A neural network temperature field reconstruction method embedded with physical knowledge

Abstract

The application discloses a neural network temperature field reconstruction method embedded with physical knowledge and belongs to the field of physical knowledge neural networks. The neural network calculation method comprises loss function definition, network structure definition, data set generation and network training. The application defines a brand-new loss function to meet partial differential equations, boundary conditions and initial conditions, and proposes a batch training scheme for self-adaptive normalization of each item of the loss function in the training process, so that the calculation burden during training can be reduced and the accuracy can be improved, thereby realizing the application of the neural network in temperature field reconstruction and enabling the neural network to be used for solving heat conduction partial differential equations (PDE) under the condition of providing initial conditions and boundary conditions.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of neural networks, and particularly relates to a neural network temperature field reconstruction method embedded with physical knowledge. BACKGROUND

[0002] With the rapid development of computer technology, digital circuit technology has become the core technology of modern electronic equipment. However, due to the strict requirements of manufacturing process on the temperature field of a chip, once the temperature is not up to the standard, the performance of the entire equipment will be affected, and even the production safety will be affected. According to statistics, more than 55% of electronic equipment failures are caused by high temperature, and with the increase of temperature, the failure rate of components also increases exponentially, which reduces the reliability of electronic equipment to different degrees. Therefore, in the thermal design process of a chip, the heat dissipation problem in the chip is a problem that designers have to consider. How to accurately estimate the internal temperature field of the chip so as to predict the possible temperature situation after the chip failure and avoid excessive consumption of materials in the chip is a problem that needs to be solved at present. Chip temperature field reconstruction is to reconstruct the actual temperature of each node of the chip under different environmental temperatures by analyzing the average temperature of each node of the chip, so as to improve the system performance, reduce the power consumption and prolong the service life of the equipment. Therefore, it is particularly important to quickly and accurately reconstruct the temperature field.

[0003] However, in the existing research on neural network temperature field reconstruction, most of them are based on a supervised learning strategy, which requires a data set with labels (i.e. real values) to train the model. However, this method not only requires a large amount of real data, but also cannot guarantee the generalization of the model (from one experimental condition to another). This requires a higher number of training samples. Since the training data needs to be obtained through experiments, this increases the time and economic cost and makes the training of the model extremely difficult. More importantly, they do not directly consider the basic physical principles of heat transfer. SUMMARY

[0004] The application aims to provide a neural network temperature field reconstruction method embedded with physical knowledge to overcome the deficiencies mentioned in the background art.

[0005] The technical solution for achieving the application is as follows:

[0006] A neural network temperature field reconstruction method embedded with physical knowledge comprises the following steps:

[0007] Defining a loss function of a reconstruction object: determining a heat transfer partial differential equation of the reconstruction object according to the heat transfer mode of the reconstruction object, so as to set a total loss function of the reconstruction object, which comprises three loss functions of the heat transfer partial differential equation, boundary conditions and initial time;

[0008] Define the network structure: set the pre-input layer in time and space, process the input in time and space with the corresponding function to obtain the input of the neural network, and set 6 hidden layers, each layer has 32 nodes, the activation function adopts the Tanh function, and finally the output is the temperature under the time and space;

[0009] Generate the data set: determine the boundary conditions and numerical values of the reconstructed object, and randomly combine the time position points to generate the data set;

[0010] Network training: the samples of the three kinds of loss functions are trained in different batches respectively, and the adam optimizer is used to optimize the parameters during the training process, and the proportion of each loss function in the total loss function is self-adaptive to make the network more accurate.

[0011] Compared with the prior art, the present application has the following advantages:

[0012] (1) Compared with the traditional neural network temperature field reconstruction, the neural network driven by the differential equation does not need to prepare the experimental data set, and the data set can be obtained for training without experiment, thereby reducing the training cost of the neural network.

[0013] (2) Compared with the finite element temperature field reconstruction method, the neural network driven by the differential equation has faster calculation speed, thereby reducing the time cost of the temperature field reconstruction.

[0014] (3) Through the adaptive training of the neural network, the relative size of the three kinds of loss functions can be controlled within a certain range, so that the training process is not dominated by a certain loss function to cause the training failure.

[0015] (4) Through the batch training of the three kinds of loss function samples of the neural network, the iteration number required for training can be reduced, and the training speed of the neural network can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 is an example schematic diagram of the present application

[0017] Figure 2 is a neural network structure schematic diagram.

[0018] Figure 3 is a batch training structure diagram.

[0019] Figure 4 is an adaptive training parameter update flowchart. DETAILED DESCRIPTION

[0020] The present application will be further described below in combination with the drawings and specific embodiments.

[0021] In combination with Figure 1The neural network temperature field reconstruction method embedded with physical knowledge provided by the embodiment, a neural network embedded with physical knowledge (PINN) for temperature field reconstruction of a chip using liquid cooling at the top and the bottom, the top heat exchange coefficient being h1 and the bottom heat exchange coefficient being h2, comprises the following steps:

[0022] Step 1: loss function definition, according to the selected heat transfer partial differential equation (PDE), boundary condition equation (BC), initial time equation (IN) setting to ensure that the solution obtained by final training can meet the requirements of the three equations to the maximum extent, in this example f(x, t, h1, h2) is the solution of the heat equation, that is, the temperature under the boundary condition, position and time.

[0023] Combined with Figure 1 In this example, it is one-dimensional heat transfer without internal heat source, so the heat transfer partial differential equation is:

[0024]

[0025] Where T is the chip temperature, t is the time, x is the x-direction coordinate, that is, the chip width direction, and a is the thermal diffusivity of the chip.

[0026] Therefore, the neural network error value caused by the heat transfer partial differential equation (PDE) is:

[0027]

[0028] Where f(x, t, h1, h2) is the temperature corresponding to the position x, time t, and top and bottom heat exchange coefficients h1 and h2.

[0029] The boundary condition equation in this example is:

[0030]

[0031]

[0032] Where k is the chip conductivity, h1 is the top heat exchange coefficient, T ∞1 is the fluid temperature used by the top liquid cooling, T top is the chip boundary temperature, is the value obtained by taking the derivative of T with respect to x at the top, h2 is the bottom heat exchange coefficient, T ∞2 is the fluid temperature used by the top liquid cooling, T bottom is the chip boundary temperature, is the value obtained by taking the derivative of T with respect to x at the bottom.

[0033] Therefore, the neural network error value caused by the top boundary condition is:

[0034]

[0035] where x1 is the x coordinate value corresponding to the top of the chip, T ∞1 (t) is the fluid temperature used by the top liquid cooling at time t. f(x1,t,h1,h2) is the temperature at position x1, time t, and heat transfer coefficients of the top and bottom are h1 and h2 respectively.

[0036] And the neural network error value caused by the bottom boundary condition is:

[0037]

[0038] where x2 is the x coordinate value corresponding to the bottom of the chip, T ∞2 (t) is the fluid temperature used by the bottom liquid cooling at time t. f(x2,t,h1,h2) is the temperature at position x2, time t, and heat transfer coefficients of the top and bottom are h1 and h2 respectively.

[0039] The initial time equation in this example is:

[0040] T ∞ (0) = f(x,0,h1,h2)

[0041] Therefore, the neural network error value caused by the initial time is:

[0042] Error IN = T ∞ (0) - f(x,0,h1,h2)

[0043] where T ∞ (0) is the fluid temperature used by the liquid cooling at time t = 0, and f(x,0,h1,h2) is the temperature of the chip at position x, top and bottom heat transfer coefficients h1 and h2 respectively at t = 0.

[0044] Further, the loss function is defined according to the selected heat transfer partial differential equation, boundary condition equation, and initial time equation:

[0045]

[0046] where λ0, λ1, λ2 are adaptive parameters of the neural network error values caused by the heat transfer partial differential equation, boundary condition, and initial time respectively, N PDE is the number of data points of the heat transfer partial differential equation, N BC is the number of data points of the boundary condition equation, N IN is the number of data points of the initial time equation, Error BCThe neural network error value caused by the boundary condition, including the neural network error value caused by the top and bottom boundary conditions, i.e., Error BC = Error BC1 + Error BC2 ;

[0047] Step 2: Network structure definition, combined with Figure 2 The neural network first obtains the position pre-input x and the time pre-input t, applies a sine activation function to the position pre-input x, applies an exponential activation function to the time pre-input t, and then multiplies the two to obtain the input layer of the neural network, i.e., the data form of the input layer is:

[0048]

[0049] Where a, a0, b, and b0 are network parameters that change with the number of iterations.

[0050] After that, six hidden layers are set, each with 32 nodes, and the activation function uses the Tanh function. Finally, the chip temperature T under the input position x and time t is obtained. The heat transfer partial differential equation loss function value, the boundary condition loss function value, and the initial time loss function value are calculated using the obtained chip temperature T, and the final loss function value is obtained by adding them together. Based on this, the network parameters are feedback adjusted until the loss function value reaches the predetermined precision to stop training, and the final neural network is obtained.

[0051] Step 3: Data set generation, combined with Figure 1 According to the situation in the figure, the boundary conditions in this example are convective heat transfer with the top and bottom and the fluid, with heat transfer coefficients h1 and h2, respectively. The chip width is 100 mm, and the time is taken from 0 to 900 s. Then, randomly combine the time and position points to generate the data set input. In this example, 50 position points are randomly selected, and 200 time points are randomly selected for each position point, resulting in a total of 10,000 input data.

[0052] Step 4: Network training, combined with Figure 3 The samples of the three loss functions are trained in different batches. First, divide the three loss function samples (data sets) into n samples each. Then, in each training, randomly select one sample from the n partial differential equation (PDE) samples, n boundary condition (BC) samples, and n initial condition (IN) samples as input. In one iteration process, n training is performed. In each training, the adam optimizer is used to optimize the network, thereby reducing the number of iterations and improving the network accuracy. In this example, n = 10.

[0053] Then, combined with Figure 4, training loss function parameter self-adaptation by every certain number of iterations, the ratio between each error value and the maximum error value to determine the new adaptive parameters. Set 0.1 as the threshold size, first compare the maximum value of the three loss function, then the partial differential error value and the maximum error value, if the error value is greater than or equal to 0.1, the relative size of the error value and the maximum error value is within 0.1, the adaptive parameter of the error value caused by the partial differential function is set to 1; If less than 0.1, it proves that the error value is much smaller than the maximum error value, and the adaptive parameter of the error value caused by the partial differential function needs to be set to 0.1 divided by the loss ratio, so that the relative size of the two is within 0.1; After that, the boundary condition error value and the initial time error value are treated in the same way to obtain the adaptive parameters of the other two. Then use this method as the main method to train the neural network for 10000 times to get the final result, thus completing the whole process of neural network construction and training, providing a new method for temperature field reconstruction.

Claims

1. A neural network temperature field reconstruction method with embedded physical knowledge, characterized in that: include: Define the loss function of the reconstructed object: According to the heat transfer mode of the reconstructed object, determine the heat transfer partial differential equation of the reconstructed object, and thus set the total loss function of the reconstructed object, which includes three loss functions: the heat transfer partial differential equation, the boundary conditions, and the loss function caused by the initial time; Define the network structure: set up pre-input layers in time and space, and obtain the input of the neural network after performing corresponding function processing on the input of time and space. Set up 6 hidden layers, each with 32 nodes, and use the Tanh function as the activation function. The final output is the temperature at that time and space. Generate a data set: Determine the boundary conditions and values ​​of the reconstructed object, and randomly combine and generate time and position points as a data set; Network training: Samples of the three loss functions are trained in different batches. During the training process, the Adam optimizer is used to optimize the parameters and adapt the proportion of each loss function in the total loss function to make the network more accurate. The total loss function of the reconstructed object is: Where λ0, λ1, and λ2 are adaptive parameters of the neural network error caused by the heat transfer partial differential equation, boundary conditions, and initial moments, respectively. PDE is the number of data points of the heat transfer partial differential equation, N BC is the number of data points of the boundary condition equation, N IN is the number of data points of the equation at the initial moment, Error PDE Represents the neural network error value caused by the heat transfer partial differential equation, Error BC Represents the neural network error value caused by boundary conditions, Error IN Represents the neural network error value caused by the initial moment; Neural network error caused by the heat transfer partial differential equation PDE for: Where t is time, x is the x-direction coordinate, i.e. the chip width direction, α is the thermal diffusion coefficient of the chip, and f(x, t, h1, h2) is the temperature at the corresponding position x, time t, and the top and bottom heat transfer coefficients h1 and h2 respectively; Neural network error caused by boundary conditions Error BC Contains the neural network error values ​​caused by the top and bottom boundary conditions, where the error caused by the top boundary condition is: The error caused by the bottom boundary condition is: Where t is time, x is the x-direction coordinate, i.e. the chip width direction, x1 is the x-coordinate value corresponding to the top of the chip, T ∞1 (t) is the fluid temperature of the top liquid cooling corresponding to time t, f(x1,t,h1,h2) is the temperature at the corresponding position x1, time t, and the top and bottom heat transfer coefficients h1 and h2 respectively; x2 is the x coordinate value corresponding to the bottom of the chip, T ∞2 (t) is the fluid temperature used for bottom liquid cooling corresponding to time t, f(x2,t,h1,h2) is the temperature at position x2, time t, top and bottom heat transfer coefficients h1 and h2 respectively, and k is the chip conductivity; Neural network error value Error caused by the initial moment IN for: Error IN =T ∞ (0)-f(x,0,h1,h2) Where x is the x-direction coordinate, i.e. the chip width direction, T ∞ (0) is the fluid temperature used for liquid cooling at time t = 0, and f(x, 0, h1, h2) is the chip temperature corresponding to the heat transfer coefficients of position x, top and bottom at t = 0, h1 and h2 respectively.

2. The neural network temperature field reconstruction method with embedded physical knowledge according to claim 1 is characterized in that: In defining the network structure, a sinusoidal activation function is applied to the position pre-input x, and an exponential activation function is applied to the time pre-input t. Then, the two are multiplied 1:1 to obtain the input layer of the neural network. That is, the data format of the input layer is: Where a, a0, b, b0 are network parameters.

3. The neural network temperature field reconstruction method with embedded physical knowledge according to claim 1 is characterized in that: The specific process of adaptation is as follows: First, compare and obtain the largest value among the three loss functions, then compare the partial differential error value with the maximum error value. If the ratio of the error values ​​is greater than or equal to the set threshold, the adaptive parameter of the error value caused by the partial differential function is set to unit 1; if it is less than the set threshold, the adaptive parameter of the error value caused by the partial differential function is set to the set threshold divided by the loss ratio; then the boundary condition error value and the initial moment error value are treated in the same way as the error value caused by the partial differential function, and the adaptive parameters corresponding to the other boundary condition error values ​​and the initial moment error values ​​can be obtained.

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