor chip in the package structure based on the thermal field distribution.

10. A neural network-based TSV three-dimensional SiP packaging thermal field distribution prediction system, characterized in that, The prediction system includes: processor; The memory stores a computer program that, when executed by a processor, implements the neural network-based method for predicting the thermal field distribution of TSV three-dimensional SiP packaging as described in any one of claims 1 to 9.

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