Reactor core nuclear thermal coupling calculation method based on embedded physical knowledge neural network

Abstract

The invention discloses a reactor core nuclear thermal coupling calculation method based on an embedded physical knowledge neural network. The method comprises the following steps: 1, dividing reactor core nodes of a nuclear reactor; 2, initializing neutron physical field parameters and thermal hydraulic parameters of the reactor core; 3, building, training and storing an embedded physical knowledge neural network model; 4, predicting the neutron number density of each node of the reactor core by using the stored model to obtain neutron flux distribution; 5, calculating reactor core power distribution according to neutron flux distribution; 6, calculating and updating the thermal hydraulic parameters of the reactor core at the tn + 1 moment by using a system analysis program; 7, calculating and updating reactivity of each node of the reactor core; and 8, judging whether the appointed calculation time is reached, if so, ending, otherwise, returning to the step 4. The method is based on an embedded physical knowledge neural network method, an accurate and efficient calculation method is provided for solving distribution of the neutron physical field and the thermal field in the reactor core, and the method has important significance on reactor design optimization.

Description

Technical Field

[0001] The present invention belongs to the technical field of nuclear-thermal coupling calculation of reactor cores, and particularly relates to a method for calculating nuclear-thermal coupling of reactor cores based on a physics-informed neural network. Background Art

[0002] There is a complex nuclear-thermal coupling physical field inside the reactor core. Neutron kinetic parameters determine the core power distribution, thus affecting the thermal-hydraulic state, and the thermal-hydraulic parameters affect the neutron physical field through reactivity feedback and other means. A coupling interface is developed to call the neutron kinetics program and the thermal-hydraulic program simultaneously for data transfer to achieve the analysis and calculation of the nuclear-thermal coupling physical field.

[0003] Currently, there are one-dimensional system programs and CFD programs that can perform nuclear-thermal coupling calculations on reactor cores. However, the accuracy of calculating the neutron physical field using system programs is low, and the convergence speed is slow and computational resources are consumed when using CFD programs for coupling calculations. Currently, there is a lack of a fast, efficient, and high-precision program for calculating nuclear-thermal coupling of reactor cores. Summary of the Invention

[0004] To fill the gaps in the above-mentioned existing technologies, the purpose of the present invention is to provide a method for calculating nuclear-thermal coupling of reactor cores based on a physics-informed neural network, which can quickly, efficiently, and accurately solve the nuclear-thermal coupling physical field of reactor cores and is of great significance for the design and optimization of reactor cores.

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

[0006] A method for calculating nuclear-thermal coupling of reactor cores based on a physics-informed neural network includes the following steps:

[0007] Step 1: Determine the geometric shape of the reactor core and perform node division. Axially divide it into m nodes and radially divide it into n rings;

[0008] Step 2: Initialize the state parameters, specifically including the following content:

[0009] Step 2-1: Initialize the core fuel, coolant temperature, and power thermal-hydraulic state parameters;

[0010] Step 2-2: Initialize the reactivity and neutron number density of each node in the core;

[0011] Step 3: At time t n Build a physics-informed neural network in the deep learning framework DeepXDE, and train and optimize the built physics-informed neural network to solve the neutron diffusion equation, obtaining a model for calculating the neutron number density of each node in the core;

[0012] Step 4: Use the trained model to predict the neutron number density \(n(r,t)\) at each node in the core and calculate the neutron flux distribution in the core;

[0013] Step 5: Convert the neutron flux distribution in the core obtained in Step 4 into the core power distribution through the following formula:

[0014] \(P(r,t)=E\) f \(\sum\) f5 \(\varphi V\)

[0015] In the formula:

[0016] \(P(r,t)\): The power distribution of the node at position \(r\) at time \(t\); n

[0017] \(E\) f : The energy released per fission;

[0018] \(\sum\) f5 : The macroscopic cross-section of thermal neutrons of \(U\) 235 ;

[0019] \(\varphi\): The neutron flux in the node;

[0020] \(V\): The volume of the node;

[0021] Step 6: Fill the core power distribution obtained in Step 5 into the input card of the nuclear reactor thermal-hydraulic analysis software MELCOR as the energy source term. This software is a one-dimensional system analysis program, and calculate the thermal-hydraulic state parameters of each node in the core at time \(t\): coolant temperature and fuel temperature; n+1

[0022] Step 7: Calculate the total reactivity of each node at time \(t\) based on the core thermal-hydraulic parameters and reactivity feedback relationship obtained in Step 6 n+1 ;

[0023] \(\rho=\rho_0+\rho\) ext +\(\rho\) D +\(\rho\) f,a +\(\rho\) f,r +\(\rho\) c

[0024] In the formula:

[0025] \(\rho\) —— The total reactivity of the node at the end of the time step \(t\) n+1 ;

[0026] \(\rho_0\) —— The total reactivity of the node at the beginning of the time step \(t\) n ;

[0027] \(\rho\) ext —— The external reactivity introduced into the node within the time step \(\Delta\tau\);

[0028] \(\rho\) D—— Reactivity caused by the fuel Doppler effect within the time step Δτ;

[0029] ρ f,a —— Reactivity caused by the axial thermal expansion of the fuel within the time step Δτ;

[0030] ρ f,r —— Reactivity caused by the radial thermal expansion of the fuel within the time step Δτ;

[0031] ρ c —— Reactivity caused by the thermal expansion of the coolant within the time step Δτ;

[0032]

[0033] ρ f,a =α f,a (T f -T f,0 )

[0034] ρ f,r =α f,r (T f -T f,0 )

[0035] ρ c =α c (T c -T c,0 )

[0036] Where:

[0037] K D —— Fuel Doppler coefficient;

[0038] α f,a —— Axial thermal expansion feedback coefficient of the fuel;

[0039] α f,r —— Radial thermal expansion feedback coefficient of the fuel;

[0040] α c —— Coolant thermal expansion feedback coefficient;

[0041] T f —— Fuel temperature at the initial time node t of the time step n ;

[0042] T f,0 —— Fuel temperature at the initial time node t of the previous time step n-1 ;

[0043] T c —— Coolant temperature at the initial time node t of the time step n ;

[0044] T c,0——Initial time step \(t\) of the previous step n-1 Coolant temperature at the time node

[0045] Step 8: Take \(t\) n+1 at the moment as the new \(t\) n at the moment, and repeat Steps 4 to 7 until the specified calculation time is reached.

[0046] Step 3 is specifically as follows:

[0047] Step 3-1: Build a neural network structure in the deep learning framework DeepXDE;

[0048] Adopt a fully connected neural network structure, set the depth, the number of neurons in the middle layer, the activation function, the boundary weight, the learning rate, the optimizer, and the number of training times, and initialize the network using the Gaussian distribution random sampling method;

[0049] Step 3-2: Record the output of the fully connected layer of the neural network built in Step 3-1: The predicted value \(n\) of the neutron number density of each node pred and the predicted value \(C\) of the delayed neutron precursor number density ipred ;

[0050] Step 3-3: Calculate the loss value of the physics-informed neural network, including three parts: the PDE operator loss of the neutron diffusion equation, the observation loss, and the regularization loss:

[0051] 1) Calculate the PDE operator loss of the neutron diffusion equation, which specifically includes the following:

[0052] a. The neutron diffusion equation is as follows:

[0053]

[0054] In the formula:

[0055] \(n(r,t)\): Neutron number density at position \(r\) at time \(t\) n ;

[0056] \(S(r,t)\): Exogenous neutron number density at position \(r\) at time \(t\) n ;

[0057] \(\rho(r,t)\): Total reactivity of the node at position \(r\) at time \(t\) n ;

[0058] \(\beta\): Total fraction of delayed neutrons

[0059] \(\Lambda\): Neutron generation time

[0060] \(\lambda\) i : Decay constant of the \(i\)-th group of delayed neutron precursors

[0061] \(C\) i(r, t): The number density of the i-th group of delayed neutron precursors at position r at time t;

[0062] β i : The fraction of the i-th group of delayed neutrons;

[0063] b. Use the automatic differentiation function in the deep learning framework DeepXDE to calculate the derivatives of n(r, t) and with respect to time and space respectively;

[0064] c. Construct the PDE operator of the neutron diffusion equation:

[0065]

[0066] In the formula:

[0067] n (t) : The first-order derivative of n(r, t) with respect to time t;

[0068] n (rr) : The second-order derivative of n(r, t) with respect to position r;

[0069] n pred : The predicted value of n(r, t) by the neural network;

[0070] C ipred : The predicted value of C i (r, t) by the neural network;

[0071] d. Use the deep learning framework DeepXDE to calculate the PDE operator loss Loss o ;

[0072] 2) Calculate the value of the total loss function Loss:

[0073] Loss = λ d Loss d + λ o Loss o + λ reg Loss2

[0074] In the formula:

[0075] λ d : The observation loss coefficient;

[0076] λ o : The PDE operator loss coefficient;

[0077] λ reg : The regularization coefficient;

[0078] Loss d : The observation loss;

[0079] Loss2: Parameter L2 regularization loss;

[0080]

[0081] In the formula:

[0082] N: Number of samples;

[0083] w ij : Weight connecting the i-th sample and the j-th neuron;

[0084] Step 3-4: Determine whether the set number of training rounds in Step 3-1 or the target value set by the loss function is reached. If so, terminate the training; otherwise, proceed to Step 3-5;

[0085] Step 3-5: Repeat Steps 3-2 to 3-4 to train and optimize the embedded physics knowledge neural network;

[0086] 1) Read the output of the fully connected layer at each step in Step 3-2, calculate the loss function value in Step 3-3, and minimize the loss;

[0087] 2) Record the total loss function value and the total loss decrease data in 2) of Step 3-3 after each training;

[0088] Step 3-6: Save the trained model for calculating the neutron number density at each node of the reactor core.

[0089] Compared with the prior art, the present invention has the following advantages:

[0090] 1. The present invention calculates the thermal-hydraulic parameters based on a one-dimensional system analysis program and calculates the neutron physics field based on the embedded physics knowledge neural network method, which not only ensures high calculation accuracy of the neutron physics field but also ensures a fast convergence speed and low calculation resource consumption in the entire coupling calculation process;

[0091] After the embedded physics knowledge neural network model is trained and saved, when calculating at each time step, only the trained model needs to be called to quickly solve the neutron number density at each node of the reactor core, which ensures the calculation speed of the neutron physics field, thereby improving the calculation speed of the core nuclear-thermal coupling and having low calculation resource consumption;

[0092] 2. The present invention realizes the core nuclear-thermal coupling calculation and analysis through the two-way data exchange between the neutron physics field parameters and the thermal-hydraulic parameters of the nuclear reactor core. Brief Description of the Drawings

[0093] Figure 1 It is a flow chart of the reactor core nuclear-thermal coupling calculation method based on the embedded physics knowledge neural network;

[0094] Figure 2Schematic diagram of core node division;

[0095] Figure 3 It is a flow chart for solving the core neutron flux distribution by embedding a physics knowledge neural network. Specific implementation manner

[0096] The present invention will be described in detail below in conjunction with the accompanying drawings.

[0097] The present invention provides a reactor core nuclear thermal coupling calculation method based on an embedded physics knowledge neural network, and the specific process is as Figure 1 shown, including the following steps:

[0098] Step 1: Determine the geometric shape of the reactor core and perform node division, as Figure 2 shown: The reactor core is set to be cylindrical, with a height of h, a radius of r, axially divided into 10 nodes, and radially divided into 4 rings;

[0099] Step 2: Initialize the state parameters, specifically including the following contents:

[0100] Step 2-1: Initialize the thermal-hydraulic state parameters of each node in the core: fuel temperature, coolant temperature, and core power;

[0101] Step 2-2: Initialize the neutron physics field parameters of each node in the core: reactivity and neutron number density;

[0102] Step 3: At time t n , build an embedded physics knowledge neural network in the deep learning framework DeepXDE, and train and optimize the built embedded physics knowledge neural network to solve the neutron diffusion equation, and obtain a model for calculating the neutron number density of each node in the core, as Figure 3 , specifically including the following contents:

[0103] Step 3-1: Build a neural network structure in the deep learning framework DeepXDE, specifically including the following contents:

[0104] Adopt a fully connected neural network structure, with a depth l = 16, the number of neurons in the middle layer s = 20, the activation function selects the hyperbolic tangent function tanh, the boundary weight P b = 100, the learning rate lr = 0.001, the optimizer selects Adam, uses the Gaussian distribution random sampling method to initialize the network, sets the number of training rounds N_train = 100000 as the stop condition, and sets the target value of the loss function to 0.001;

[0105] Step 3-2: Record the output of the fully connected layer of the neural network built in Step 3-1: the predicted value n of the neutron number density of each node predAnd the number density C of the delayed neutron precursors ipred ;

[0106] Step 3-3: Calculate the loss value of the embedded physics knowledge neural network, which includes three parts: the PDE operator loss of the neutron diffusion equation, the observation loss, and the regularization loss:

[0107] 1) Calculate the PDE operator loss of the neutron diffusion equation, which specifically includes the following:

[0108] a. The neutron diffusion equation is as follows:

[0109]

[0110] In the formula:

[0111] n(r,t): The neutron number density at position r at time t n ;

[0112] S(r,t): The external neutron number density at position r at time t n ;

[0113] ρ(r,t): The total reactivity of the node at position r at time t n ;

[0114] β: The total fraction of delayed neutrons;

[0115] Λ: The neutron generation time;

[0116] λ i : The decay constant of the i-th group of delayed neutron precursors;

[0117] C i (r,t): The number density of the i-th group of delayed neutron precursors at position r at time t;

[0118] β i : The fraction of the i-th group of delayed neutrons;

[0119] b. Use the automatic differentiation function in the deep learning framework DeepXDE to calculate the first derivative of n(r,t) with respect to time t and the second derivative with respect to the spatial position r in the neutron diffusion equation respectively;

[0120] c. Construct the PDE operator of the neutron diffusion equation:

[0121]

[0122] In the formula:

[0123] n (t) : The first derivative of n(r,t) with respect to time t;

[0124] n (rr): The second derivative of n(r, t) with respect to the position r;

[0125] n pred : The predicted value of n(r, t) by the neural network;

[0126] C ipred : The predicted value of C by the neural network i (r, t); d. Use the deep learning framework DeepXDE to calculate the PDE operator loss Loss o , specifically:

[0127] Loss o = PDE 2

[0128] 2) Calculate the value of the total loss function Loss:

[0129] Loss = λ d Loss d + λ o Loss o + λ reg Loss2

[0130] In the formula:

[0131] λ d : Observation loss coefficient;

[0132] λ o : PDE operator loss coefficient;

[0133] λ reg : Regularization coefficient;

[0134] Loss d : Observation loss;

[0135] Loss o : PDE operator loss;

[0136] Loss2: Parameter L2 regularization loss;

[0137] Since the neural network with embedded physical knowledge is used for nuclear thermal coupling calculation in the present invention, which belongs to a regression problem, the mean square error is selected as the observation loss function Loss d :

[0138]

[0139] In the formula:

[0140] N: Number of samples;

[0141] w ij : The weight connecting the i-th sample and the j-th neuron;

[0142] Step 3-4: Determine whether the set number of training rounds in Step 3-1 or the target value set by the loss function is reached. If so, terminate the training; otherwise, proceed to Step 3-5;

[0143] Step 3-5: Repeat Steps 3-2 to 3-4 to train and optimize the physics-embedded neural network;

[0144] 1) Read the output of the fully connected layer at each step in Step 3-2, calculate the loss function value in Step 3-3, and minimize the loss;

[0145] 2) Record the total loss function value and the total loss reduction data in 2) of Step 3-3 after each training;

[0146] Step 3-6: Save the trained model for calculating the neutron number density of each node in the core;

[0147] Step 4: Use the trained model to predict the neutron number density n(r,t) of each node in the core and calculate the neutron flux distribution in the core:

[0148] φ(r,t) = n(r,t)v

[0149] v: Neutron velocity;

[0150] φ(r,t): Neutron flux at time node t n ;

[0151] Step 5: Convert the neutron flux distribution in the core at time t obtained in Step 4 into the core power distribution through the following formula: n P(r,t) = E

[0152] Σ f φV f5

[0153] Where:

[0154] P(r,t): Power distribution of the node at position r at time t n ;

[0155] E f : Energy released per fission;

[0156] Σ f5 : Macroscopic cross section of thermal neutrons of U 235 ;

[0157] φ: Neutron flux in the node;

[0158] V: Volume of the node;

[0159] ​Step 6: Use the core power distribution obtained in Step 5 as the energy source term and fill it into the input card of the nuclear reactor thermal-hydraulic analysis software MELCOR. This software is a one-dimensional system analysis program, and the thermal-hydraulic state parameters of each node in the core at time t are calculated: coolant temperature and fuel temperature; n+1 At time t, the thermal-hydraulic state parameters of each node in the core: coolant temperature and fuel temperature;

[0160] Step 7: Calculate the total reactivity of each node at time t based on the core thermal-hydraulic parameters and reactivity feedback relationships obtained in Step 6; n+1 At time t, the total reactivity of each node;

[0161] ρ = ρ0 + ρ ext + ρ D + ρ f,a + ρ f,r + ρ c

[0162] Where:

[0163] ρ —— The total reactivity of the node at the end of the time step t n+1 At time t;

[0164] ρ0 —— The total reactivity of the node at the beginning of the time step t n At time t;

[0165] ρ ext —— The external reactivity introduced into the node within the time step Δτ;

[0166] ρ D —— The reactivity caused by the fuel Doppler effect within the time step Δτ;

[0167] ρ f,a —— The reactivity caused by the axial thermal expansion of the fuel within the time step Δτ;

[0168] ρ f,r —— The reactivity caused by the radial thermal expansion of the fuel within the time step Δτ;

[0169] ρ c —— The reactivity caused by the thermal expansion of the coolant within the time step Δτ;

[0170]

[0171] ρ f,a = α f,a (T f - T f,0 )

[0172] ρ f,r = α f,r (T f - T f,0 )

[0173] ρ c = αc (T c -T c,0 )

[0174] In the formula:

[0175] K D —— Fuel Doppler coefficient;

[0176] α f,a —— Fuel axial thermal expansion feedback coefficient;

[0177] α f,r —— Fuel radial thermal expansion feedback coefficient;

[0178] α c —— Coolant thermal expansion feedback coefficient;

[0179] T f —— Initial step t n Fuel temperature at the time node;

[0180] T f,0 —— Initial t of the previous step n-1 Fuel temperature at the time node;

[0181] T c —— Initial step t n Coolant temperature at the time node;

[0182] T c,0 —— Initial t of the previous step n-1 Coolant temperature at the time node;

[0183] Step 8: Take the t n+1 time as the new t n time, and repeat Steps 4 to 7 until the specified calculation time is reached.

[0184] The above content is a further detailed description of the present invention in combination with specific preferred embodiments. It cannot be determined that the specific embodiments of the present invention are limited to this. For those of ordinary skill in the technical field to which the present invention belongs, without departing from the concept of the present invention, several simple deductions or substitutions can still be made, and all should be regarded as belonging to the patent protection scope determined by the claims submitted by the present invention.

Claims

1. A method for calculating the nuclear-thermal coupling of a reactor core based on a neural network embedded with physical knowledge, characterized in that: It includes the following steps: Step 1: Determine the geometry of the reactor core and perform node division. Axially divide it into m nodes and radially divide it into n rings; Step 2: Initialize the state parameters, which specifically include the following: Step 2-1: Initialize the state parameters of the core fuel, coolant temperature, and power thermohydraulics; Step 2-2: Initialize the reactivity and neutron number density of each node in the core; Step 3: t n At this moment, build a physics-informed neural network in the deep learning framework DeepXDE, and train and optimize the built physics-informed neural network to solve the neutron diffusion equation, obtaining a model for calculating the neutron number density at each node of the reactor core; Step 4: Use the trained model to predict the neutron number density n(r,t) of each node in the core and calculate the neutron flux distribution in the core; Step 5: Convert the neutron flux distribution in the core obtained in Step 4 into the core power distribution through the following formula: P(r,t) = E f Σ f5 φV In the formula: P(r,t): the power distribution of the node at position r at time t n The power distribution of the node at position r at time t E f : Energy released per fission; Σ f5 : U 235 thermal neutron macroscopic cross section of; φ: Neutron flux in the node; V: Volume of the node; Step 6: Fill the core power distribution obtained in Step 5 into the input card of the nuclear reactor thermal-hydraulic analysis software MELCOR as the energy source term. This software is a one-dimensional system analysis program, and the thermal-hydraulic state parameters of each node in the core at time t n+1 are calculated: coolant temperature and fuel temperature; Step 7: Calculate the total reactivity of each node at time t based on the core thermal-hydraulic parameters and reactivity feedback relationship obtained in Step 6 n+1 ; ρ = ρ0 + ρ ext + ρ D + ρ f,a + ρ f,r + ρ c In the formula: ρ——step size end t n+1 Total reactivity of the time node; ρ0——Initial step size t n Total reactivity at the time node ρ ext —— The external reactivity introduced at the node within the time step Δτ; ρ D —— Reactivity caused by the fuel Doppler effect within the time step of Δτ; ρ f,a —— Reactivity caused by axial thermal expansion of fuel within the time step Δτ; ρ f,r —— Reactivity caused by the radial thermal expansion of the fuel within the time step of Δτ; ρ c —— Reactivity caused by the thermal expansion of the coolant within the time step Δτ; ρ f,a = α f,a (T f - T f,0 ) ρ f,r = α f,r (T f - T f,0 ) ρ c = α c (T c - T c,0 ) In the formula: K D —— Fuel Doppler coefficient; α f,a —— Fuel axial thermal expansion feedback coefficient; α f,r —— Fuel radial thermal expansion feedback coefficient; α c —— Coolant thermal expansion feedback coefficient; T f ——Initial step size t n Fuel temperature at the time node T f,0 —— Initial step length t in the previous step n-1 Fuel temperature at the time node T c —— Initial step size t n Coolant temperature at the time node T c,0 —— Initial step length t of the previous step n-1 Coolant temperature at the time node Step 8: Take the t n+1 moment as the new t n moment, and repeat steps 4 to 7 until the specified calculation time is reached.

2. The method for calculating the nuclear-thermal coupling of a reactor core based on a physics-informed neural network according to claim 1, characterized in that: Step 3 is specifically as follows: Step 3-1: Build a neural network structure in the deep learning framework DeepXDE; Adopt a fully connected neural network structure, set the depth, the number of neurons in the middle layer, the activation function, the boundary weights, the learning rate, the optimizer, and the number of training times, and initialize the network using the Gaussian distribution random sampling method; Step 3-2: Record the outputs of the fully connected layer of the neural network built in Step 3-1: the predicted value n of the neutron number density of each node pred and the predicted value C of the number density of the delayed neutron precursor ipred ; Step 3-3: Calculate the loss value of the neural network embedded with physical knowledge, including three parts: the PDE operator loss of the neutron diffusion equation, the observation loss, and the regularization loss: 1) Calculate the PDE operator loss of the neutron diffusion equation, which specifically includes the following: a. The neutron diffusion equation is as follows: In the formula: n(r,t): t n Neutron number density at position r at time t; S(r,t): t n The density of external source neutrons at position r at time t; ρ(r,t): t n Total reactivity of the node at position r at time t; β: Total fraction of delayed neutrons; Λ: Neutron generation time; λ i : Decay constant of the delayed neutron precursor in the i-th group; C i (r, t): the number density of the i-th group of delayed neutron precursor at position r at time t; β i : The delayed neutron fraction of the i-th group; b. Use the automatic differentiation function in the deep learning framework DeepXDE to calculate the derivatives of \(n(r, t)\) with respect to time and space respectively; with respect to time and space; c. Construct the PDE operator of the neutron diffusion equation: In the formula: n (t) : The first derivative of n(r, t) with respect to time t; n (rr) : the second derivative of n(r, t) with respect to the position r; n pred : The predicted value of the neural network for n(r, t); C ipred : Predicted value of the neural network for C i (r, t); d. Calculate the PDE operator loss Loss using the deep learning framework DeepXDE o ; 2) Calculate the value of the total loss function Loss: Loss=λ d Loss d +λ o Loss o +λ reg Loss2 In the formula: λ d : Observation loss coefficient; λ o : Loss coefficient of the PDE operator; λ reg : Regularization coefficient; Loss d : Observation loss; Loss2: Parameter L2 regularization loss; In the formula: N: Number of samples; w ij : The weight connecting the i-th sample and the j-th neuron; Step 3-4: Determine whether the set number of training rounds in Step 3-1 or the target value set by the loss function is reached. If so, terminate the training; otherwise, go to Step 3-5; Step 3-5: Repeat Steps 3-2 to 3-4 to train and optimize the neural network embedded with physical knowledge; 1) Read the output of the fully connected layer in each step of Step 3-2, calculate the loss function value in Step 3-3, and minimize the loss; 2) Record the total loss function value and the total loss decrease data in 2) of Step 3-3 after each training; Step 3-6: Save the trained model for calculating the neutron number density of each node in the core.

Images