Unsteady heat conduction calculation method based on physically embedded attention network

Abstract

The invention discloses an unsteady heat conduction calculation method based on a physically embedded attention network, and the method comprises the steps: firstly carrying out the data preprocessing, then extracting the space-time local features of a temperature field through employing a convolutional neural network, carrying out the weight adjustment through employing an attention mechanism-based long-short-term memory neural network, and carrying out the calculation of the unsteady heat conduction. A physical information neural network is introduced to perform physical constraint on data prediction, an attention mechanism-physical information neural network is constructed, data preprocessing is performed on a data set, then the data set is divided into a training set and a verification set, and the attention mechanism-physical information neural network is trained and verified. If training does not reach the number of cycles and the total loss function does not meet the requirement during training or the total loss function does not meet the requirement during verification, calculating the gradient of each node through automatic differential in back propagation, and performing parameter optimization of the attention mechanism-physical information neural network. According to the method, the transient thermal response of the material interface can be accurately captured during feature extraction, and the global thermal diffusion trend is macroscopically analyzed.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of deep learning heat conduction, and particularly relates to a non-steady heat conduction calculation method based on a physically embedded attention network. BACKGROUND

[0002] In recent years, with the development of industrial equipment towards light weight, the importance of transient heat conduction problems in the fields of spacecraft thermal maintenance and electronic device heat dissipation is increasingly prominent. Traditional numerical methods dominate in engineering thermal analysis due to their universality, but there are significant problems in dealing with non-steady transient heat conduction problems. Among them, the strict stability condition of time step leads to low efficiency of long time simulation, especially in the scene of temperature gradient changing dramatically, dynamic space-time grid is often needed to ensure accuracy. On the other hand, in the case of multi-physical field coupling, traditional methods need to solve the control equation iteratively, and the computational cost increases exponentially. Secondly, although adaptive grid technology can improve local accuracy, it will destroy the topological structure and bring difficulties to subsequent data-driven modeling. These problems limit the application of traditional numerical solution methods in solving transient heat conduction problems.

[0003] At the same time, deep learning technology shows innovative potential in solving transient heat conduction problems. If a non-steady transient heat conduction calculation method based on attention mechanism, long short-term memory network and physical embedding can be proposed, the advantages of convolutional neural network in extracting spatial topological features can be combined with the ability of long short-term memory network to handle time sequence dependence, and the attention mechanism is embedded to make the network observe the rapidly changing temperature gradient, and the physical information neural network is designed to embed the loss function through the control equation, so as to realize data-driven solving under physical constraints, which can provide a new idea for heat conduction modeling of space-time coupling. SUMMARY

[0004] The purpose of the present application is to overcome the shortcomings of the prior art and provide a non-steady heat conduction calculation method based on a physically embedded attention network.

[0005] To achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0006] The application discloses a non-steady heat conduction calculation method based on a physical embedded attention network, which comprises the following steps: firstly, data preprocessing is performed; then, a convolutional neural network is used to extract the spatiotemporal local features of a temperature field, and a long short-term memory neural network based on an attention mechanism is used to adjust the weight, and a physical information neural network is introduced to physically constrain the data prediction, so as to construct an attention mechanism-physical information neural network; finally, after the data set is preprocessed, the data set is divided into a training set and a verification set, the attention mechanism-physical information neural network is trained and verified, and when the training does not reach the cycle number and the total loss function does not reach the requirement during the training, or when the total loss function does not reach the requirement during the verification, the gradient of each node is calculated through automatic differentiation in the back propagation, and the parameter optimization of the attention mechanism-physical information neural network is performed through an Adamw optimizer.

[0007] Preferably, the data preprocessing is specifically as follows: the node data containing temperature, spatial coordinates and time in the irregular grid calculated by the finite element method is interpolated into the regular grid divided by SciPy in Python, and each node has temperature, spatial coordinates and time data; and then the temperature, spatial coordinates and time are normalized, and the normalized temperature is organized into a fixed-dimensional tensor temperature field according to time.

[0008] Preferably, the convolutional neural network extracts the spatiotemporal local features of the temperature field, and the specific process is as follows: the temperature field after data preprocessing is input into the bottom convolutional layer of the convolutional neural network, the local temperature gradient features are extracted, and the output of the bottom convolutional layer is input into the high-level convolutional layer of the convolutional neural network to identify the macro temperature diffusion trend.

[0009] More preferably, the bottom convolutional layer of the convolutional neural network adopts a skip connection to extract features, and the specific process is as follows: the temperature field features generated by the last convolutional layer of the bottom convolutional layer are directly connected to the full connection layer, and the temperature field features are also sent to the high-level convolutional layer; the full connection layer maps the channel number to the channel number of the high-level convolutional layer through 1x1 convolution, the output temperature field features are fused with the temperature field features output by the high-level convolutional layer, and finally the spatiotemporal local features of the temperature field are output.

[0010] Preferably, the time series extracted from the spatiotemporal local features of the temperature field are weighted using an attention mechanism-based long short-term memory neural network, as follows: the bottom layer of the long short-term memory neural network processes the time series of a single grid node or a local area, and the time features output by the bottom layer are input into the upper layer of the long short-term memory neural network, which integrates the global temperature field; a query matrix, a key matrix, and a value matrix are constructed according to the output features obtained by the upper layer, and then a scaled dot product is used to calculate an attention score matrix, which is multiplied by the value matrix to obtain the features after reweighting, and finally the features after reweighting and the features obtained by the upper layer are spliced through a fully connected layer as the final global temperature field feature output of the long short-term memory neural network.

[0011] More preferably, an attention mechanism-physical information neural network is constructed, specifically: a physical information neural network is introduced; the global temperature field feature output of the long short-term memory neural network is substituted into the transient heat conduction partial differential equation, and the residual error is calculated and used as a loss term, wherein the gradient term is calculated using automatic differentiation, and the total loss function of the physical information neural network is composed of the residual errors related to the boundary conditions, initial conditions, and continuity conditions, thereby constructing the attention mechanism-physical information neural network.

[0012] More preferably, the transient heat conduction partial differential equation of the pth subdomain at time t is defined as:

[0013]

[0014] x p represents a sequence composed of the coordinates of all nodes in the pth subdomain in each dimension, represents the x p component in the ith dimension, λ p (T p ) represents the thermal conductivity of the pth subdomain corresponding to T p (x p , t), ρ p (T p ) represents the density of the pth subdomain corresponding to T p (x p , t), c p (T p ) represents the specific heat capacity of the pth subdomain corresponding to T p (x p , t), and T p (x p , t) represents the temperature field of the pth subdomain at time t.

[0015] The residual error of the transient heat conduction partial differential equation of the pth subdomain at time t is defined as:

[0016]

[0017] the trainable grid parameter matrix of the pth subdomain of the attention mechanism-physical information neural network ω k denotes the kth layer neuron weight matrix of the pth subdomain, b k denotes the kth layer neuron bias matrix of the pth subdomain, and L denotes the total number of layers of the pth subdomain. denotes the number of nodes in the pth subdomain, denotes the coordinates of the jth node in the pth subdomain.

[0018] More preferably, the total loss function is represented as:

[0019]

[0020] where w1, w2, w3, w4, w5 are respectively the weights of the terms.

[0021] More preferably, the initial condition related residual of the pth subdomain is represented as:

[0022]

[0023] where denotes the number of nodes of the pth subdomain under the initial condition, denotes the jth node coordinates of the pth subdomain under the initial condition, denotes the known initial condition of the jth node of the pth subdomain, denotes the initial condition prediction result of the jth node of the pth subdomain.

[0024] The temperature boundary condition related residual of the pth subdomain at time t is represented as:

[0025]

[0026] where denotes the number of nodes related to the temperature boundary condition in the pth subdomain, denotes the jth node coordinates related to the temperature boundary condition in the pth subdomain, is the known temperature boundary condition of the jth node related to the temperature boundary condition in the pth subdomain at time t, is the temperature boundary condition prediction result of the jth node related to the temperature boundary condition in the pth subdomain at time t.

[0027] More preferably, the residual related to the heat flow boundary condition of the pth subdomain at time t is represented as:

[0028] ​

[0029] wherein represents the number of nodes related to the heat flow boundary condition in the pth subdomain, represents the jth node coordinate related to the heat flow boundary condition in the pth subdomain, is the known heat flow boundary condition of the jth node related to the heat flow boundary condition in the pth subdomain at time t, is the temperature prediction result of the jth node related to the heat flow boundary condition in the pth subdomain at time t, λ p (T 3,p ) is the thermal conductivity of the jth node related to the heat flow boundary condition in the pth subdomain at time t, n p (j, t) represents the heat flow boundary normal vector of the jth node related to the heat flow boundary condition in the pth subdomain at time t.

[0030] The residual of the pth subdomain and the adjacent (p+1)th subdomain at the common interface is represented as:

[0031]

[0032] wherein represents the number of nodes related to the heat flow boundary condition in the pth subdomain, represents the jth node coordinate related to the heat flow boundary condition in the pth subdomain, is the temperature prediction result of the jth node related to the heat flow boundary condition in the pth subdomain at time t, λ p (T 4,p ) is the thermal conductivity of the jth node related to the heat flow boundary condition in the pth subdomain at time t, n p,p+1 (j, t) represents the heat flow boundary normal vector of the jth node related to the heat flow boundary condition in the pth subdomain at time t.

[0033] The present application has the following beneficial effects:

[0034] The present application is a non-steady heat conduction calculation method based on a physical embedded attention network. The attention mechanism-physical information neural network constructed can accurately capture the transient thermal response of the material interface when extracting features, and analyze the global thermal diffusion trend macroscopically. Specifically, it fully utilizes the ability of the convolutional neural network to extract spatial features and the ability of the long short-term memory neural network of the attention mechanism to extract time features. The loss function is designed to be related to the Euclidean space distance of the physical information residual, has good physical interpretability, and the attention mechanism can accurately capture the area and time that greatly affect temperature changes in the complex heat conduction process by dynamically allocating weights, and can enhance the sensitivity of the model to important information. Attached Figure Description

[0035] Figure 1 This is a flowchart of the present invention.

[0036] Figure 2 This is a diagram of the network model structure of the present invention. Detailed Implementation

[0037] The present invention will now be further described with reference to the accompanying drawings.

[0038] like Figure 1 and Figure 2 As shown, a method for calculating unsteady heat conduction based on a physically embedded attention network is presented. First, data preprocessing is performed. Then, a convolutional neural network is used to extract spatiotemporal local features of the temperature field, and a long short-term memory neural network based on an attention mechanism is used for weight adjustment. Simultaneously, a physical information neural network is introduced to impose physical constraints on data prediction, constructing an attention mechanism-physical information neural network that allows the model to learn data features while adhering to physical laws. Finally, after data preprocessing, the dataset is divided into a training set and a validation set (in this embodiment, a random 70% portion of the dataset is used as the training set, and the remaining 30% as the validation set). The attention mechanism-physical information neural network is then trained and validated. If the training does not reach the required number of iterations and the total loss function during training does not meet the requirements, or if the total loss function during validation does not meet the requirements, the gradient of each node is calculated by automatic differentiation during backpropagation. The parameters of the attention mechanism-physical information neural network (including the parameters of the convolutional neural network, the long short-term memory neural network, and the physical information neural network) are optimized using the Adamw optimizer.

[0039] The data preprocessing is as follows: The node data containing temperature, spatial coordinates, and time in the irregular mesh obtained by the finite element method (FEM) are interpolated (using bilinear or trilinear interpolation for two-dimensional or three-dimensional cases respectively) into a regular mesh generated by SciPy in Python. This allows the data to be imported into the convolutional neural network, with each node containing temperature, spatial coordinates, and time data. Preferably, ABAQUS or ANSYS is used for the finite element method calculation, and the regular mesh can be tetrahedral or wedge-shaped elements. Temperature, spatial coordinates, and time are then normalized to ensure the input data is within [0,1], improving the stability and convergence speed of model training. The normalized temperature is organized into a fixed-dimensional tensor temperature field according to time, clearly representing the relationship between the temperature field and time and space, facilitating subsequent model input. The formulas for normalizing temperature, spatial coordinates, or time are as follows:

[0040]

[0041] Among them B norm B represents the normalized temperature, spatial coordinates, or time, and B represents the temperature, spatial coordinates, or time before normalization. min B represents the minimum value of temperature, spatial coordinates, or time over the entire time domain. max It represents the maximum value of temperature, spatial coordinates, or time over the entire time domain.

[0042] The spatiotemporal local features of the temperature field are extracted using a convolutional neural network (CNN). Specifically, the preprocessed temperature field is input into the bottom convolutional layer of the CNN. This bottom layer uses two 3×3 convolutional kernels with a stride of 1 and 128 output channels. The Leaky ReLU activation function is used to extract local temperature gradient features and capture microscopic heat conduction patterns. The output of the bottom convolutional layer is then input into the higher convolutional layers of the CNN. These higher layers use two 7×7 convolutional kernels with Leaky ReLU activation and 64 output channels. Dilated convolutions are combined to expand the receptive field and identify macroscopic heat diffusion trends. Within the 3×3 convolutional kernel, for the output corresponding to a specific position (i,j,k) in the input X, the convolution operation can be written as: Where Y(i,j,k) represents the value of the output tensor at spatial location (i,j,k), and C in Let W(c,n,m,p) represent the total number of input channels, W(c,n,m,p) represent the weight value of the c-th input channel at offset position (n,m,p) within the kernel, and b represent the bias term. In a 7×7 large kernel convolutional network, for the output corresponding to a certain position (i′,j′,k′) in the input X′, the convolution operation can be written as: Where Y′(i,j,k) represents the value of the output tensor at spatial location (i′,j′,k′), C in′ W′(c,n,m,p) represents the total number of input channels, W′(c,n,m,p) represents the weight value of the c-th input channel in the convolution kernel weight tensor at the offset position (n,m,p) within the kernel, b′ represents the bias term, and d is the dilation coefficient.

[0043] The bottom convolutional layers use skip connections for feature extraction. Specifically, the temperature field features generated by the last convolutional layer in the bottom layer are directly connected to the fully connected layer, while the temperature field features are also fed into higher-level convolutional layers. The fully connected layer uses a 1×1 convolution to map the number of channels from 128 to 64, and then fuses the output temperature field features with those from the higher-level convolutional layers to finally output the spatiotemporal local features of the temperature field. The feature fusion is expressed as: F l ′ ocal =F global +Conv 1×1 (F local ), where Fl ′ ocal This represents the spatiotemporal local features of the temperature field after feature fusion. F local The temperature field features generated by the last convolutional layer of the bottom convolutional layers, Conv 1×1 F represents a fully connected layer. global This represents the temperature field characteristics of the output of a high-level convolutional layer.

[0044] A Long Short-Term Memory (LSTM) neural network based on an attention mechanism is used to adjust the weights of time series extracted from spatiotemporal local features of the temperature field. Specifically, this discussion focuses on unsteady heat conduction within one second, with a time step of 0.01, although non-uniform time steps are also allowed. The bottom layer of the LSM processes time series from a single grid node or local region, with two layers and a hidden state dimension of 64, focusing on short-term temperature fluctuations. The time features output from the bottom layer are input to the upper layer of the LSM. The upper layer is a single-layer network with a hidden state dimension that can be set to 128. This upper layer integrates the global temperature field, capturing macroscopic temperature diffusion trends. The output features from the upper layer are represented as matrices, constructing a query matrix, a key matrix, and a value matrix. Then, an attention score matrix is ​​calculated using a scaled dot product. The attention score matrix is ​​multiplied by the value matrix to obtain reweighted features. Finally, the reweighted features are concatenated with the features from the upper layer through a fully connected layer to provide the final global temperature field feature output of the LSM. Therefore, the contribution of the features at each time step to the final output can be utilized, making the model pay more attention to key time information.

[0045] Specifically, three linear transformations are used to generate the query matrix, key matrix, and value matrix:

[0046] Q = X W ·W Q

[0047] K = X W ·W k

[0048] V = X W ·W v

[0049] Among them W Q W k and W v X represents the trainable parameter matrices for the query matrix, key matrix, and value matrix, respectively. W Let Q represent the output feature matrix of the upper layer of the Long Short-Term Memory Neural Network, where Q, K, and V are the query matrix, key matrix, and value matrix, respectively.

[0050] Attention score matrix

[0051]

[0052] Where Softmax is the activation function, and T and d k These represent the number of rows and columns of the trainable parameter matrix, respectively.

[0053] Multiplying the attention score matrix by the value matrix yields the reweighted features:

[0054] O = A·V

[0055] The attention mechanism-physical information neural network is constructed as follows: a physical information neural network is introduced; the global temperature field feature output of the long short-term memory neural network is substituted into the transient heat conduction partial differential equation, the residual is calculated and used as the loss term, where the gradient term is calculated by automatic differentiation, and the total loss function of the physical information neural network is constructed by combining the residuals related to the boundary (temperature boundary, heat flow boundary) conditions, initial conditions, and continuity (common interface) conditions, thereby constructing the attention mechanism-physical information neural network.

[0056] Here, the transient heat conduction partial differential equation of the p-th subdomain at time t is defined as follows:

[0057]

[0058] x p It represents the p-th subfield Ω p (In a regular grid divided into multiple subdomains) all nodes contain a sequence of coordinates in each dimension. x represents p The component corresponding to the i-th dimension, λ p (T p ) represents the p-th subfield and T p (x p The thermal conductivity corresponding to ,t), ρ p (T p ) represents the p-th subfield and T p (x p The density corresponding to ,t), c p (T p ) represents the p-th subfield and T p (x p The specific heat capacity corresponding to t), T p (x p ,t) represents the temperature field of the p-th subdomain at time t (i.e., the global temperature field feature output of the long short-term memory neural network at time t in the p-th subdomain).

[0059] Here, the residual of the transient heat conduction partial differential equation of the p-th subdomain at time t is defined as follows:

[0060]

[0061] Attention mechanism - Trainable grid parameter matrix of the p-th subdomain of a physical information neural network ω k Let b represent the weight matrix of the k-th layer neurons in the p-th subdomain. k Let L represent the bias matrix of the k-th layer neurons in the p-th subdomain, and L represent the total number of layers in the p-th subdomain. This represents the number of nodes in the p-th subdomain. This represents the coordinates of the j-th node in the p-th subdomain.

[0062] The residual related to the initial conditions (temperature at the initial moment) of the p-th subdomain is expressed as:

[0063]

[0064] in This represents the number of nodes in the p-th subdomain under the initial conditions. This represents the coordinates of the j-th node in the p-th subdomain under the initial conditions. This represents the known initial conditions of the j-th node in the p-th subdomain, which are obtained in advance through experiments, simulations, or calculations using existing formulas. This represents the initial condition prediction result of the j-th node in the p-th subdomain (i.e., the temperature output of the long short-term memory neural network at the initial time of the j-th node in the p-th subdomain).

[0065] The temperature boundary (boundary of the entire regular mesh) condition-related residual of the p-th subdomain at time t is expressed as:

[0066]

[0067] in This represents the number of nodes in the p-th subdomain that are related to the temperature boundary condition. This represents the coordinates of the j-th node in the p-th subdomain that are related to the temperature boundary conditions. The known temperature boundary conditions at time t for the j-th node in the p-th subdomain that are related to the temperature boundary conditions are obtained in advance through experiments, simulations, or calculations using existing formulas. This is the temperature boundary condition prediction result of the j-th node in the p-th subdomain that is related to the temperature boundary condition at time t (i.e., the temperature output of the j-th node in the p-th subdomain that is related to the temperature boundary condition at time t).

[0068] The heat flux boundary conditions of the p-th subdomain at time t The relevant residuals are expressed as follows:

[0069]

[0070] in This represents the number of nodes in the p-th subdomain that are related to the heat flux boundary condition. This represents the coordinates of the j-th node in the p-th subdomain that are related to the heat flux boundary conditions. The known heat flux boundary conditions at time t for the j-th node in the p-th subdomain, which are related to the heat flux boundary conditions, are obtained in advance through experiments, simulations, or calculations using existing formulas. λ represents the temperature prediction result of the j-th node in the p-th subdomain related to the heat flux boundary condition at time t (i.e., the temperature output of the j-th node in the p-th subdomain related to the heat flux boundary condition at time t). p (T 3,p ) represents the j-th node in the p-th subdomain that is related to the heat flux boundary condition at time t (i.e., with The corresponding thermal conductivity, n p (j,t) represents the heat flow boundary normal vector of the j-th node in the p-th subdomain that is related to the heat flow boundary condition at time t.

[0071] The residual between the p-th subdomain and its adjacent p+1-th subdomain at the common interface is represented as:

[0072]

[0073] in This represents the number of nodes on the common interface between the p-th subdomain and its adjacent p+1-th subdomain. This represents the coordinates of the j-th node on the common interface between the p-th subdomain and its adjacent (p+1)-th subdomain. Let λ be the temperature prediction result at time t of the common interface between the p-th subdomain and its adjacent p+1-th subdomain at the j-th node (i.e., the temperature output at time t of the Long Short-Term Memory Neural Network at the j-th node of the common interface between the p-th subdomain and its adjacent p+1-th subdomain), and let λ be the temperature prediction result at time t of the common interface between the p-th subdomain and its adjacent p+1-th subdomain. p (T 4,p ) represents the node j on the common interface between the p-th subdomain and its adjacent (p+1)-th subdomain at time t (i.e., with The corresponding thermal conductivity, n p,p+1 (j,t) represents the normal vector at time t between the p-th subdomain and the (p+1)-th adjacent subdomain at the j-th node of the common interface.

[0074] The total loss function is expressed as:

[0075]

[0076] Where w1, w2, w3, w4, and w5 are respectively The weight of the item.

[0077] As a preferred option, if a subdomain is a two-dimensional rectangular planar region, then its upper and lower boundaries are considered to be adiabatic. In this case, the residual terms and their weights for the adiabatic upper and lower boundaries need to be added to the total loss function.

[0078] The residual of the lower boundary adiabatic insulation is expressed as:

[0079]

[0080] Where N botm x is the number of nodes on the lower boundary of the p-th two-dimensional rectangular planar region. 1,j The x-coordinate of the j-th node at the lower boundary is represented by y. min T is the ordinate of the lower boundary. 5,p (x 1,j ,y min ,t) represents the temperature prediction result at time t for the j-th node in the p-th subdomain, λ p (T 5,p ) is the j-th node at time t of the lower boundary (i.e., at time T) 5,p (x 1,j ,y min The thermal conductivity of ,t) corresponds to ).

[0081] The residual of the upper boundary adiabatic layer is expressed as:

[0082]

[0083] Where N top x is the number of nodes on the upper boundary of the p-th two-dimensional rectangular planar region. 2,j The x-coordinate of the j-th node at the upper boundary is represented by y. max The coordinates of the upper boundary, T 6,p (x 2,j ,y max ,t) represents the temperature of the j-th node at time t on the upper boundary, λ p (T 6,p ) is the j-th node at time t on the upper boundary (i.e., at time T) 6,p (x 2,j ,y max The thermal conductivity of ,t) corresponds to ).

Claims

1. A method for calculating unsteady heat conduction based on physically embedded attention networks, characterized in that, Includes the following steps: First, data preprocessing is performed. Then, a convolutional neural network is used to extract the spatiotemporal local features of the temperature field, and a long short-term memory neural network based on an attention mechanism is used for weight adjustment. At the same time, a physical information neural network is introduced to impose physical constraints on the data prediction, thus constructing an attention mechanism-physical information neural network. Finally, after data preprocessing, the dataset is divided into a training set and a validation set to train and validate the attention mechanism-physical information neural network. If the training does not reach the required number of iterations and the total loss function does not meet the requirements during training, or if the total loss function does not meet the requirements during validation, the gradient of each node is calculated by automatic differentiation during backpropagation, and the parameters of the attention mechanism-physical information neural network are optimized by the Adamw optimizer.

2. The nonsteady heat conduction calculation method based on physically embedded attention networks according to claim 1, characterized in that, The data preprocessing is as follows: The node data containing temperature, spatial coordinates, and time in the irregular mesh calculated by the finite element method are interpolated into the regular mesh divided by SciPy in Python, and each node has temperature, spatial coordinates, and time data; then the temperature, spatial coordinates, and time are normalized, and the normalized temperature is organized into a temperature field of fixed-dimensional tensor according to time.

3. The nonsteady heat conduction calculation method based on physically embedded attention networks according to claim 1, characterized in that, The convolutional neural network extracts spatiotemporal local features of the temperature field as follows: the preprocessed temperature field is input into the bottom convolutional layer of the convolutional neural network to extract local temperature gradient features, and the output of the bottom convolutional layer is then input into the higher convolutional layer of the convolutional neural network to identify macroscopic temperature diffusion trends.

4. The method for calculating unsteady heat conduction based on physically embedded attention networks according to claim 3, characterized in that, The bottom convolutional layer of the convolutional neural network uses skip connections for feature extraction. Specifically, the temperature field features generated by the last convolutional layer of the bottom convolutional layer are directly connected to the fully connected layer. At the same time, the temperature field features are also sent to the higher convolutional layers. The fully connected layer uses 1×1 convolution to map the number of channels to be consistent with the number of channels in the higher convolutional layers. The output temperature field features are fused with the temperature field features output by the higher convolutional layers to finally output the spatiotemporal local features of the temperature field.

5. The nonsteady heat conduction calculation method based on physically embedded attention networks according to claim 1, characterized in that, A long short-term memory (LSTM) neural network based on an attention mechanism is used to adjust the weights of time series extracted from spatiotemporal local features of the temperature field. Specifically, the bottom layer of the LSM processes the time series of a single grid node or local region. The time features output by the bottom layer are input into the upper layer of the LSM, which integrates the global temperature field. Based on the output features obtained from the upper layer, a query matrix, a key matrix, and a value matrix are constructed. Then, an attention score matrix is ​​calculated using a scaled dot product. The attention score matrix is ​​multiplied by the value matrix to obtain the reweighted features. Finally, the reweighted features and the features obtained from the upper layer are concatenated through a fully connected layer to obtain the final global temperature field feature output of the LSM.

6. The method for calculating unsteady heat conduction based on physically embedded attention networks according to claim 5, characterized in that, The attention mechanism-physical information neural network is constructed as follows: a physical information neural network is introduced; the global temperature field feature output of the long short-term memory neural network is substituted into the transient heat conduction partial differential equation, the residual is calculated and used as the loss term, where the gradient term is calculated by automatic differentiation, and the total loss function of the physical information neural network is constructed by combining the residuals related to the boundary conditions, initial conditions and continuity conditions, thereby constructing the attention mechanism-physical information neural network.

7. The method for calculating unsteady heat conduction based on physically embedded attention networks according to claim 6, characterized in that, Define the transient heat conduction partial differential equation for the p-th subdomain at time t: x p This represents a sequence consisting of the coordinates of all nodes in the p-th subdomain, including the coordinates of each dimension. x represents p The component corresponding to the i-th dimension, λ p (T p ) represents the p-th subfield and T p (x p The thermal conductivity corresponding to ,t), ρ p (T p ) represents the p-th subfield and T p (x p The density corresponding to ,t), c p (T p ) represents the p-th subfield and T p (x p The specific heat capacity corresponding to t), T p (x p (,t) represents the temperature field of the p-th subdomain at time t; Define the residual of the transient heat conduction partial differential equation for the p-th subdomain at time t: Attention mechanism - Trainable grid parameter matrix of the p-th subdomain of a physical information neural network ω k Let b represent the weight matrix of the k-th layer neurons in the p-th subdomain. k Let L represent the bias matrix of the k-th layer neurons in the p-th subdomain, and L represent the total number of layers in the p-th subdomain. This represents the number of nodes in the p-th subdomain. This represents the coordinates of the j-th node in the p-th subdomain.

8. The nonsteady heat conduction calculation method based on physically embedded attention networks according to claim 7, characterized in that, The total loss function is expressed as: Where w1, w2, w3, w4, and w5 are respectively The weight of the item.

9. A method for calculating unsteady heat conduction based on a physically embedded attention network as described in claim 8, characterized in that, The initial condition-related residual of the p-th subdomain is expressed as: in This represents the number of nodes in the p-th subdomain under the initial conditions. This represents the coordinates of the j-th node in the p-th subdomain under the initial conditions. Let represent the known initial conditions of the j-th node in the p-th subdomain. This represents the initial condition prediction result for the j-th node in the p-th subdomain; The temperature boundary condition-related residual of the p-th subdomain at time t is expressed as: in This represents the number of nodes in the p-th subdomain that are related to the temperature boundary condition. This represents the coordinates of the j-th node in the p-th subdomain that are related to the temperature boundary conditions. Let be the known temperature boundary conditions at time t for the j-th node in the p-th subdomain that are related to the temperature boundary conditions. This is the predicted temperature boundary condition of the j-th node in the p-th subdomain that is related to the temperature boundary condition at time t.

10. A method for calculating unsteady heat conduction based on a physically embedded attention network as described in claim 9, characterized in that, The heat flux boundary conditions of the p-th subdomain at time t The relevant residuals are expressed as follows: in This represents the number of nodes in the p-th subdomain that are related to the heat flux boundary condition. This represents the coordinates of the j-th node in the p-th subdomain that are related to the heat flux boundary conditions. Let be the known heat flux boundary conditions at time t for the j-th node in the p-th subdomain that are related to the heat flux boundary conditions. λ represents the temperature prediction result of the j-th node in the p-th subdomain related to the heat flux boundary condition at time t. p (T 3,p Let be the thermal conductivity of the j-th node in the p-th subdomain related to the heat flux boundary condition at time t, and n be the thermal conductivity of the node in the p-th subdomain. p (j,t) represents the heat flow boundary normal vector of the j-th node in the p-th subdomain that is related to the heat flow boundary condition at time t; The residual between the p-th subdomain and its adjacent p+1-th subdomain at the common interface is represented as: in This represents the number of nodes on the common interface between the p-th subdomain and its adjacent p+1-th subdomain. This represents the coordinates of the j-th node on the common interface between the p-th subdomain and its adjacent (p+1)-th subdomain. Let λ be the temperature prediction result at time t of the p-th subdomain and the (p+1)-th adjacent subdomain at the j-th node of the common interface. p (T 4,p Let be the thermal conductivity of the p-th subdomain and its adjacent (p+1)-th subdomain at the j-th node of the common interface at time t, and n be the thermal conductivity of the subdomain. p,p+1 (j,t) represents the normal vector at time t between the p-th subdomain and the (p+1)-th adjacent subdomain at the j-th node of the common interface.

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