Chip packaging material design method and system based on multi-task learning neural network

Abstract

The application discloses a chip packaging material design method and system based on a multi-task learning neural network, which comprises the following steps: label coding the category features of formula data and mapping the label coded category features into dense continuous vectors through a learnable linear embedding layer, and splicing the dense continuous vectors with numerical features to obtain input feature vectors; a multi-task performance prediction model composed of a shared feature extraction network and multiple task-specific output networks is constructed; a two-stage progressive training strategy is adopted to train the learnable linear embedding layer and the model, in the first stage, the embedding layer, the shared layer and all task heads are jointly trained, and a gradient balance mechanism is introduced to dynamically adjust the loss weight, in the second stage, the parameters of the embedding layer and the shared layer are frozen, and only the task heads are fine-tuned; the trained embedding layer and the model are used to batch predict multiple performance indicators, and the optimal formula is output according to the constraint conditions and the weight. The application can realize high-precision synchronous prediction of multiple performances under the condition of a small sample and automatically recommend the optimal formula, and the research and development cycle is significantly shortened.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of chip packaging and computational materials science, specifically involving a chip packaging material design method and system based on a multi-task learning neural network. Background Technology

[0002] As Moore's Law approaches its physical limits, simply relying on shrinking feature sizes to improve chip performance is becoming increasingly difficult and costly. Against this backdrop, advanced packaging technology, as a key solution for continuously improving system performance in the post-Moore's Law era, has received widespread attention from industry and academia. To meet the urgent demands of electronic products for higher performance, greater reliability, richer functionality, and smaller size, advanced packaging is driving the rapid development of chip structures towards higher integration, higher complexity, and higher power density.

[0003] In the packaging material system, epoxy resin has become an indispensable basic material due to its excellent mechanical properties, electrical insulation properties, ease of processing, low cost, and excellent adhesive properties. Especially in the field of integrated circuit (IC) packaging, epoxy-based thermosetting materials account for as much as 90%. From traditional packaging to high-performance packaging to advanced packaging, each generation of chip iteration has put forward different requirements for the performance of packaging materials, making the diversified design of packaging materials key to meeting different packaging needs. As packaging structures become increasingly complex and power density continues to rise, chip packaging materials face more stringent performance challenges: materials not only need to have excellent mechanical properties to protect the fragile chip structure and good electrical insulation to ensure interconnect reliability, but also must have excellent thermal management capabilities to cope with the heat dissipation problems caused by high heat flux density, while meeting the requirements of advanced packaging processes for material flowability and molding precision.

[0004] In general, the optimization design of chip packaging materials mainly involves two technical paths: one is the exploration of novel particle filling and gradation strategies, and the other is the exploration of novel epoxy resin crosslinking systems. However, both of these material design paths require extensive experimental data acquisition, which is time-consuming and costly, and few studies can simultaneously consider the synergistic design of the filling system and the matrix crosslinking system. Furthermore, due to high testing costs and limited testing conditions, the obtained datasets are generally incomplete, further exacerbating the difficulties in material development. In addition, the design of chip packaging materials typically needs to consider multiple performance indicators, and in the process of optimizing these multiple performance indicators, there are often complex interrelationships between them. How to synergistically optimize these interdependent performance indicators has become a technical challenge. Therefore, there is an urgent need for a material design method that can efficiently predict multiple performance characteristics and achieve rapid formulation recommendation using limited, highly incomplete data.

[0005] Therefore, there is an urgent need to develop a material design method that can use limited small samples and high missing data to achieve efficient prediction of multiple properties and quickly recommend optimized formulations. Summary of the Invention

[0006] To address the aforementioned issues, this invention proposes a chip packaging material design method and system based on a multi-task learning neural network. By densely encoding class features through a learnable linear embedding layer, and combining a shared residual feature network with a multi-task output network, as well as a two-stage progressive training strategy, this method achieves high-precision synchronous prediction of multiple performance indicators of chip packaging materials and automatic recommendation of optimal formulations under conditions of small sample size and high data loss.

[0007] The technical solution adopted in this invention is as follows:

[0008] In a first aspect, the present invention discloses a chip packaging material design method based on a multi-task learning neural network, comprising the following steps:

[0009] S1. Feature encoding is performed on the formulation data of chip packaging materials. During feature encoding, the category features in the formulation data are first encoded by labels and mapped into dense continuous vectors through a learnable linear embedding layer. Then, they are concatenated with numerical features to obtain an input feature vector of the same dimension.

[0010] S2. Construct a multi-task performance prediction model. The model includes a shared feature extraction network and multiple task-specific output networks. The shared feature extraction network is composed of a linear mapping layer and multiple residual connection modules stacked together. Each task-specific output network consists of a residual connection module and a performance output layer. The performance includes the coefficient of thermal expansion, glass transition temperature, flexural strength, Young's modulus, thermal conductivity, and viscosity.

[0011] S3. A two-stage progressive training strategy is adopted to train the learnable linear embedding layer and the multi-task performance prediction model. In the first stage, the learnable linear embedding layer, the shared feature extraction network, and all task-specific output networks are jointly trained, and a gradient balancing mechanism is introduced during the training process to dynamically adjust the loss weights of each task. In the second stage, the parameters of the learnable linear embedding layer and the shared feature extraction network are frozen, and only the all-task-specific output networks are fine-tuned.

[0012] S4. Utilize the trained learnable linear embedding layer and multi-task performance prediction model to predict multiple performance indicators in batches within the feasible domain of the formulation, and output the optimal formulation based on the user-defined constraints and performance weights.

[0013] Furthermore, the category characteristics include monomer type, curing agent type and filler particle type, and the numerical characteristics include total filler volume fraction, particle size of each particle and relative volume fraction of each particle.

[0014] Furthermore, in the formula data, there is one type of filler particle, and the particle size specification of this filler particle is at most three types; the learnable linear embedding layer maps 3-dimensional category features to dense continuous vectors, and the dimension of the dense continuous vectors is greater than 3; the linear mapping layer in the shared feature extraction network maps the input feature vector of the same dimension to the same dimension as the input and output dimensions of the residual connection module.

[0015] Furthermore, the residual connection modules in the shared feature extraction network and all task-specific output networks have the same structure. Each residual connection module includes two fully connected layers, and a noise module is provided before each fully connected layer to inject Gaussian noise during the training phase.

[0016] Furthermore, the standard deviation of the Gaussian noise is set to 0.005 to 0.05.

[0017] Furthermore, each fully connected layer is followed by a ReLU activation function and a Dropout layer; the dropout rate of the Dropout layer is set to 0 to 0.5.

[0018] Furthermore, in the task-specific output network, the dropout rate of each Dropout layer is set differently according to different performance prediction tasks. Specifically, for tasks predicting thermal expansion coefficient, glass transition temperature, and Young's modulus, the dropout rate is set to 0–0.2; for tasks predicting flexural strength, the dropout rate is set to 0.1–0.3; for tasks predicting thermal conductivity, the dropout rate is set to 0–0.2; and for tasks predicting viscosity, the dropout rate is set to 0.3–0.5.

[0019] Furthermore, the gradient balancing mechanism includes:

[0020] A learnable scalar parameter is assigned to each performance prediction task, and the dynamic loss weight of the task is obtained by mapping the scalar parameter.

[0021] After each training batch, the gradient norm of each task relative to the parameters of the shared feature extraction network is calculated based on the average loss of each task and the current dynamic loss weights; the average gradient norm of all tasks in the current training round is taken as the average gradient norm.

[0022] The target gradient for each task is obtained by multiplying the average gradient norm by a specified power of the relative loss rate of each task; the relative loss rate is the proportion of the current average unweighted loss of the task to the sum of the average unweighted losses of all tasks; the specified power is an asymmetric hyperparameter, preferably 0.12 to 0.22.

[0023] The sum of squared differences between the gradient norm of each task and the target gradient is calculated to obtain the gradient balancing loss, and the learnable scalar parameters of each task are updated based on the gradient balancing loss.

[0024] Furthermore, the average loss for each task is as follows: after each training batch, the mean squared error loss of each sample in each task within that batch is accumulated, and then divided by the total number of samples for that task within that batch to obtain the average loss of that task in that training round.

[0025] Furthermore, the gradient balancing mechanism is only executed in the first training phase. In the second training phase, the gradient balancing mechanism is stopped while the shared feature extraction network is frozen, and the dynamic loss weights of each task are no longer updated.

[0026] Furthermore, the step of outputting the optimal formula based on user-defined constraints and performance weights includes:

[0027] Based on the upper and lower limits of various performance indicators set by the user, candidate formulations that meet the conditions are screened from the database; the performance indicators of each candidate formulation are normalized, and a comprehensive score is calculated in combination with the performance weights set by the user; the formulations are sorted in descending order of comprehensive score, and the top-scoring recommended formulations are output, along with a radar chart comparing the predicted performance indicators of the recommended formulations with the user's target requirements.

[0028] Secondly, the present invention discloses a chip packaging material design system based on a multi-task learning neural network, which is used to implement the above-mentioned chip packaging material design method based on a multi-task learning neural network.

[0029] The beneficial effects of this invention are:

[0030] (1) This invention uses a learnable linear embedding layer to perform dense continuous vectorization encoding of category features, replacing the traditional sparse encoding method, so that the neural network can learn the microscopic intrinsic properties of materials more fully, thereby achieving high-precision feature representation even under small sample data conditions.

[0031] (2) The present invention constructs a multi-task performance prediction model consisting of a shared feature extraction network and multiple task-specific output networks. The shared layer extracts common features among multiple performance indicators through stacked residual connection modules. Each task head independently outputs the prediction results of a single performance indicator, realizing high-precision synchronous prediction of multiple performance indicators such as thermal expansion coefficient, glass transition temperature, bending strength, Young's modulus, thermal conductivity and viscosity, overcoming the defect of neglecting the correlation between performance in traditional single-task modeling.

[0032] (3) The present invention adopts a two-stage progressive training strategy. In the first stage, the embedding layer, the shared layer and all task heads are trained together and a gradient balancing mechanism is introduced to dynamically adjust the loss weights of each task, which effectively alleviates gradient conflict and negative transfer in multi-task learning. In the second stage, the parameters of the embedding layer and the shared layer are frozen and only the task heads are fine-tuned, avoiding catastrophic forgetting and significantly improving the generalization ability and prediction stability of the model in small sample scenarios.

[0033] (4) This invention utilizes the trained embedding layer and model to predict multiple performance indicators in batches within the feasible domain of the formulation, and automatically outputs the optimal formulation according to the user-defined constraints and performance weights. This reduces the cycle of several days or even weeks in traditional material design, which relies on a large number of experimental trials, to minutes, greatly reducing R&D costs and providing a new technical paradigm for the efficient design and iteration of chip packaging materials. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating a chip packaging material design method based on multi-task learning neural networks;

[0035] Figure 2 This is a schematic diagram of the feature encoding and multi-task performance prediction model;

[0036] Figure 3 This is a structural schematic diagram of the residual connection module;

[0037] Figure 4 This is a schematic diagram of a two-stage progressive training strategy;

[0038] Figure 5 This is a schematic diagram of the framework of a chip packaging material design system based on a multi-task learning neural network. Detailed Implementation

[0039] The present invention will be further described and illustrated below with reference to specific embodiments. The embodiments described are merely examples of the content of this disclosure and do not limit the scope of the invention. The technical features of each embodiment in the present invention can be combined accordingly, provided that there is no mutual conflict.

[0040] The accompanying drawings are merely illustrative of the invention and are not necessarily drawn to scale. Some of the block diagrams shown in the drawings are functional entities and do not necessarily correspond to physically or logically independent entities. These functional entities can be implemented in software, in one or more hardware modules or integrated circuits, or in different network and / or processor devices and / or microcontroller devices.

[0041] The flowchart shown in the attached diagram is merely an illustrative example and does not necessarily include all steps. For example, some steps may be broken down, while others may be combined or partially combined; therefore, the actual execution order may change depending on the specific circumstances.

[0042] like Figure 1 As shown, this invention proposes a chip packaging material design method based on a multi-task learning neural network, which mainly includes four steps: dataset construction and processing, model design and training, database generation, and design of a visualization interface for multi-objective material design.

[0043] S1. Feature encoding is performed on the formulation data of chip packaging materials. Its purpose is to build a database that can be learned by machine learning models. It should contain complete input features and output performance indicators.

[0044] This invention selects a particulate-filled resin system as the research object of chip packaging material. This system is composed of a crosslinking system (including monomer type and curing agent type) and a particulate-filled system (including the type of filling particles, particle size and relative volume fraction).

[0045] The monomer types include common resin systems such as bisphenol A epoxy resin and bisphenol F epoxy resin; the curing agent types include commonly used resin curing agents such as 2-ethyl-4-methylimidazolium, 2-aminoimidazolium, diethyltoluenediamine, and methylhexahydrophthalic anhydride; the filler particle types mainly include commonly used industrial particles such as silica and alumina; the preferred particle size is 20nm to 70um; the relative volume fraction refers to the relative volume fraction of each particle relative to the total filler volume fraction.

[0046] Data was acquired through a combination of literature review and system experiments, covering performance test results under various formulation combinations. Specifically, the dataset includes 10 input features and 6 output performance metrics.

[0047] The input features include: monomer type, curing agent type, filler particle type, total filler volume fraction, particle size of particle 1, relative volume fraction of particle 1, particle size of particle 2, relative volume fraction of particle 2, particle size of particle 3, and relative volume fraction of particle 3. This input feature contains 3 categorical features and 7 numerical features.

[0048] like Figure 2As shown, in terms of feature engineering, to replace traditional numerical-category-based encoding, this invention first uses a global label encoder to uniformly encode the three category features—monomer type, curing agent type, and filler particle type—as integer indices. Then, a learnable linear embedding layer is introduced to map the integer indices of the above category features into a 5-dimensional dense continuous vector, enhancing the neural network's ability to represent the intrinsic mechanical and thermophysical properties of materials. This 5-dimensional dense vector is then concatenated with the remaining 7 numerical features to finally construct a unified 12-dimensional input feature vector, thus achieving feature encoding.

[0049] The learnable linear embedding layer is a front-end component of the shared feature extraction network. It is jointly trained with the shared feature extraction network and the task-specific output network in the first stage of the subsequent two-stage progressive training, and is frozen in the second stage. In this embodiment, considering the distribution characteristics of viscosity data spanning multiple orders of magnitude, the invention first employs logarithmic transformation, followed by standardization using StandardScaler; other output metrics are directly pre-processed with standardization to eliminate the influence of dimensions.

[0050] Output performance indicators include: coefficient of thermal expansion (CTE), glass transition temperature (Tg), flexural strength, Young's modulus, thermal conductivity, and viscosity.

[0051] The test methods for various output performance indicators of the particulate-filled resin system composite material are as follows:

[0052] The three-point bend test is used to characterize the mechanical behavior of composite materials under bending loads, primarily obtaining bending strength and modulus. The test was conducted using an Instron 5465 universal testing machine, following ISO 178 standards. The specimen was a long strip, either injection-molded or cut, with dimensions of 56 mm × 10 mm × 2 mm. During the test, the specimen was placed on two support rollers with an effective span of 32 mm. A bending load was applied downwards at a constant rate of 1 mm / min until the specimen fractured or reached the specified strain. The load-displacement curve recorded by the testing machine was used to calculate the material strength and modulus using the following formulas.

[0053]

[0054]

[0055] in, For bending strength, F is the maximum load applied when the specimen breaks, L is the span between the support rollers (effective span), b is the width of the specimen, and h is the thickness of the specimen. The Young's modulus of the material. This represents the load change corresponding to the linear segment of the load-displacement curve. To and The corresponding displacement change (deflection change).

[0056] Rheological experiments were conducted to determine the viscosity of uncured epoxy resin filler precursor solutions. An HR20 rotational rheometer was used, equipped with a 20 mm diameter TA standard stainless steel parallel plate fixture. First, the epoxy resin monomers, curing agent, and filler particles were thoroughly mixed according to the designed formulation to obtain a homogeneous precursor solution. A small amount of the precursor solution was placed on the lower plate of the rheometer, and the upper plate was slowly lowered to the set gap. Excess sample was scraped off. The test conditions were: constant shear rate 1 s. -1 The test temperature was controlled at 25 ℃ (room temperature), and viscosity data was collected after the temperature reached equilibrium. The viscosity data was mainly calculated using the following formula.

[0057]

[0058] in, Let be the shear viscosity, M be the torque applied to the rotor, h be the gap between the upper and lower parallel plates, and R be the radius of the parallel plate rotor. ω is the angular velocity of the rotor.

[0059] The thermal conductivity test was conducted using a TPS 2500 S-type thermal conductivity meter, based on the transient planar heat source method (TPS method), and the test standard was in accordance with GB / T 42919.1—2023. The sample was a square block with dimensions of 30 mm × 30 mm × 6 mm. Before testing, a double-sided spiral planar sensor was clamped between two identical samples, and a constant pressure was applied to ensure good thermal contact. The test was conducted at room temperature (23 ℃). The sensor simultaneously acted as a heat source and temperature detector: a constant electrical power was applied, and the heating time was typically several tens of seconds. By recording the sensor resistance change and fitting a heat transfer model, the thermal conductivity of the material was directly calculated.

[0060]

[0061] in, The thermal conductivity of the material. To provide a constant heating power to the sensor, The sensor's detection radius. This represents the average temperature rise on the sensor surface. The time is a dimensionless characteristic time.

[0062] The coefficient of thermal expansion and glass transition temperature were tested using a horizontal pusher thermal dilatometer, according to ISO 11359-2 testing standard. The sample was a long rectangular block, 20 mm × 4 mm × 4 mm in size. During testing, the sample was placed on a quartz support, and a very low constant compressive force (e.g., 0.05 N) was applied above it to maintain probe contact. The sample was heated from room temperature to 200 °C at a rate of 5 °C / min. The instrument recorded the change in sample length as a function of temperature. By analyzing the thermal expansion curve, the linear coefficient of thermal expansion in two stages could be calculated: CTE1 (in ppm / °C) in the glassy region (below Tg) and CTE2 in the rubbery region (above Tg). Simultaneously, the glass transition temperature Tg (in °C) was determined from the inflection point (extrapolation start point or midpoint) of the expansion curve. Specifically, the coefficient of thermal expansion in the output performance indicators of this invention refers to the linear coefficient of thermal expansion CTE1 in the glassy region.

[0063] The formula for calculating the linear thermal expansion coefficient is:

[0064]

[0065] Where CTE is the coefficient of linear thermal expansion, and L is the original length of the sample at the initial temperature. This represents the change in sample length with temperature. This represents the change in temperature.

[0066] S2. Construct a multi-task performance prediction model, and use a two-stage progressive training strategy to train the learnable linear embedding layer applied to the feature encoding part and the multi-task performance prediction model.

[0067] This invention employs a multi-task performance prediction model based on a shared residual network, such as... Figure 2 As shown, its overall architecture adopts a design paradigm of shared underlying parameters and task-specific adaptation, including a shared feature extraction network and six task-specific output networks (also known as task heads). The shared feature extraction network is located at the front end and consists of a linear mapping layer and two sequentially stacked residual connection modules, used to learn common representations among different performance metrics. Each task-specific output network implements a performance prediction task, consisting of a residual connection module and a performance output layer, taking the shared features as input and outputting the predicted value of the corresponding performance metric. The network structures of the residual connection modules in the shared feature extraction network and the task-specific output networks are identical.

[0068] like Figure 3As shown, in a specific embodiment of the present invention, the residual connection module comprises two fully connected layers with the same number of neurons, meaning the input and output dimensions of the residual connection module are identical, achieving an identity mapping. To enhance generalization ability, each residual connection module is injected with two independent rounds of Gaussian noise during the training phase. A noise module is set before each fully connected layer, and the standard deviation of the noise applied by the noise module can be set between 0.005 and 0.05, preferably between 0.01 and 0.02. Addressing the inherent measurement errors in experimental data and the risk of overfitting in small sample scenarios, the present invention systematically introduces a combined regularization strategy of data noise injection and Dropout fusion, with a ReLU activation function and a Dropout layer after each fully connected layer. The number of neurons in the fully connected layer is 8 to 32; in this embodiment, the number of neurons is 16, meaning the output dimension of the residual connection module is 16. Since the dimension of the input feature vector is inconsistent with the output dimension of the fully connected layer inside the residual connection module, to ensure the effectiveness of the residual connection, the 12-dimensional input feature vector is mapped to 16 dimensions in the linear mapping layer of the shared feature extraction network to unify the dimensions. Subsequent residual connection modules have consistent input and output dimensions, eliminating the need for further alignment.

[0069] The dropout rate of the Dropout layer can be set between 0 and 0.5, and the Dropout rate is set differently according to the characteristics of the task. In different task-specific output networks, for tasks predicting thermal expansion coefficient, glass transition temperature, and Young's modulus, the Dropout rate is preferably 0 to 0.2; for tasks predicting flexural strength, the Dropout rate is preferably 0.1 to 0.3; for tasks predicting thermal conductivity, the Dropout rate is preferably 0 to 0.2; and for tasks predicting viscosity, the Dropout rate is preferably 0.3 to 0.5.

[0070] The performance output layer in the output network for each task is a fully connected layer. Its input is a 16-dimensional feature vector output by the residual connection module, and its output is a 1-dimensional scalar value, corresponding to the prediction result of a single performance index.

[0071] To address the characteristics of multi-task learning and mitigate gradient conflicts and negative transfer in multi-task learning, this invention employs a two-stage progressive training strategy, such as... Figure 4 As shown:

[0072] In the first training phase, the learnable linear embedding layer, the shared feature extraction network, and all task-specific output networks participate in the training simultaneously; in this embodiment, the first training phase is set to 800 rounds.

[0073] In the second training phase, the weight parameters of the learnable linear embedding layers and the shared feature extraction network are frozen, and fine-tuning is performed only on the six independent task-specific output networks. The learning rate in the second training phase is adjusted to 0.1-0.8 times that in the first training phase, and the learning rate factor is preferably 0.1-0.8.

[0074] The learnable linear embedding layers and multi-task performance prediction models (shared feature extraction network and all task-specific output networks) obtained after training constitute a multi-task learning neural network.

[0075] This training strategy effectively avoids catastrophic forgetting and significantly improves the model's generalization ability.

[0076] The loss function is the same for both training phases:

[0077]

[0078] in, This represents the total prediction loss, and T represents the number of performance prediction tasks. In this example, T=6. Let represent the mean absolute error (MAE) of the i-th performance prediction task. This represents the dynamic loss weight for the i-th performance prediction task. The total model loss uses L1 loss (MAE) as the base loss function for each subtask, and a dynamically weighted total loss for multi-task learning is constructed based on this. Since MAE uses absolute values, it has stronger robustness in small sample data, avoiding overfitting of the model to a few outlier samples. During training, the Adam optimizer is used, with an initial learning rate of 0.005 and a weight decay of 1e. -4 Gradient clipping is used to stabilize the training.

[0079] In one specific embodiment of the present invention, a gradient balancing mechanism is introduced in the first training phase to dynamically adjust the loss weights based on the relative magnitude of the losses of each task. The calculation process is as follows:

[0080] Define a learnable scalar parameter for each task. The final task weight The dynamic loss weights, obtained through the Softmax function mapping, are used to calculate the total prediction loss. The calculation formula is:

[0081]

[0082] Where t represents the current training round, and k represents the k-th performance prediction task.

[0083] During normal model training within each training batch, the code accumulates the mean squared error loss for each sample in each task. After the batch training is completed, the average loss for each task in the current training epoch is calculated. :

[0084]

[0085] in, This represents the number of training samples for the i-th performance prediction task in the current training round. Let represent the mean squared error loss of the b-th sample in the current training round for the i-th performance prediction task;

[0086] Calculate the gradient norm of each task relative to the parameters of the shared feature extraction network. :

[0087]

[0088] in, This represents the gradient norm of the i-th performance prediction task in the current training epoch t. The value represents the loss weight of the i-th task in the current training round t. The subscript W represents the parameters of the shared feature extraction network. The gradient norm is the L2 norm of the gradient of the weighted loss of each task with respect to the parameters W of the shared feature extraction network.

[0089] Calculate the average gradient norm of the current training epoch. :

[0090]

[0091] Calculate the relative loss rate for each task. :

[0092]

[0093] Calculate the target gradient for the current training epoch. :

[0094]

[0095] in, Indicates asymmetric hyperparameters. Set to 0.12~0.22, in this embodiment .

[0096] Calculate the GradNorm loss for the current training epoch. :

[0097]

[0098] Update scalar parameters:

[0099]

[0100] in, express The weight learning rate is typically set to 0.001~0.01. In this embodiment... .

[0101] This invention makes three important improvements to the original GradNorm, aiming to enhance training stability and engineering practicality: First, it replaces the gradient loss function from L1 loss to L2 squared loss, utilizing the characteristic of automatic gradient decay as the error approaches zero, making the update of task weights more gradual during the convergence phase and effectively suppressing weight oscillations caused by gradient norm fluctuations in mini-batch training; Second, it increases the relative loss rate... The calculation is simplified from the initial loss normalization to the current loss proportion, i.e. This approach avoids weight interference caused by the random initial loss anomaly in the first training batch, while ensuring that the weight response is entirely based on the current training state, providing more agile adjustment capabilities for tasks with sudden loss rebounds during training. Furthermore, it innovatively introduces a two-stage frozen training strategy: the first stage jointly trains the learnable linear embedding layer, shared layer, and task head, and enables GradNorm; the second stage freezes the shared layer and stops GradNorm weight updates, allowing only probe fine-tuning. This design effectively prevents the fine-tuning stage from destroying the general representations already learned by the shared layer, while avoiding interference from frequent weight changes on local optimum searches, making it particularly suitable for small-sample, multi-task material performance prediction scenarios.

[0102] S3. Utilize the trained learnable linear embedding layer and multi-task performance prediction model to predict multiple performance indicators in batches within the feasible domain of the formulation, generating a structured formulation-performance database.

[0103] Define the feasible domain range for all input features. The input features include two categories: categorical features and numerical features. Categorical features include: a list of possible monomer types (e.g., bisphenol A epoxy resin, bisphenol F epoxy resin, etc.), a list of possible curing agent types (e.g., 2-ethyl-4-methylimidazolium, 2-aminoimidazolium, diethyltoluenediamine, methylhexahydrophthalic anhydride, etc.), and a list of possible filler particle types (e.g., silica, alumina, etc.). Numerical features include: upper and lower limits of the total filler volume fraction, the particle size range for each particle type, and the relative volume fraction range for each particle type. The values ​​for all categorical features are derived from the known types covered in the dataset of step S1, and the value ranges for all numerical features are set according to the actual process feasibility.

[0104] System sampling is performed within the feasible region of the above-mentioned input features. The sampling method can be grid sampling, random sampling, or Latin hypercube sampling, etc., to generate multiple candidate formulations covering the feasible region. Each candidate formulation contains a complete set of 10 input features, namely monomer type, curing agent type, filler particle type, total filler volume fraction, particle 1 particle size, particle 1 relative volume fraction, particle 2 particle size, particle 2 relative volume fraction, particle 3 particle size, and particle 3 relative volume fraction.

[0105] For each candidate formulation, the input features undergo the same feature engineering process as in step S1: the categorical features are encoded into integer indices by a label encoder, then mapped to a 5-dimensional dense continuous vector by a trained learnable linear embedding layer, and concatenated with the remaining 7 numerical features to obtain a 12-dimensional input feature vector. Subsequently, this input feature vector is input into the trained learnable linear embedding layer and the multi-task performance prediction model, which simultaneously predicts six performance indicators of the candidate formulation: coefficient of thermal expansion, glass transition temperature, flexural strength, Young's modulus, thermal conductivity, and viscosity.

[0106] All candidate formulations' formulation parameters and their corresponding six predicted performance indicators are stored in a structured format, forming a formulation-performance database. This database records the complete input characteristics and output performance correspondence for each candidate formulation.

[0107] S4. Output the optimal formula based on the constraints and performance weights set by the user.

[0108] This invention, based on the formulation-performance database generated in step S3, receives user-defined constraints and optimization weights for various performance indicators. The constraints include target upper and lower limits for each performance indicator, such as the coefficient of thermal expansion not exceeding a certain value, the glass transition temperature not falling below a certain value, and the flexural strength not being less than a certain value. The optimization weights are used to quantify the relative importance of each performance indicator in formulation decisions; a higher weight indicates a greater priority for that indicator in optimization.

[0109] Based on user-defined constraints, the system automatically retrieves all candidate formulations from the formulation-performance database, selecting those that meet all predicted performance indicators to form a candidate formulation set. Then, for each candidate formulation in this set, its predicted performance indicators are normalized to eliminate differences in units and numerical ranges between different performance indicators. The normalized performance indicators are then combined with user-defined performance weights to calculate a comprehensive score for each candidate formulation. A higher comprehensive score indicates that the overall performance of the formulation is closer to the user's desired outcome.

[0110] All candidate formulations are sorted in descending order of their comprehensive scores, and the top few recommended formulations are output. A visual recommendation interface can be set up to facilitate interaction with the user, visually displaying the comparison between the predicted performance indicators of each recommended formulation and the user's set requirements in the form of a radar chart. This allows users to quickly evaluate the strengths and weaknesses of the recommended formulations across various performance dimensions. The visual recommendation interface provides a formulation list display area, a performance comparison radar chart display area, and a constraint and weight setting area for user interaction and adjustment.

[0111] In this invention, the entire retrieval, scoring, sorting, and display process can be completed automatically within minutes, significantly shortening the cycle of several days or even weeks that relies on repeated experiments and trials based on human experience in traditional material design, and significantly improving the R&D efficiency of chip packaging materials.

[0112] To comprehensively evaluate the performance of the proposed multi-task performance prediction model, this experiment selected ten representative traditional machine learning and ensemble learning models as comparison baselines, covering a wide range of categories including linear models, distance-based models, kernel methods, ensemble tree models, and probabilistic models. Specifically, these models include: XGBoost, Random Forest (RF), Support Vector Regression (SVR), Extra TreesRegressor (ETR), K-Nearest Neighbors (KNN), Multi-Task Learning (MTL), Ridge Regression, LASSO Regression, LightGBM, and Gaussian Process Regression (GP).

[0113] The aforementioned traditional models (including XGBoost, RF, SVR, KNN, LASSO, Ridge, LightGBM, GP, and ETR) all employ a single-task independent modeling strategy. Specifically, for each of the six target attributes—coefficient of thermal expansion, glass transition temperature, flexural strength, Young's modulus, thermal conductivity, and viscosity—an independent predictor is trained for each task. All models maintain consistent input features, including monomer type encoding, curing agent type encoding, encoding of the three particle types, total filler volume fraction, and the three particle sizes and their corresponding relative volume fractions. Each model independently learns the mapping relationship from formulation parameters to specific performance indicators. Furthermore, to fully exploit the potential of each model and ensure optimal performance on its respective task, this study systematically tuned the hyperparameters of all traditional models using grid search to select the best parameter configuration for final evaluation.

[0114] Given the common challenges in materials science, such as high data acquisition costs and limited effective sample sizes, the six performance index datasets used in this experiment are all typically small in scale. Traditional methods of fixed-split training and test sets are prone to evaluation bias due to the randomness of data partitioning, making it difficult to accurately reflect the model's generalization performance. Therefore, this experiment introduces Leave-One-out Cross-Validation (LOOCV) as the core evaluation strategy. The core idea of ​​LOCV is to fully utilize every finite sample: in each round of validation, a unique sample is randomly selected from the dataset as the validation set, and all other samples are used as the training set for model training. The model's predictive performance is then evaluated on the validation set. This process is repeated 40 times, ensuring that different samples in each task have a chance to be selected as validation samples, thus obtaining a robust estimate of the model's prediction error. Compared to traditional K-fold cross-validation, LOCV maximizes the training set size in small-sample scenarios (removing only one sample each time) while providing unbiased performance estimates. In addition, to eliminate the randomness interference introduced by a single data partition, all comparative experiments used the same random seed and validation index to ensure the consistency of the evaluation benchmark.

[0115] This experiment selects Mean Absolute Percentage Error (MAPE) and Standard Deviation (SD) as the core evaluation metrics for model prediction accuracy. MAPE measures the relative deviation between predicted and true values ​​as a percentage, offering advantages such as intuitiveness and scale independence, facilitating cross-sectional comparisons across tasks with different scales. Furthermore, to assess the predictive stability of the model across different validation rounds, this experiment calculates the standard deviation (SD) of MAPE obtained by each model in 40 rounds of leave-one-out validation. SD measures the degree of fluctuation in model prediction performance across different data subsets: a smaller SD indicates lower sensitivity to data partitioning and more stable generalization performance, which is particularly valuable in small-sample scenarios. It is worth noting that for viscosity, a target variable spanning multiple orders of magnitude, all models are trained and predicted in log space, and MAPE is also calculated in log space to mitigate numerical instability caused by scale differences; the other five tasks are evaluated on the original physical scale. Tables 1 and 2 summarize the MAPE, SD results, and their average values ​​for each model across the six performance prediction tasks.

[0116] Table 1. MAPE results and average values ​​of each model on six performance prediction tasks.

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[0118] Table 2. SD results and average values ​​of each model on six performance prediction tasks.

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[0120] Experimental results show that the multi-task performance prediction model constructed in this invention achieves the best overall prediction performance and stability among all comparative models. The average MAPE of the six tasks is 10.56%, and the average SD is 16.57%, which is significantly better than other comparative methods, verifying the effectiveness and superiority of the multi-task learning strategy in predicting the performance of small sample materials.

[0121] To delve into the independent contributions of each key design component in the multi-task performance prediction model proposed in this invention to the model performance, this embodiment designed an ablation experiment. Specific architectural components were removed or disabled one by one, and the changes in model performance were observed to quantitatively evaluate the actual contribution of each component to the overall prediction accuracy and stability. The effects of gradient balancing, residual connection, noise injection, and parameter freezing modules on the model prediction results were verified, and the results are shown in Table 3.

[0122] Table 3 Ablation Experiment Results

[0123]

[0124] The results of the four ablation experiments show that the complete model exhibits the best average performance across all six tasks, with no obvious performance bottlenecks. This ablation experiment system validates the effectiveness and synergistic gains of each design component, providing strong experimental evidence for the scientific validity and rationality of the proposed model architecture.

[0125] It should also be noted that the chip packaging material design method based on multi-task learning neural networks in the above embodiments can essentially be executed by a computer program or module. Therefore, similarly, another preferred embodiment of the present invention also provides a chip packaging material design system based on multi-task learning neural networks corresponding to the above embodiments, such as... Figure 5 As shown, it includes:

[0126] The feature encoding module is used to encode the formula data of chip packaging materials. During feature encoding, the category features in the formula data are first encoded by labels and mapped into dense continuous vectors through a learnable linear embedding layer. Then, they are concatenated with numerical features to obtain an input feature vector of the same dimension.

[0127] The model building and training module is used to construct a multi-task performance prediction model. A two-stage progressive training strategy is employed to train the learnable linear embedding layer and the multi-task performance prediction model. The multi-task performance prediction model includes a shared feature extraction network and multiple task-specific output networks. The shared feature extraction network consists of a linear mapping layer and multiple stacked residual connection modules. Each task-specific output network consists of a residual connection module and a performance output layer. The two-stage progressive training strategy includes: in the first stage, jointly training the learnable linear embedding layer, the shared feature extraction network, and all task-specific output networks, and introducing a gradient balancing mechanism to dynamically adjust the loss weights for each task during training; in the second stage, freezing the parameters of the learnable linear embedding layer and the shared feature extraction network, and only fine-tuning the parameters of all task-specific output networks.

[0128] The chip packaging material formulation recommendation module is used to predict multiple performance indicators in batches within the formulation feasible domain by utilizing a trained learnable linear embedding layer and a multi-task performance prediction model, and output the optimal formulation based on user-defined constraints and performance weights.

[0129] It should also be noted that those skilled in the art will understand that, for the sake of convenience and brevity, the specific working process of the system described above can be referred to the corresponding process in the foregoing method embodiments, and will not be repeated here. In the embodiments provided in this application, the division of steps or modules in the system and method is merely a logical functional division, and there may be other division methods in actual implementation. For example, multiple modules or steps may be combined or integrated together, and a module or step may also be split.

[0130] The system embodiments of the present invention can be applied to any device with data processing capabilities, such as a computer or other similar device. The system embodiments can be implemented in software, hardware, or a combination of both. Taking software implementation as an example, as a logical device, it is formed by the processor of any data processing device loading the corresponding computer program instructions from non-volatile memory into memory for execution.

[0131] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the invention. Those skilled in the art can make various changes and modifications without departing from the spirit and scope of the invention. Therefore, all technical solutions obtained through equivalent substitution or transformation fall within the protection scope of the present invention.

Claims

1. A chip packaging material design method based on a multi-task learning neural network, characterized in that, Includes the following steps: S1. Feature encoding is performed on the formulation data of chip packaging materials. During feature encoding, the category features in the formulation data are first encoded by labels and mapped into dense continuous vectors through a learnable linear embedding layer. Then, they are concatenated with numerical features to obtain an input feature vector of the same dimension. S2. Construct a multi-task performance prediction model. The model includes a shared feature extraction network and multiple task-specific output networks. The shared feature extraction network is composed of a linear mapping layer and multiple residual connection modules stacked together. Each task-specific output network consists of a residual connection module and a performance output layer. S3. A two-stage progressive training strategy is adopted to train the learnable linear embedding layer and the multi-task performance prediction model. In the first stage, the learnable linear embedding layer, the shared feature extraction network, and all task-specific output networks are jointly trained, and a gradient balancing mechanism is introduced during the training process to dynamically adjust the loss weights of each task. In the second stage, the parameters of the learnable linear embedding layer and the shared feature extraction network are frozen, and only the all-task-specific output networks are fine-tuned. S4. Utilize the trained learnable linear embedding layer and multi-task performance prediction model to predict multiple performance indicators in batches within the feasible domain of the formulation, and output the optimal formulation based on the user-defined constraints and performance weights.

2. The chip packaging material design method based on multi-task learning neural network according to claim 1, characterized in that, The category characteristics include monomer type, curing agent type and filler particle type, and the numerical characteristics include total filler volume fraction, particle size of each particle and relative volume fraction of each particle.

3. The chip packaging material design method based on multi-task learning neural networks according to claim 2, characterized in that, In the formula data, there is one type of filling particle, and the particle size of this filling particle can be up to three types; the learnable linear embedding layer maps 3-dimensional category features to dense continuous vectors, and the dimension of the dense continuous vectors is greater than 3; the linear mapping layer in the shared feature extraction network maps the input feature vector of the same dimension to the same dimension as the input and output dimensions of the residual connection module.

4. The chip packaging material design method based on multi-task learning neural network according to claim 1, characterized in that, The residual connection modules in the shared feature extraction network and all task-specific output networks have the same structure. Each residual connection module includes two fully connected layers, and a noise module is provided before each fully connected layer to inject Gaussian noise during the training phase.

5. The chip packaging material design method based on a multi-task learning neural network according to claim 4, characterized in that, The standard deviation of the Gaussian noise is set to 0.005 to 0.

05.

6. The chip packaging material design method based on multi-task learning neural network according to claim 4, characterized in that, Each fully connected layer is followed by a ReLU activation function and a Dropout layer; the dropout rate of the Dropout layer is set to 0 to 0.

5. Furthermore, in the task-specific output network, the dropout rate of each Dropout layer is set differently according to different performance prediction tasks. Specifically, for tasks predicting thermal expansion coefficient, glass transition temperature, and Young's modulus, the dropout rate is set to 0–0.2; for tasks predicting flexural strength, the dropout rate is set to 0.1–0.3; for tasks predicting thermal conductivity, the dropout rate is set to 0–0.2; and for tasks predicting viscosity, the dropout rate is set to 0.3–0.

5.

7. The chip packaging material design method based on multi-task learning neural network according to claim 1, characterized in that, The gradient balancing mechanism includes: A learnable scalar parameter is assigned to each performance prediction task, and the dynamic loss weight of the task is obtained by mapping the scalar parameter. After each training batch, the gradient norm of each task relative to the parameters of the shared feature extraction network is calculated based on the average loss of each task and the current dynamic loss weights; the average gradient norm of all tasks in the current training round is taken as the average gradient norm. The target gradient for each task is obtained by multiplying the average gradient norm by a specified power of the relative loss rate for each task; the relative loss rate is the proportion of the current average unweighted loss of the task to the sum of the average unweighted losses of all tasks. The sum of squared differences between the gradient norm of each task and the target gradient is calculated to obtain the gradient balancing loss, and the learnable scalar parameters of each task are updated based on the gradient balancing loss.

8. The chip packaging material design method based on a multi-task learning neural network according to claim 1 or 7, characterized in that, The gradient balancing mechanism is executed only in the first training phase. In the second training phase, the gradient balancing mechanism is stopped while the shared feature extraction network is frozen, and the dynamic loss weights of each task are no longer updated.

9. The chip packaging material design method based on multi-task learning neural network according to claim 1, characterized in that, The process of outputting the optimal formula based on user-defined constraints and performance weights includes: Based on the upper and lower limits of various performance indicators set by the user, candidate formulations that meet the conditions are screened from the database; the performance indicators of each candidate formulation are normalized, and a comprehensive score is calculated in combination with the performance weights set by the user; the formulations are sorted in descending order of comprehensive score, and the top-scoring recommended formulations are output, along with a radar chart comparing the predicted performance indicators of the recommended formulations with the user's target requirements.

10. A chip packaging material design system based on a multi-task learning neural network, used to implement the chip packaging material design method based on a multi-task learning neural network as described in claim 1, characterized in that, The system includes: The feature encoding module is used to encode the formula data of chip packaging materials. During feature encoding, the category features in the formula data are first encoded by labels and mapped into dense continuous vectors through a learnable linear embedding layer. Then, they are concatenated with numerical features to obtain an input feature vector of the same dimension. The model building and training module is used to construct a multi-task performance prediction model. A two-stage progressive training strategy is employed to train the learnable linear embedding layer and the multi-task performance prediction model. The multi-task performance prediction model includes a shared feature extraction network and multiple task-specific output networks. The shared feature extraction network consists of a linear mapping layer and multiple stacked residual connection modules. Each task-specific output network consists of a residual connection module and a performance output layer. The two-stage progressive training strategy includes: in the first stage, jointly training the learnable linear embedding layer, the shared feature extraction network, and all task-specific output networks, and introducing a gradient balancing mechanism to dynamically adjust the loss weights for each task during training; in the second stage, freezing the parameters of the learnable linear embedding layer and the shared feature extraction network, and only fine-tuning the parameters of all task-specific output networks. The chip packaging material formulation recommendation module is used to predict multiple performance indicators in batches within the formulation feasible domain by utilizing a trained learnable linear embedding layer and a multi-task performance prediction model, and output the optimal formulation based on user-defined constraints and performance weights.

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