Rigid chemical kinetic equation solving method based on hard conservation constraint PINN model

Abstract

The invention discloses a rigid chemical kinetic equation solving method based on a hard conservation constraint PINN model, and belongs to the technical field of chemical kinetic equation solving. According to the method, a hard conservation constraint strategy is introduced into the PINN, only calculation is carried out in the calculation process, s3 and s1 are indirectly deduced through a conservation expression, it is ensured that the PINN can conform to the solution of an equation set in the training process, meanwhile, the material conservation law is strictly obeyed, and the invariance of the material conservation quantity is ensured. Compared with a neural network model depending on pure data driving or a soft constraint mode adopted in a PINN, the method has the advantages that the prediction precision is improved on the basis of ensuring physical consistency, and the relative error between a prediction solution and a numerical solution is effectively reduced.

Description

Technical Field

[0001] This invention relates to the field of chemical kinetic equation solving technology, specifically to a method for solving rigid chemical kinetic equations based on the hard conservation constraint PINN model. Background Technology

[0002] Rigid chemical kinetic equations are a set of coupled, multi-scale, strongly nonlinear ordinary differential equations (ODEs) widely used in atmospheric chemistry, biological sciences, environmental engineering, and other fields. Their characteristic is the coexistence of fast and slow reaction processes, leading to non-uniform timescales and exhibiting rigidity. This rigidity means that traditional numerical methods, such as commonly used rigid ODE solvers (Rosenbrock and BDF), while capable of handling rigid problems, rely heavily on linear operations and matrix storage, significantly increasing computational overhead and storage requirements.

[0003] To address this problem, Physical-Informed Neural Networks (PINN) have attracted widespread attention in recent years as a novel numerical solution method. PINN solves partial differential equations (PDEs) by directly adding physical constraints to the loss function of the neural network and optimizing the loss function, thus avoiding complex mesh generation. It shows great potential in high-dimensional problems and complex geometries, and has already demonstrated excellent performance in fields such as fluid mechanics, materials science, and biomedicine.

[0004] However, PINN still faces challenges in dealing with rigid chemical kinetic equations. Due to the multi-scale and strongly nonlinear characteristics of the system, its rigidity makes it difficult for PINN to obtain accurate solutions, and even leads to convergence failure. In particular, for systems involving mass conservation, failure to strictly maintain mass conservation during the solution process may result in biased simulation results or even loss of physical meaning. Therefore, this invention introduces hard conservation constraints into PINN and uses conservation expressions for variable calculation to ensure strict mass conservation, thus becoming an effective means of solving rigid chemical kinetic equations. Summary of the Invention

[0005] The technical problem to be solved by this invention is: how to address the problems of convergence difficulties and gradient explosion that easily occur in the numerical solution process when simulating rigid chemical kinetic equations using standard physical information neural networks, due to the rigidity of the equations. This invention provides a solution method for rigid chemical kinetic equations based on the PINN model with hard conservation constraints. Although the soft constraints in the existing technology can effectively cope with this, they cannot strictly satisfy the invariance of matter conservation. In order to further improve the performance of physical information neural networks, this invention introduces hard conservation constraints, aiming to improve the stability and accuracy of the simulation of rigid chemical kinetic equations.

[0006] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0007] S1: By preprocessing the rigid chemical kinetic equations, the equations to be solved are obtained;

[0008] S2: Construct a PINN model based on a multi-layer fully connected neural network, wherein the network structure of the PINN model adopts a shared-branch mode;

[0009] S3: Introduce hard conservation constraints through the expression of conservation variables to ensure that the material conservation relationship is satisfied during training;

[0010] S4: Introduce a threshold setting mechanism to switch optimizers during iterative optimization of the PINN model;

[0011] S5: Train the PINN model by optimizing the loss function to obtain the trained PINN model;

[0012] S6: Using time t as input, the trained PINN model generates and verifies the predicted solution to the equation to be solved.

[0013] Furthermore, in step S1, the rigid chemical kinetic equation is a classical rigid chemical kinetic equation for autocatalytic reaction kinetics, specifically as follows:

[0014]

[0015] The initial conditions for the rigid chemical kinetic equations are:

[0016] s1(0)=1, s2(0)=0, s3(0)=0;

[0017] Where t∈[0,1], s1, s2 and s3 represent the concentrations of the three chemical substances, and k1, k2 and k3 are all reaction rate constants.

[0018] Furthermore, in step S1, the preprocessing procedure is as follows:

[0019] S11: Preprocessing of s2, k2, and k3 in rigid chemical kinetic equations, specifically: Where β = 10 -4 ;

[0020] S12: The equation to be solved is as follows:

[0021]

[0022] The initial conditions for the equation to be solved are:

[0023]

[0024] Furthermore, in step S2, the PINN model includes a shared network, a first branch network, and a second branch network. The shared network comprises a 7-layer fully connected neural network, and the first and second branch networks each comprise a 5-layer fully connected neural network, using the output of the shared network as input. The processing formulas for the shared network, the first branch network, and the second branch network are as follows:

[0025] Shared network: h shared =tanh(W7tanh(W6tanh(…tanh(W2tanh(W1t+b1)+b2)…)+b6)+b7);

[0026] First branch network:

[0027] Second branch network:

[0028] Output layer:

[0029] In the shared network, t represents the input variable, W1 to W7 represent the weight matrices from layer 1 to layer 7, and b1 to b7 represent the corresponding biases; in the first branch network, W b1,1 ~W b1,4 , These represent the weight matrices and biases of layers 1 through 4, respectively; W in the second branch network b2,1 ~W b2,4 , W represents the weight matrix and bias of layers 1 through 4, respectively. out1 (W out2 b out1 (b out2 ) represent the weight matrix and bias of the output layer, respectively, and tanh is the activation function. The fifth layer in both the first and second branch networks is the output layer.

[0030] Furthermore, in step S3, the material conservation condition for rigid chemical reaction kinetics is:

[0031]

[0032] The corresponding loss function is in the form of:

[0033]

[0034] Where E represents the theoretical value of the matter conservation constraint, and L con N represents the mass conservation loss function, used to measure the deviation between predicted and theoretical values. con The number of sampling points representing the conservation constraints; for the value of s1, it is determined by the hard conservation expression. Obtained indirectly.

[0035] Furthermore, in step S4, when the SOAP optimizer is performing optimization, if the loss value drops below a preset threshold, the optimizer is switched to the L-BFGS optimizer.

[0036] Furthermore, in step S5, the specific processing procedure is as follows:

[0037] S51: The total loss function is determined as follows:

[0038] L=λ f L f +λ ic L ic

[0039] Where L represents the total loss function, λ f and λ ic The weighting coefficients for each loss term;

[0040] L f The sum of the loss functions of the three ordinary differential equations is calculated using the following formula:

[0041] L f =L f1 +L f2 +L f3

[0042] in, N f1 N f2 N f3 The number of sampling points for the residuals of each equation in the equation to be solved;

[0043] L ic The sum of losses for the three initial conditions is calculated using the following formula:

[0044] L ic =L ic1 +L ic2 +L ic3

[0045] in, N ic1 N ic2 N ic3 For the initial conditions in the equation to be solved, corresponding to s1, The number of sampling points for s3;

[0046] S52: Design the form of the total loss function. The first form is to remove the equations related to s1 and retain... The correlation equation with s3 is given by the total loss function L = λ. f (L f2 +L f3 )+λ ic (L ic2 +L ic3 The second form retains the equations related to s1, in which case the total loss function is L = λ. f (L f1 +L f2 +L f3 )+λ ic (L ic1 +L ic2 +L ic3 ), where L f1 It is the loss term in the equation related to s1, L ic1 It is the initial conditional loss term corresponding to s1;

[0047] S53: Optimize the total loss function in both forms mentioned above to gradually approximate the numerical solution of the equation, and then obtain the trained PINN model.

[0048] Furthermore, in step S6, after obtaining the predicted solution, the results of the predicted solution and the numerical solution are compared, and the relative error formula in the form of L2 norm is used to evaluate the prediction accuracy and precision of the trained PINN model; the conserved quantity is calculated through the hard conservation expression to determine whether it satisfies the law of conservation of matter.

[0049] Furthermore, the relative error formula in L2 norm form is as follows:

[0050]

[0051] Among them, s real For numerical solutions, s pred ε is a constant set to avoid division by zero in order to predict the solution.

[0052] The present invention has the following advantages over the prior art:

[0053] 1. This invention introduces a hard conservation constraint strategy into PINN, and only calculates during the computation process. S3 and S1 are indirectly derived through conservation expressions, ensuring that PINN not only satisfies the solution of the equation system during training but also strictly adheres to the law of conservation of matter, ensuring the invariance of conserved matter. Compared to neural network models that rely on purely data-driven approaches or the soft constraint method used in PINN, this invention improves prediction accuracy while ensuring physical consistency, effectively reducing the relative error between predicted and numerical solutions.

[0054] 2. The present invention can accurately predict the dynamic evolution behavior of chemical kinetic systems with rigid characteristics through the above processing, overcoming the problems of insufficient accuracy and gradient explosion that are prone to occur in the simulation of such problems by existing technologies. Attached Figure Description

[0055] Figure 1 This is a flowchart of the method for solving the rigid chemical kinetic equation in an embodiment of the present invention (t=1);

[0056] Figure 2 In this embodiment of the invention, the rigid chemical kinetic equations under hard conservation (form one) constraints are s1, Comparison chart of predicted and actual solutions for s3;

[0057] Figure 3 This is the loss function of the rigid chemical kinetic equation under hard conservation (form 1) constraints in the embodiments of the present invention;

[0058] Figure 4 This is a comparison diagram of the amount of matter conserved under the hard conservation (Form 1) constraint of the rigid chemical kinetic equation in the embodiments of the present invention;

[0059] Figure 5 In this embodiment of the invention, the rigid chemical kinetic equations under hard conservation (form two) constraints are s1, Comparison chart of predicted and actual solutions for s3;

[0060] Figure 6 This is the loss function of the rigid chemical kinetic equation under hard conservation (form two) constraints in the embodiments of the present invention;

[0061] Figure 7 This is a comparison diagram of the amount of matter conserved under the hard conservation (Form 2) constraint of the rigid chemical kinetic equation in the embodiments of the present invention;

[0062] Figure 8 In this embodiment of the invention, the rigid chemical kinetic equations are subjected to hard conservation (form two) constraints, and a threshold switching mechanism is used for s1, Comparison chart of predicted and actual solutions for s3;

[0063] Figure 9 The loss function of the rigid chemical kinetic equation under hard conservation (form two) constraints in this embodiment of the invention is the threshold switching mechanism.

[0064] Figure 10 This is a network structure diagram of the hard conservation constraint PINN model in an embodiment of the present invention. Detailed Implementation

[0065] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0066] This embodiment provides a technical solution: a method for solving rigid chemical kinetic equations based on the hard conservation constraint PINN model, including the following steps:

[0067] S1: By preprocessing the rigid chemical kinetic equation to reduce its rigidity, the equation to be solved is obtained;

[0068] S2: Construct a PINN model based on a multi-layer fully connected neural network, wherein the network structure of the PINN model adopts a shared-branch mode;

[0069] S3: By introducing hard conservation constraints through the expression of conservation variables, we can ensure that the material conservation relationship is strictly satisfied during the training process;

[0070] S4: Employ a threshold setting mechanism to switch optimizers during iterative optimization of the PINN model;

[0071] S5: Train the PINN model by optimizing the loss function to obtain the trained PINN model;

[0072] S6: Using time t as input, generate and verify the predicted solution of the equation through the trained PINN model.

[0073] In this embodiment, the rigid chemical kinetic equation is preprocessed to reduce its rigidity, resulting in the equation to be solved, including:

[0074] The classical rigid chemical kinetics problem of autocatalytic reaction kinetics is:

[0075]

[0076] Without loss of generality, the initial conditions for the system of equations are as follows:

[0077] s1(0)=1, s2(0)=0, s3(0)=0.

[0078] Where t∈[0,1], s1, s2, and s3 represent the concentrations of the three chemical substances (these concentrations have been normalized before pretreatment), and k1, k2, and k3 are all reaction rate constants. It is worth noting that t, β, k1, k2, k3, and s1, s2, and s3 in this invention are all dimensionless constants. The above parameters are set as follows: k1 = 4 × 10⁻⁶ -2 k2 = 3 × 10 7 k3 = 1 × 10 4 .

[0079] Summing the above system of equations, we find that the sum on the left side is always zero, indicating that the entire system has natural conservation properties. Adding the initial conditions, we get E = s1(t) + s2(t) + s3(t) = s1(0) + s2(0) + s3(0) = 1.

[0080] Because the reaction rate constants involved in the equations differ by orders of magnitude, especially k2 and k3 which are much larger than k1, the system exhibits significant time-scale imbalance in different reaction processes. Specifically, variable s2 changes drastically in certain time periods, while other variables change relatively smoothly. This drastic time-scale difference constitutes the rigidity of the system, thus increasing the difficulty of numerical solution. To alleviate this rigidity problem, this invention preprocesses s2, k2, and k3 in the equations, specifically as follows: Where β = 10 -4 .

[0081] The system of equations to be solved after preprocessing is as follows:

[0082]

[0083] The initial conditions for the equation to be solved are:

[0084]

[0085] At this point, the total amount of the system still satisfies the conservation condition, and the corresponding mass conservation expression is:

[0086]

[0087] In this embodiment, a PINN model based on a multi-layer fully connected neural network is constructed. The network structure of the PINN model adopts a shared-branch pattern, as detailed below:

[0088] The PINN model adopts a shared-branch network structure; the shared network consists of a 7-layer fully connected neural network; the branch networks consist of branch network one and branch network two, both of which consist of a 5-layer fully connected neural network and take the output of the shared network as input.

[0089] Shared network: h shared =tanh(W7tanh(W6tanh(…tanh(W2tanh(W1t+b1)+b2)…)+b6)+b7);

[0090] Branch Network 1:

[0091] Branch Network Two:

[0092] Output layer:

[0093] In the shared network, t represents the input variable, W1 to W7 represent the weight matrices from layer 1 to layer 7, and b1 to b7 represent the corresponding biases; in the branch network, W... b1,1 ~W b1,4 , These represent the weight matrices and biases of layers 1 through 4, respectively; W in branch network 2 b2,1 ~W b2,4 , W represents the weight matrix and bias of layers 1 through 4, respectively. out1 (W out2 b out1 (b out2 ) represent the weight matrix and bias of the output layer, respectively, and tanh is the activation function. The fifth layer in both branch network one and branch network two is the output layer.

[0094] like Figure 10 As shown, this invention constructs a network architecture based on Physical Information Neural Network (PINN), employing a multi-layer fully connected neural network and two branch networks to adapt to the characteristics of the equations, enabling PINN to fully express the complex coupling relationships of rigid chemical kinetic equations.

[0095] In this embodiment, a hard conservation constraint is introduced through the expression of conservation variables to ensure that the matter conservation relationship is strictly satisfied during the training process. The specific details are as follows:

[0096] The mass conservation condition for rigid chemical reaction kinetics is:

[0097]

[0098] The corresponding loss function is in the form of:

[0099]

[0100] Where E represents the theoretical value of the mass conservation constraint, which is always 1, and L con N represents the mass conservation loss function, used to measure the deviation between predicted and theoretical values.con The number of sampling points representing the conservation constraints.

[0101] It should be noted that in this invention, hard conservation constraints are used, and the model only displays predictions. S3 and S1 are indirectly obtained through hard conservation expressions. This design directly embeds the conservation law into the model, making the conservation relationship an inevitable result of the output. It ensures that the training process and the solution result strictly satisfy the law of conservation of matter, rather than relying on the "soft constraint" approximation of the loss function. This is the new approach of this invention that distinguishes it from conventional PINN in solving rigid chemical kinetic problems.

[0102] In chemical reactions, the law of conservation of mass is a fundamental principle that must be followed, ensuring that the total amount of reactants and products in the reaction system remains constant. To ensure that the neural network output strictly satisfies the conservation relationship, this invention introduces a hard conservation constraint strategy, using variable expressions to calculate and reflect the conservation characteristics, thereby improving the reliability of PINN in handling rigid and complex problems.

[0103] Specifically, for the value of s1, this invention does not calculate it directly, but rather uses a hard conservation expression. Obtained indirectly.

[0104] In this embodiment, a threshold setting mechanism is adopted to make the setting of the optimizer iteration steps more reasonable;

[0105] During optimization, the selection of the number of iterations often involves randomness, which may affect the efficiency of the solution and the accuracy of the prediction. To address this issue, this invention introduces a threshold setting mechanism, providing a theoretical basis for PINN to switch from the SOAP optimizer to the L-BFGS optimizer.

[0106] Specifically, when the SOAP optimizer performs optimization, when the loss value drops to a pre-set threshold (1×10⁻⁶), -4 ~9×10 -6 When the condition falls below a certain threshold, the optimizer switch is triggered, and the L-BFGS optimizer is used instead. This method effectively improves the solution accuracy and overall computational efficiency.

[0107] In this embodiment, training is performed by optimizing the loss function to improve the training performance of PINN, including:

[0108] Partial differential equations and initial condition loss: by predicting the solution s1, Substitute s1 and s3 into the partial differential equation to be solved and the initial conditions to calculate the residuals, and use the sum of squares of the residuals as part of the loss function. Here, s1 is expressed by the hard conservation formula and then substituted in, specifically:

[0109] L=λ f Lf +λ ic L ic

[0110] L f =L f1 +L f2 +L f3

[0111] L ic =L ic1 +L ic2 +L ic3

[0112] The specific calculation formula is as follows:

[0113]

[0114] Where L represents the total loss function, L f L is the sum of the loss functions of the three ordinary differential equations. ic λ is the sum of the losses due to the initial conditions of the three variables. f and λ ic The weighting coefficients for each loss term, β is a coefficient in the equation, and N f1 N f2 N f3 N represents the number of sampling points for the residuals of each equation in the equation to be solved, used to indicate the number of points randomly sampled in the time domain [0,1] when calculating the residual losses Lf1, Lf2, and Lf3 of the equation; ic1 N ic2 N ic3 For the initial conditions in the equation to be solved, corresponding to s1, The number of sampling points in s3 is used to represent the initial condition loss L. ic1 L ic2 L ic3 The number of points randomly sampled at the initial time (t=0).

[0115] In this embodiment, two forms are provided for the design of the loss function. The first form removes the equations related to s1 and retains... The correlation equation with s3. At this point, the total loss function is L = λ. f (L f2 +L f3 )+λ ic (L ic2 +L ic3 Form two retains the equations related to s1, and the total loss function is L = λ. f (L f1 +L f2 +L f3 )+λ ic (L ic1+L ic2 +L ic3 ), where L f1 It is the loss term in the equation related to s1, L ic1 It is the initial condition loss term corresponding to s1.

[0116] In this embodiment, the total loss function in the two forms mentioned above is optimized during the PINN training process to gradually approximate the numerical solution of the equation, while strictly ensuring the conservation of matter.

[0117] In this embodiment, the predicted solution to the equation is generated and verified using the trained PINN, including:

[0118] By comparing the results of the predicted solution and the numerical solution, the relative error formula in the form of L2 norm is used to evaluate the accuracy and precision of PINN's prediction for this problem; the conserved quantities are calculated through hard conservation expressions to determine whether they strictly satisfy the law of conservation of matter.

[0119] The effectiveness of hard conservation constraint methods can be evaluated by comparing predicted and numerical solutions. Figure 2 , 5 As shown in Figure 8, the solid red line represents the numerical solution of s1, the dashed red line represents the predicted solution of s1, and the solid blue line represents... Numerical solution, represented by the blue dashed line. Predicted solutions; the solid black line represents the numerical solution of s3, and the dashed black line represents the predicted solution of s3. Under the hard conservation constraint, the predicted solutions and numerical solutions for the three variables are basically consistent, with the hard conservation (Form 2) performing better than the hard conservation (Form 1). A comparison of the mass conservation quantities in the two hard conservation forms shows that the predicted values ​​of the conservation quantity E in both forms fit the actual values ​​and strictly satisfy the mass conservation relationship. From... Figure 3 , 6 As can be seen from Figures 9, the loss function decreases rapidly and converges under the hard conservation constraint.

[0120] The relative errors for hard conservation (Form 1) are s1 = 0.0088%, s2 = 0.84%, and s3 = 0.43%; the relative errors for hard conservation (Form 2) are s1 = 0.0022%, s2 = 2.11%, and s3 = 0.11%; and the relative errors for hard conservation (Form 2) using the threshold switching mechanism are s1 = 0.0017%, s2 = 1.67%, and s3 = 0.08%. Comparing the relative error results of different strategies, it is evident that the strategy combining the threshold switching mechanism in hard conservation (Form 2) exhibits the best performance in terms of relative error for each substance concentration. This indicates that this mechanism can effectively improve the solution accuracy of PINN for rigid chemical kinetic equations in hard conservation (Form 2).

[0121] Specifically, the formula for the relative error in L2 norm form is: Where sreal For numerical solutions, s pred To predict the solution, ε is a constant set to avoid division by zero; in this embodiment, ε = 1 × 10⁻⁶. -10 .

[0122] This invention uses a trained physical information neural network (PINN) to solve rigid chemical kinetic equations. Taking time t as input, PINN outputs a predicted solution to the equation. Because this invention combines a physical information neural network with a hard conservation constraint training method, the obtained predicted solution not only satisfies the conditions of the partial differential equation but also strictly maintains physical conservation, ensuring that the conserved quantities remain constant.

[0123] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for solving rigid chemical kinetic equations based on the PINN model with hard conservation constraints, characterized in that, Includes the following steps: S1: By preprocessing the rigid chemical kinetic equations, the equations to be solved are obtained; S2: Construct a PINN model based on a multi-layer fully connected neural network, wherein the network structure of the PINN model adopts a shared-branch mode; S3: Introduce hard conservation constraints through the expression of conservation variables to ensure that the material conservation relationship is satisfied during training; S4: Introduce a threshold setting mechanism to switch optimizers during iterative optimization of the PINN model; S5: Train the PINN model by optimizing the loss function to obtain the trained PINN model; S6: Using time t as input, the trained PINN model generates and verifies the predicted solution to the equation to be solved.

2. The method for solving rigid chemical kinetic equations based on the PINN model with hard conservation constraints according to claim 1, characterized in that, In step S1, the rigid chemical kinetic equation is the classical rigid chemical kinetic equation for autocatalytic reaction kinetics, as follows: The initial conditions for the rigid chemical kinetic equations are: s1(0)=1, s2(0)=0, s3(0)=0; Where t∈[0,1], s1, s2 and s3 represent the concentrations of the three chemical substances, and k1, k2 and k3 are all reaction rate constants.

3. The method for solving rigid chemical kinetic equations based on the hard conservation constraint PINN model according to claim 2, characterized in that, In step S1, the preprocessing procedure is as follows: S11: Preprocessing of s2, k2, and k3 in rigid chemical kinetic equations, specifically: Where β = 10 -4 ; S12: The equation to be solved is as follows: The initial conditions for the equation to be solved are: s1(0)=1, s3(0)=0.

4. The method for solving rigid chemical kinetic equations based on the PINN model with hard conservation constraints according to claim 3, characterized in that, In step S2, the PINN model includes a shared network, a first branch network, and a second branch network. The shared network comprises a 7-layer fully connected neural network, and the first and second branch networks each comprise a 5-layer fully connected neural network, with the output of the shared network serving as the input. The processing formulas for the shared network, the first branch network, and the second branch network are as follows: Shared network: h shared =tanh(W7tanh(W6tanh(…tanh(W2tanh(W1t+b1)+b2)…)+b6)+b7); First branch network: Second branch network: Output layer: In the shared network, t represents the input variable, W1 to W7 represent the weight matrices from layer 1 to layer 7, and b1 to b7 represent the corresponding biases; in the first branch network, W b1,1 ~W b1,4 , These represent the weight matrices and biases of layers 1 through 4, respectively; W in the second branch network b2,1 ~W b2,4 , W represents the weight matrix and bias of layers 1 through 4, respectively. out1 (W out2 b out1 (b out2 ) represent the weight matrix and bias of the output layer, respectively, and tanh is the activation function. The fifth layer in both the first and second branch networks is the output layer.

5. The method for solving rigid chemical kinetic equations based on the hard conservation constraint PINN model according to claim 4, characterized in that, In step S3, the mass conservation condition for rigid chemical reaction kinetics is: The corresponding loss function is in the form of: Where E represents the theoretical value of the matter conservation constraint, and L con N represents the mass conservation loss function, used to measure the deviation between predicted and theoretical values. co x represents the number of sampling points for the conservation constraints; for the value of s1, it is determined by the hard conservation expression. Obtained indirectly.

6. The method for solving rigid chemical kinetic equations based on the hard conservation constraint PINN model according to claim 1, characterized in that, In step S4, when the SOAP optimizer is performing optimization, if the loss value drops below a preset threshold, the optimizer is switched to the L-BFGS optimizer.

7. The method for solving rigid chemical kinetic equations based on the hard conservation constraint PINN model according to claim 5, characterized in that, In step S5, the specific processing procedure is as follows: S51: The total loss function is determined as follows: L=λ f L f +λ ic L ic Where L represents the total loss function, λ f and λ ic The weighting coefficients for each loss term; L f The sum of the loss functions of the three ordinary differential equations is calculated using the following formula: L f =L f1 +L f2 +L f3 in, N f1 N f2 N f3 The number of sampling points for the residuals of each equation in the equation to be solved; L ic The sum of losses for the three initial conditions is calculated using the following formula: L ic =L ic1 +L ic2 +L ic3 in, N ic1 N ic2 N ic3 For the initial conditions in the equation to be solved, corresponding to s1, The number of sampling points for s3; S52: Design the form of the total loss function. The first form is to remove the equations related to s1 and retain... The correlation equation with s3 is given by the total loss function L = λ. f (L f2 +L f3 )+λ ic (L ic2 +L ic3 The second form retains the equations related to L1, in which case the total loss function is s = λ. f (L f1 +L f2 +L f3 )+λ ic (L ic1 +L ic2 +L ic3 ), where L f1 It is the loss term in the equation related to s1, L ic1 It is the initial conditional loss term corresponding to s1; S53: Optimize the total loss function in both forms mentioned above to gradually approximate the numerical solution of the equation, and then obtain the trained PINN model.

8. The method for solving rigid chemical kinetic equations based on the PINN model with hard conservation constraints according to claim 1, characterized in that, In step S6, after obtaining the predicted solution, the results of the predicted solution and the numerical solution are compared. The relative error formula in the form of L2 norm is used to evaluate the prediction accuracy and precision of the trained PINN model. The conserved quantity is calculated through the hard conservation expression to determine whether it satisfies the law of conservation of matter.

9. The method for solving rigid chemical kinetic equations based on the hard conservation constraint PINN model according to claim 8, characterized in that, The relative error formula in L2 norm form is as follows: Among them, s real For numerical solutions, s pred ε is a constant set to avoid division by zero in order to predict the solution.

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