Method for simulating electroslag remelting process physical field based on physical information neural network

Abstract

The invention provides a method for simulating a physical field in an electroslag remelting process based on a physical information neural network, and the method comprises the steps: combining the physical law of the physical field involved in the electroslag remelting process with a deep learning network through the physical information neural network, and embedding physical constraints, thereby achieving the effective solving of a partial differential equation; minimizing a loss function formed by a data error term, a physical information error term and a boundary condition error term by using a physical information neural network; by considering physical laws and boundary condition constraints involved in the electroslag remelting process, high solving precision of a partial differential equation is kept under different temporal-spatial resolutions; adjusting and optimizing network parameters by using an automatic differential technology and a gradient descent algorithm; and the result is compared with a high-fidelity CFD simulation result. The method can effectively overcome the limitation problems of high experiment cost, large data volume, high computing power requirement and the like in the existing physical field distribution simulation realized by depending on a thermal state experiment or a first principle.

Description

Technical Field

[0001] The invention belongs to the technical field of intelligent control processes, and in particular relates to a method for simulating the physical field of an electroslag remelting process based on a physical information neural network. Background Art

[0002] Electroslag remelting is an advanced smelting technology that improves consumable electrode materials by remelting consumable electrodes, refining slag and solidifying them. The electroslag remelting process of high-quality special steel uses the Joule heat generated by electric current in high-resistance slag to heat and melt the consumable electrode. The molten metal droplets formed after the special steel consumable electrode is melted pass through the slag pool and converge in the molten metal pool, and further solidify into steel ingots in a water-cooled copper crystallizer from bottom to top. The molten metal droplets undergo a refining reaction with the slag in the process of passing through the slag pool, effectively removing large-sized inclusions and harmful impurity elements in the metal. The physical fields involved in the electroslag remelting process are coupled with each other, affecting physical and chemical phenomena such as electrode melting, refining reaction, and solidification of ingots. Therefore, studying the coupled physical field simulation and transmission phenomena in the electroslag remelting process is of great significance for achieving precise control of the solidification structure and chemical composition of the ingot.

[0003] Since the ESR process is carried out under high temperature and high pressure, and the smelting material is opaque, it is very difficult to accurately measure key variables and collect data in a high temperature environment. It is very difficult to collect and measure data in fully enclosed ESR processes such as protective atmosphere ESR and pressurized ESR. The use of hot experiments to analyze coupled multi-physical field transmission phenomena has the disadvantages of high experimental cost and less measurable data. Hot experiments cannot provide sufficiently rich and comprehensive information to deeply understand and analyze the complex multi-physical field coupling phenomena in the ESR process. In contrast, the use of numerical simulation to study the coupled physical field transmission phenomena in the ESR process has better convenience, flexibility and experimental cost savings. However, conventional machine learning techniques that rely solely on data are purely to identify undetermined parameters by minimizing the loss function. This process requires a large amount of data. This condition is not suitable for high-fidelity simulation of closed ESR processes. At the same time, it also limits and hinders the direct application of big data-based machine learning techniques for predicting physical field distribution in the ESR process.

[0004] To this end, there is an urgent need to provide a method that can combine physical prior knowledge with limited data to achieve efficient and high-precision prediction of the multi-physical fields of the electroslag remelting process, so as to overcome the problems of high cost and insufficient data of traditional hot experiments and to solve the limitations of conventional machine learning on big data. Summary of the invention

[0005] In view of the problems existing in the above-mentioned prior art, the present invention provides a method for simulating the physical field of the electroslag remelting process based on a physical information neural network. The method has low implementation cost, can achieve high-precision prediction of the physical field distribution when data is scarce, and can effectively solve the difficult problems of traditional simulation methods such as strong dependence on data, high computing power requirements, high experimental cost, and poor adaptability. It has a strong value for promotion and application, and can provide a reliable technical basis for the optimization control of special steel production processes.

[0006] In order to achieve the above object, the present invention provides a method for simulating the physical field of an electroslag remelting process based on a physical information neural network, comprising the following steps:

[0007] Step 1: Analyze the physical structure and characteristics of the electroslag remelting process;

[0008] Step 2: Use the data acquisition module to collect physical field data and constraint information during the electroslag remelting process. The specific process is as follows:

[0009] S21: Measure the geometric dimensions and related physical parameters of the ingot;

[0010] S22: measuring the ambient temperature of the upper and lower boundaries and the side boundaries of the ingot in contact with the outside world, and determining the convection heat transfer coefficient of each boundary;

[0011] Step 3: Construct the partial differential equation describing the physical field of the electroslag remelting process. The specific process is as follows:

[0012] S31: Establish the governing equations for heat transfer in the metal pool, two-phase region and ingot;

[0013] A1: Determine the governing equations for the ingot casting part;

[0014] A11: Determine the general equation; use the general equation in formula (1) to describe the quasi-steady-state heat distribution process in the electrode, metal pool, two-phase region and ingot;

[0015] ρ i C Pi (V i ▽T)=▽·K i ▽T+S T,i (1);

[0016] Where i represents the index of electrode e or metal pool l or two-phase region m or ingot s; V i is the growth rate of the ingot; ρ i It can be expressed as the density of the electrode e or the metal pool l or the two-phase region m or the ingot s; C Pi is the specific heat capacity; K i is the temperature-dependent thermal conductivity; S T,i As heat source; is the temperature gradient;

[0017] A12: In the cylindrical coordinate system, convert formula (1) into formula (2) to obtain the control equation;

[0018]

[0019] Where r and z are the radial distance and height coordinates in the cylindrical coordinate system, respectively;

[0020] A2: Determine the heat source term formula;

[0021] A21: Determination of heat source terms for the liquid and solid parts; when considering the metal molten pool of the liquid part and the ingot of the solid part, the heat source terms for the liquid and solid parts are expressed using formula (3);

[0022] S T,l =S T,s =0(3);

[0023] A22: Determination of the heat source term formula in the two-phase region; In the two-phase region, the heat source term in the two-phase region is calculated using formula (4);

[0024]

[0025] Where λ is the latent heat of the melt; f s is the solid percentage in the two-phase region, where T l,m and T s,m are the liquidus and solidus temperatures of the ingot, respectively; V c is the ingot rising rate; ρ m is the density of the two-phase region m;

[0026] A23: Transform formula (4) to obtain formula (5), and use formula (5) to reorganize the heat source term in the two-phase region;

[0027]

[0028] S32: Determine the boundary conditions of the ingot temperature field; there are three boundary heat transfer conditions around the ingot, namely, side wall cooling, bottom water tank cooling, top molten droplet and slag pool heat transfer. When considering the boundary conditions of the temperature field, pay attention to the third type of boundary conditions, namely, Robin conditions or convection boundary conditions, and use formula (6) to characterize the convection heat transfer of the boundary;

[0029]

[0030] In the formula, T is the temperature on the boundary; T0 is the ambient temperature; h is the convective heat transfer coefficient; is the derivative of temperature along the normal direction outside the boundary;

[0031] Step 4: Integrate the deep learning network with physical information. The specific process is as follows:

[0032] S41: Build a deep neural network model;

[0033] B1: Use formula (7) to build a conventional deep neural network;

[0034]

[0035] Where x is the input vector, h (l) represents the output of the lth layer, l = 1, 2, ..., L, is the output vector, L represents the total number of hidden layers;

[0036] B2: Use formula (8) to calculate the input of the lth layer as z (l) At the same time, in the calculation process, the activation function g(·) is introduced to enhance the nonlinear expression ability of the model, and the role of the activation function is expressed by formula (9);

[0037] z (l) =W (l) h (l-1) +b (l) (8);

[0038] h (l) =g(z (l) )(9);

[0039] Where W (l) is the weight matrix of the lth layer, b (l) is the bias vector;

[0040] B3: Use the composite function form in formula (11) to represent the output of the entire neural network;

[0041]

[0042] Where, θ={W (l) ,b (l) |l=1,2,…,L} represents the parameter set of the neural network;

[0043] S42: Introduce the control equation into the deep learning network and construct the loss function of the physical information neural network;

[0044] C1: Convert physical equations into residual terms;

[0045] C11: Convert the control equation into a residual term; the input of the physical information neural network is the cylindrical coordinate x i (r i ,z i ), the output is the predicted temperature value T i, transform formula (2) into the physical residual equation (11);

[0046]

[0047] C12: Convert boundary conditions into residual terms; convert the boundary convection heat transfer equation (6) into the residual equation (12);

[0048]

[0049] C2: construct the total loss function term;

[0050] C21: Construct data loss term; the data loss term is used to ensure that the model can fit the existing observation data, and the data loss term is calculated using formula (13);

[0051]

[0052] In the formula, is the predicted value of the neural network, T i (x i ) is the actual observation value, N is the number of prior data points;

[0053] C22: Construct the control equation loss term; the control equation loss term ensures that the model prediction results conform to the physical partial differential equation. For each training point, the residual loss term of the control equation is calculated using formula (14);

[0054]

[0055] In the formula, R T (x j ; θ) is the physical residual equation term given in C11, and M is the number of collocation points used to calculate the control equation;

[0056] C23: construct boundary condition loss term; the boundary condition loss term is used to ensure that the model prediction meets the boundary conditions. For the boundary conditions, the boundary loss term is calculated using formula (15);

[0057]

[0058] In the formula, R bc (x k ; θ) is the boundary condition residual term given in C12, and P is the number of boundary condition training points taken;

[0059] C24: Construct the total loss function of PINN; the total loss function of PINN calculated using formula (16) is the weighted sum of data loss, control equation loss and boundary condition loss;

[0060]

[0061] In the formula, λ data is the weight coefficient of the data loss term, which is used to balance the impact of data loss; PDE is the residual loss term, which is used to balance the impact of residual loss; BC is the weight coefficient of the boundary loss term, which is used to balance the impact of the boundary loss;

[0062] Step 5: Train the constructed network model. The specific process is as follows:

[0063] S51: Optimize and adjust hyperparameters; use grid search to determine the number of prior data points, the number of matching points, the number of boundary points, and the network hyperparameters;

[0064] S52: training the network; training the network model in batch training mode, and optimizing the network parameters using an optimization algorithm to minimize the value of the loss function;

[0065] Step 6: Verify the experimental results; visually compare the training results of the physical information neural network with the Fluent simulation results, and use regression indicators to evaluate the difference between the predicted results and the simulation results.

[0066] As a preferred embodiment, in step 2 S21, a three-dimensional scanner is used to measure the geometric dimensions and related physical parameters of the ingot.

[0067] As a preference, in B1 of S41 of step 4, L=8.

[0068] As a preference, in step five S52, tanh is used as the activation function in the training process.

[0069] As a preferred embodiment, in step five S52, the L-BFGS optimization algorithm is used to optimize the network parameters.

[0070] Compared with the prior art, the present invention has the following beneficial effects:

[0071] During the electroslag remelting process, the coupled transmission of the physical field is an important factor affecting the smelting quality and process stability. Since electroslag remelting is carried out in high temperature, high pressure or a closed environment, data collection is difficult, and there is a lack of real-time monitoring technology for key variables, resulting in limitations in high-precision simulation of traditional experimental and numerical simulation methods. Based on a physical information neural network, the present invention proposes a general method for simulating the physical field distribution of the electroslag remelting process of high-quality special steel, so as to achieve high-precision prediction of multi-physical field coupling phenomena. In order to solve the problem of limited data in actual production, a physical information neural network is used to embed physical laws as prior knowledge into the network structure, which reduces dependence on big data, improves simulation accuracy and generalization ability, and reduces data sampling costs. At the same time, the present invention calculates the PDE residual through automatic differentiation technology, and adds it to the loss function as a regularization term, so as to obtain a solution that is consistent with the actual physical laws and has good generalization ability. Compared with traditional neural networks, the prediction results of physical information neural networks have better physical interpretability and generalization ability due to the embedded specific physical prior knowledge information. It can maintain high accuracy at different time and space resolutions, thereby improving the credibility of the simulation results, which also makes it particularly suitable for simulating multi-physical field transmission phenomena in the electroslag remelting process. By introducing data loss, control equation loss and boundary condition loss to construct multiple loss terms, it can ensure that the model meets the physical laws of the electroslag remelting process while meeting the actual observation data, thereby significantly improving the prediction accuracy of the model.

[0072] The present invention provides a general simulation method for the electroslag remelting process of high-quality special steel based on a physical information neural network. It only requires a small amount of experimental data to effectively replace hot experiments, effectively improves the simulation accuracy and the adaptability of the model, and can achieve high-precision prediction of the physical field distribution when data is scarce. It has good physical interpretability and credibility. At the same time, it effectively solves a series of problems of traditional simulation methods such as strong data dependence, high computing power requirements, high experimental costs, and poor adaptability. It has a strong value for promotion and application, and provides a reliable physical field prediction model for the optimization control of special steel production processes. BRIEF DESCRIPTION OF THE DRAWINGS

[0073] Figure 1 It is the method flow of the present invention;

[0074] Figure 2 The geometric data and external environment data of the ingot part used in the present invention;

[0075] Figure 3 It is a comparison chart of the predicted temperature results and the Fluent simulation results in the present invention;

[0076] Figure 4It is the residual diagram of the prediction result in the present invention and the Fluent simulation result. DETAILED DESCRIPTION

[0077] The present invention will be further described below in conjunction with the accompanying drawings.

[0078] like Figures 1 to 4 As shown, the present invention provides a method for simulating the physical field of an electroslag remelting process based on a physical information neural network, comprising the following steps:

[0079] Step 1: Analyze the physical structure and characteristics of the electroslag remelting process;

[0080] Step 2: Use the data acquisition module to collect physical field data and constraint information during the electroslag remelting process. The specific process is as follows:

[0081] S21: Measure the geometric dimensions and related physical parameters of the ingot;

[0082] S22: measuring the ambient temperature of the upper and lower boundaries and the side boundaries of the ingot in contact with the outside world, and determining the convection heat transfer coefficient of each boundary;

[0083] Step 3: Construct the partial differential equation describing the physical field of the electroslag remelting process. The specific process is as follows:

[0084] S31: Establish the governing equations for heat transfer in the metal pool, two-phase region and ingot;

[0085] A1: Determine the governing equations for the ingot casting part;

[0086] A11: Determine the general equation; use the general equation in formula (1) to describe the quasi-steady-state heat distribution process in the electrode, metal pool, two-phase region and ingot;

[0087]

[0088] Where i represents the index of electrode e or metal pool l or two-phase region m or ingot s; V i is the growth rate of the ingot; ρ i It can be expressed as the density of the electrode e or the metal pool l or the two-phase region m or the ingot s; C Pi is the specific heat capacity; K i is the temperature-dependent thermal conductivity; S T,i is the heat source; ▽T is the temperature gradient;

[0089] A12: In the cylindrical coordinate system, convert formula (1) into formula (2) to obtain the control equation;

[0090]

[0091] Where r and z are the radial distance and height coordinates in the cylindrical coordinate system, respectively;

[0092] A2: Determine the heat source term formula;

[0093] A21: Determination of heat source terms for the liquid and solid parts; when considering the metal molten pool of the liquid part and the ingot of the solid part, the heat source terms for the liquid and solid parts are expressed using formula (3);

[0094] S T,l =S T,s =0(3);

[0095] A22: Determination of the heat source term formula in the two-phase region; In the two-phase region, the heat source term in the two-phase region is calculated using formula (4);

[0096]

[0097] Where λ is the latent heat of the melt; f s is the solid percentage in the two-phase region, where T l,m and T s,m are the liquidus and solidus temperatures of the ingot, respectively; V c is the ingot rising rate; ρ m is the density of the two-phase region m;

[0098] A23: Transform formula (4) to obtain formula (5), and use formula (5) to reorganize the heat source term in the two-phase region;

[0099]

[0100] S32: Determine the boundary conditions of the ingot temperature field; there are three boundary heat transfer conditions around the ingot, namely, side wall cooling, bottom water tank cooling, top molten droplet and slag pool heat transfer. When considering the boundary conditions of the temperature field, pay attention to the third type of boundary conditions, namely, Robin conditions or convection boundary conditions, and use formula (6) to characterize the convection heat transfer of the boundary;

[0101]

[0102] In the formula, T is the temperature on the boundary; T0 is the ambient temperature; h is the convective heat transfer coefficient; is the derivative of temperature along the normal direction outside the boundary;

[0103] Step 4: Integrate the deep learning network with physical information. The specific process is as follows:

[0104] S41: Build a deep neural network model;

[0105] B1: Use formula (7) to build a conventional deep neural network;

[0106]

[0107] Where x is the input vector, h (l) represents the output of the lth layer, l = 1, 2, ..., L, is the output vector, L represents the total number of hidden layers;

[0108] B2: Use formula (8) to calculate the input of the lth layer as z (l) At the same time, in the calculation process, the activation function g(·) is introduced to enhance the nonlinear expression ability of the model, and the role of the activation function is expressed by formula (9);

[0109] z (l) =W (l) h (l-1) +b (l) (8);

[0110] h (l) =g(z (l) )(9);

[0111] Where W (l) is the weight matrix of the lth layer, b (l) is the bias vector;

[0112] B3: Use the composite function form in formula (11) to represent the output of the entire neural network;

[0113]

[0114] Where, θ={W (l) ,b (l) |l=1,2,...,L} represents the parameter set of the neural network;

[0115] S42: Introduce the control equation into the deep learning network and construct the loss function of the physical information neural network;

[0116] C1: Convert physical equations into residual terms;

[0117] C11: Convert the control equation into a residual term; the input of the physical information neural network is the cylindrical coordinate x i (r i ,z i ), the output is the predicted temperature value T i , transform formula (2) into the physical residual equation (11);

[0118]

[0119] C12: Convert boundary conditions into residual terms; convert the boundary convection heat transfer equation (6) into the residual equation (12);

[0120]

[0121] C2: construct the total loss function term;

[0122] C21: Construct data loss term; the data loss term is used to ensure that the model can fit the existing observation data, and the data loss term is calculated using formula (13);

[0123]

[0124] In the formula, is the predicted value of the neural network, T i (x i ) is the actual observation value, N is the number of prior data points;

[0125] C22: Construct the control equation loss term; the control equation loss term ensures that the model prediction results conform to the physical partial differential equation. For each training point, the residual loss term of the control equation is calculated using formula (14);

[0126]

[0127] In the formula, R T (x j ; θ) is the physical residual equation term given in C11, and M is the number of collocation points used to calculate the control equation;

[0128] C23: construct boundary condition loss term; the boundary condition loss term is used to ensure that the model prediction meets the boundary conditions. For the boundary conditions, the boundary loss term is calculated using formula (15);

[0129]

[0130] In the formula, R bc (x k ; θ) is the boundary condition residual term given in C12, and P is the number of boundary condition training points taken;

[0131] C24: Construct the total loss function of PINN; the total loss function of PINN calculated using formula (16) is the weighted sum of data loss, control equation loss and boundary condition loss;

[0132]

[0133] In the formula, λ data is the weight coefficient of the data loss term, which is used to balance the impact of data loss; PDE is the residual loss term, which is used to balance the impact of residual loss; BC is the weight coefficient of the boundary loss term, which is used to balance the impact of the boundary loss;

[0134] Step 5: Train the constructed network model. The specific process is as follows:

[0135] S51: Optimize and adjust hyperparameters; use grid search to determine the number of prior data points, the number of matching points, the number of boundary points, and the network hyperparameters;

[0136] S52: training the network; training the network model in batch training mode, and optimizing the network parameters using an optimization algorithm to minimize the value of the loss function;

[0137] Step 6: Verify the experimental results; visually compare the training results of the physical information neural network with the Fluent simulation results, and use regression indicators to evaluate the difference between the predicted results and the simulation results.

[0138] As a preferred embodiment, in step 2 S21, a three-dimensional scanner is used to measure the geometric dimensions and related physical parameters of the ingot.

[0139] As a preference, in B1 of S41 of step 4, L=8.

[0140] As a preference, in step five S52, tanh is used as the activation function in the training process.

[0141] As a preferred embodiment, in step five S52, the L-BFGS optimization algorithm is used to optimize the network parameters.

[0142] Example:

[0143] This application takes the ingots in the electroslag remelting process of high-quality special steel as the object, and collects the geometric data and external environment data of the ingot part in the actual factory production process, such as Figure 2 The relevant physical property parameters of the ingot used are shown in Table 1.

[0144] Table 1: Physical properties of ingot metal

[0145]

[0146] For the ingot part, 70 points were randomly selected from the left and right boundaries, 30 points were randomly selected from the upper and lower boundaries, and a total of 200 boundary points were used as boundary condition points. 60 points were randomly selected from the internal phase change zone, and a total of 260 points were used as prior data points. Latin hypercube sampling was used to sample 10,000 points inside the ingot. The deep neural network used 8 hidden layers, and each hidden layer used 200 neurons for training. The activation function used tanh, and the L-BFGS optimization algorithm was used for network parameter optimization. After 1554 rounds of iterative calculations, the model converged.

[0147] Compare the training results of the physical information neural network with the Fluent simulation results, such as Figure 3 The temperature distribution obtained by the two is subtracted, and the error distribution of the physical information neural network training result is obtained, as shown in Figure 4 As shown in Figure 2, it can be seen that the results obtained by the physical information neural network and Fluent are very consistent. The experiment shows that the proposed method can well predict the internal temperature distribution of the ingot during electroslag remelting.

[0148] In order to further quantitatively verify the effectiveness of the proposed prediction method, the root mean square error Mean absolute error Coefficient of determination And the relative L2 error The prediction index is calculated to evaluate the difference between the prediction results of the invention and the simulation results of Fluent. The evaluation index results are shown in Table 2. It can be seen that the prediction results are highly accurate, which reflects the effectiveness and superiority of the proposed model.

[0149] Table 2: Regression index results of prediction results

[0150]

[0151] During the electroslag remelting process, the coupled transmission of the physical field will affect the smelting quality and process stability. Since electroslag remelting is carried out in a high temperature and high pressure environment, data collection is difficult. Traditional experimental and numerical simulation methods have certain limitations in high-precision simulation. Based on a physical information neural network, the present invention proposes a general method for simulating the physical field distribution in the electroslag remelting process of high-quality special steel, so as to achieve high-precision prediction of multi-physical field coupling phenomena. In order to solve the problem of limited data in actual production, the physical information neural network is used to embed the physical laws as prior knowledge into the network structure, which significantly improves the simulation accuracy and generalization ability. At the same time, the introduction of multiple loss terms in the present invention can ensure that the model meets the physical laws of the electroslag remelting process while meeting the actual observation data, thereby effectively improving the accuracy and adaptability of the model.

[0152] In summary, the general simulation method for high-quality special steel electroslag remelting process based on physical information neural network provided by the present invention effectively improves the simulation accuracy and adaptability. In the case of data scarcity, the present invention can also achieve accurate prediction of physical field distribution. The present invention solves the problem of strong data dependence and poor adaptability of traditional simulation methods, has strong promotion and application value, and provides a reliable physical field model for the optimization control of special steel production process.

Claims

1. A method for simulating the physical field of electroslag remelting process based on physical information neural network, characterized in that: The following steps are involved: Step 1: Analyze the physical structure and characteristics of the electroslag remelting process; Step 2: Use the data acquisition module to collect physical field data and constraint information during the electroslag remelting process. The specific process is as follows: S21: Measure the geometric dimensions and related physical parameters of the ingot; S22: measuring the ambient temperature of the upper and lower boundaries and the side boundaries of the ingot in contact with the outside world, and determining the convection heat transfer coefficient of each boundary; Step 3: Construct the partial differential equation describing the physical field of the electroslag remelting process. The specific process is as follows: S31: Establish the governing equations for heat transfer in the metal pool, two-phase region and ingot; A1: Determine the governing equations for the ingot casting part; A11: Determine the general equation; use the general equation in formula (1) to describe the quasi-steady-state heat distribution process in the electrode, metal pool, two-phase region and ingot; Where i represents the index of electrode e or metal pool l or two-phase region m or ingot s; V i is the growth rate of the ingot; ρ i It can be expressed as the density of the electrode e or the metal pool l or the two-phase region m or the ingot s; C Pi is the specific heat capacity; K i is the temperature-dependent thermal conductivity; S T,i As heat source; is the temperature gradient; A12: In the cylindrical coordinate system, convert formula (1) into formula (2) to obtain the control equation; Where r and z are the radial distance and height coordinates in the cylindrical coordinate system, respectively; A2: Determine the heat source term formula; A21: Determination of heat source terms for the liquid and solid parts; when considering the metal molten pool of the liquid part and the ingot of the solid part, the heat source terms for the liquid and solid parts are expressed using formula (3); S T,l =S T,s =0(3); A22: Determination of the heat source term formula in the two-phase region; In the two-phase region, the heat source term in the two-phase region is calculated using formula (4); Where λ is the latent heat of the melt; f s is the solid percentage in the two-phase region, where T l,m and T s,m are the liquidus and solidus temperatures of the ingot, respectively; V c is the ingot rising rate; ρ m is the density of the two-phase region m; A23: Transform formula (4) to obtain formula (5), and use formula (5) to reorganize the heat source term in the two-phase region; S32: Determine the boundary conditions of the ingot temperature field; there are three boundary heat transfer conditions around the ingot, namely, side wall cooling, bottom water tank cooling, top molten droplet and slag pool heat transfer. When considering the boundary conditions of the temperature field, pay attention to the third type of boundary conditions, namely, Robin conditions or convection boundary conditions, and use formula (6) to characterize the convection heat transfer of the boundary; In the formula, T is the temperature on the boundary; T0 is the ambient temperature; h is the convective heat transfer coefficient; is the derivative of temperature along the normal direction outside the boundary; Step 4: Integrate the deep learning network with physical information. The specific process is as follows: S41: Build a deep neural network model; B1: Use formula (7) to build a conventional deep neural network; Where x is the input vector, h (l) represents the output of the lth layer, l = 1, 2, ..., L, is the output vector, L represents the total number of hidden layers; B2: Use formula (8) to calculate the input of the lth layer as z (l) At the same time, in the calculation process, the activation function g(·) is introduced to enhance the nonlinear expression ability of the model, and the role of the activation function is expressed by formula (9); z (l) =W (l) h (l-1) +b (l) (8); h (l) =g(z (l) )(9); Where W (l) is the weight matrix of the lth layer, b (l) is the bias vector; B3: Use the composite function form in formula (11) to represent the output of the entire neural network; Where, θ={W (l) ,b (l) |l=1,2,…,L} represents the parameter set of the neural network; S42: Introduce the control equation into the deep learning network and construct the loss function of the physical information neural network; C1: Convert physical equations into residual terms; C11: Convert the control equation into a residual term; the input of the physical information neural network is the cylindrical coordinate x i (r i ,z i ), the output is the predicted temperature value T i , transform formula (2) into the physical residual equation (11); C12: Convert boundary conditions into residual terms; convert the boundary convection heat transfer equation (6) into the residual equation (12); C2: construct the total loss function term; C21: Construct data loss term; the data loss term is used to ensure that the model can fit the existing observation data, and the data loss term is calculated using formula (13); In the formula, is the predicted value of the neural network, T i (x i ) is the actual observation value, N is the number of prior data points; C22: Construct the control equation loss term; the control equation loss term ensures that the model prediction results conform to the physical partial differential equation. For each training point, the residual loss term of the control equation is calculated using formula (14); In the formula, R T (x j ; θ) is the physical residual equation term given in C11, and M is the number of collocation points used to calculate the control equation; C23: construct boundary condition loss term; the boundary condition loss term is used to ensure that the model prediction meets the boundary conditions. For the boundary conditions, the boundary loss term is calculated using formula (15); In the formula, R bc (x k ; θ) is the boundary condition residual term given in C12, and P is the number of boundary condition training points taken; C24: Construct the total loss function of PINN; the total loss function of PINN calculated using formula (16) is the weighted sum of data loss, control equation loss and boundary condition loss; In the formula, λ data is the weight coefficient of the data loss term, which is used to balance the impact of data loss; PDE is the residual loss term, which is used to balance the impact of residual loss; BC is the weight coefficient of the boundary loss term, which is used to balance the impact of the boundary loss; Step 5: Train the constructed network model. The specific process is as follows: S51: Optimize and adjust hyperparameters; use grid search to determine the number of prior data points, the number of matching points, the number of boundary points, and the network hyperparameters; S52: training the network; training the network model in batch training mode, and optimizing the network parameters using an optimization algorithm to minimize the value of the loss function; Step 6: Verify the experimental results; visually compare the training results of the physical information neural network with the Fluent simulation results, and use regression indicators to evaluate the difference between the predicted results and the simulation results.

2. The method for simulating the physical field of electroslag remelting process based on physical information neural network according to claim 1 is characterized in that: In step 2 S21, a three-dimensional scanner is used to measure the geometric dimensions and related physical parameters of the ingot.

3. The method for simulating the physical field of electroslag remelting process based on physical information neural network according to claim 2 is characterized in that: In B1 of S41 of step 4, L=8.

4. The method for simulating the physical field of electroslag remelting process based on physical information neural network according to claim 3 is characterized in that: In step 5 S52, tanh is used as the activation function in the training process.

5. The method for simulating the physical field of electroslag remelting process based on physical information neural network according to claim 3 is characterized in that: In step five S52, the L-BFGS optimization algorithm is used to optimize network parameters.

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