Method for calculating environmental gas chemical kinetics based on physical information neural network

Abstract

This invention discloses a method for calculating the chemical kinetics of environmentally friendly gases based on a physical information neural network. It constructs a chemical reaction kinetic model of environmentally friendly gases, then builds a set of ordinary differential equations for chemical kinetics, leading to a corresponding single-hidden-layer physical information neural network architecture. The hidden layer weights and biases are randomly initialized and kept constant, while only the output layer weights are set as learnable parameters. The residuals of the control equations and the initial conditions are embedded into the loss function. The time domain is divided into multiple subdomains, and different single-layer neural networks are used to solve for different reaction particles in each subdomain. The initial values ​​are hard-coded into the neural network, and the final value after training in each subdomain is used as the initial value for the next subdomain. Training and solving are performed segment by segment in a concatenated manner. A total loss function for the neural network is constructed, and the output layer weights are iteratively updated until the loss function value decreases to a given threshold. This invention enables more efficient model calculation in strongly rigid multi-reaction coupled systems.

Description

Technical Field

[0001] This invention belongs to the interdisciplinary field of artificial intelligence and environmental gases, specifically involving a method for calculating the chemical kinetics of environmental gases based on physical information neural networks. Background Technology

[0002] With the development of ultra-high voltage (UHV) power transmission technology, gas-insulated equipment has been widely used in the power industry. Traditional SF6 insulating gas is restricted in its use due to its greenhouse effect, and new environmentally friendly gases are gradually becoming its replacements. However, due to unavoidable insulation defects, gas-insulated equipment is prone to partial discharge during actual operation, leading to the decomposition of the internal environmentally friendly gas, damaging the equipment's insulation performance, and thus threatening the safe operation of the power system. To accurately assess insulation degradation and identify gas decomposition products under different conditions, it is necessary to model and study the chemical kinetics of the environmentally friendly gas.

[0003] Traditional numerical methods are widely used in modeling and calculating chemical kinetic processes. However, they still have significant limitations in terms of solution stability and computational efficiency when dealing with problems such as multi-scale coupling, high nonlinearity, and strong rigidity in the chemical kinetics of environmental gases. In recent years, physical information neural networks have provided a new approach to solving complex chemical kinetic equations. By directly embedding physical constraints into the loss function, they can achieve efficient solutions with relatively little data.

[0004] However, traditional physical information neural networks typically require joint training in the global time domain. This can easily lead to training instability and a significant decrease in prediction accuracy when dealing with problems involving large time scales and drastic changes in physical characteristics. Furthermore, the sensitivity to numerical gradients and the difficulty in residual convergence in rigid systems can easily cause the network to get trapped in local optima, severely impacting the model's convergence and generalization. Therefore, there is an urgent need to propose an improved modeling and computational method based on physical information neural networks suitable for the chemical dynamics of environmentally friendly gases. Summary of the Invention

[0005] The purpose of this invention is to provide a method for calculating the chemical kinetics of environmentally friendly gases based on physical information neural networks, which can perform model calculations more efficiently in rigid multi-reaction coupled systems. Compared with traditional methods, this invention avoids ill-conditioned imbalances that occur during gradient calculation and backpropagation, and achieves higher accuracy and stability in chemical kinetic modeling and solving.

[0006] To achieve the above objectives, the solution of the present invention is:

[0007] A method for calculating the chemical kinetics of environmentally friendly gases based on a physical information neural network includes the following steps:

[0008] Step 1: Based on the feasible reaction pathways and reaction particles of the environmentally friendly gas reaction system, construct a chemical reaction kinetic model of the environmentally friendly gas, and construct a set of ordinary differential equations of chemical kinetics based on the chemical reaction kinetic model;

[0009] Step 2: Based on the chemical kinetic ordinary differential equations, construct the corresponding single hidden layer physical information neural network architecture, randomly initialize its hidden layer weights and biases and keep them unchanged, set only the output layer weights as learnable parameters, and embed the control equation residuals and initial conditions into the loss function.

[0010] Step 3: Divide the time domain of the chemical kinetic ordinary differential equation system into multiple subdomains. In each subdomain, use different single-layer neural networks to solve for different reaction particles. Hard-encode the initial values ​​into the neural network. Use the final value after training in each subdomain as the initial value for the next subdomain. Train and solve the subdomains one by one.

[0011] Step 4: Construct the total loss function of the neural network, iteratively update the weights of the output layer until the loss function value drops to a given threshold, and obtain the result of the evolution of the concentration of each particle in the reaction system over time.

[0012] The specific process of step 1 above is as follows:

[0013] The feasible reaction pathways of the environmentally friendly gas reaction system are determined using quantum chemistry and transition state theory. The reaction rate constants for each reaction at a given temperature are calculated, and the reaction particles are identified.

[0014] The following chemical kinetic model is constructed to describe N types of microscopic particles and M types of reactions.

[0015] ,

[0016] in, Let be the chemical symbol for the k-th particle. and These are the stoichiometric coefficients of the reactants and products of the k-th particle in the i-th reaction, respectively.

[0017] The following set of ordinary differential equations is constructed to describe the evolution of the particles participating in the reaction over time under given initial conditions.

[0018] ,

[0019] Where k is the particle number, i is the reaction number involved by the particle, and N is the total number of particles participating in the reaction. Let be the concentration of the k-th particle. These are stoichiometric coefficients. Let be the reaction rate of the i-th reaction.

[0020] The specific process of step 2 above is as follows:

[0021] Step 21: Construct a single-hidden-layer physical information neural network architecture corresponding to the chemical kinetic ordinary differential equation system, wherein the neural network takes time as input and the concentration of each particle as output;

[0022] Step 22: Randomly initialize and keep the hidden layer weights and biases of the neural network unchanged, only setting the output layer weights as learnable parameters; the physical constraint layer of the neural network includes only the governing equations and initial conditions, which satisfy the following form,

[0023] ,

[0024] ,

[0025] Where Y is the particle concentration vector. Let be the vector of the rate of change of particle concentration over time. and These are the operators for the governing equation and the initial condition equation, respectively. R is the chemical source term vector, and Y0 is the initial concentration vector of the reacting particles.

[0026] Step 23: Construct the total loss function of the neural network based on the training task. It consists of two parts: the residual loss of the governing equations and the residual loss of the initial conditions.

[0027] ,

[0028] ,

[0029] ,

[0030] in, It is the residual loss function for evaluation, N s It is the total number of time steps. This represents the residual loss function of the governing equations. The residual loss function represents the initial conditions. These are the weights of the loss function of the control equation. These are the weights of the initial conditional loss function.

[0031] In step 22 above, the method for obtaining the particle concentration vector Y is as follows:

[0032] Define the initial concentration vector of the particles participating in the reaction.

[0033] ,

[0034] in, This represents the initial concentration of the k-th type of reaction particles, where N is the total number of particles;

[0035] Solve the aforementioned set of ordinary differential equations for chemical kinetics to obtain the particle concentration vector at a specified time t.

[0036] ,

[0037] in, This represents the particle concentration of the k-th reaction.

[0038] In step 3 above, the specific process of dividing the time domain into multiple subdomains is as follows:

[0039] According to parameters Based on the set values, the following numerical transformations are performed on the time domain.

[0040] ,

[0041] Where T is the time variable, These are time mapping coefficients;

[0042] The time domain is then evenly divided to obtain multiple subdomains.

[0043] In step 3 above, different single-layer neural networks are used to solve for different reaction particles in each subdomain, and each initial value is hard-coded into the neural network as shown in the following formula.

[0044] ,

[0045] in, Represents the subdomain in the k-th time segment The neural network used above to approximate the temporal distribution of the concentration of the j-th particle. This represents the final value vector of the (k-1)th segment, where n is the total number of neurons in the hidden layer. For the i-th neuron in the hidden layer, For the selectable nonlinear activation function, denoted as the weights from the i-th hidden layer neuron to the output layer.

[0046] The specific process of step 4 above is as follows:

[0047] Step 41: After approximating all N types of particles using N independent neural networks, the total residual loss function of the neural network is constructed as shown in the following formula.

[0048] ,

[0049] in, Let represent the particle concentration vector composed of N particles in the k-th time subdomain, M be the number of residual points in the time subdomain, and R() be the chemical kinetic source term function. This represents the p-th time residual point;

[0050] Step 42, adjust the output layer weight parameters according to the loss function. The update is performed iteratively, and the update formula is shown below.

[0051] ,

[0052] ,

[0053] in, This represents the output layer weight vector of the l-th iteration. The update step size for this round is calculated using the Moore-Penrose generalized inverse. It is the Jacobian matrix of the loss function. The L2 norm of the loss function is set to specify the error limit, so that the iteration process ends when the specified error threshold is reached, thereby obtaining the simulation results of the evolution of the concentration of each particle in the reaction system over time.

[0054] After adopting the above solution, the beneficial effects of the present invention compared with the prior art are as follows:

[0055] (1) In the face of the complex environmental gas chemical dynamics modeling and calculation problem with strong rigidity and multi-scale coupling, the method of the present invention divides the time domain into segments for training and uses an independent single-layer network structure for training in each subdomain, which can solve the problem more quickly and obtain high-precision results.

[0056] (2) Compared with the traditional physical information neural network method, the method of the present invention only iteratively updates the parameters of the output layer of the neural network, avoiding the gradient ill-conditioning problem caused by backpropagation, while significantly reducing the training parameters, improving the computational efficiency, and having a stronger generalization ability. Attached Figure Description

[0057] Figure 1 This is a schematic diagram of the method flow of the present invention;

[0058] Figure 2 This is a schematic diagram of the neural network structure for solving the environmental gas chemical kinetic model in this invention;

[0059] Figure 3 This is a comparison diagram of the solution results of the method of the present invention in solving the chemical kinetics of the decomposition of pure C4F7N gas and the solution results of the main particles in the solver of the rigid ordinary differential equation system;

[0060] Among them, (a) is a comparison chart of C4F7N, (b) is a comparison chart of CF, (c) is a comparison chart of CF2, (d) is a comparison chart of CF2C, (e) is a comparison chart of CF2CCF3, (f) is a comparison chart of CF2CCN, (g) is a comparison chart of CF2CF, (h) is a comparison chart of CF2CF2, (i) is a comparison chart of CF2CF2CF2, (j) is a comparison chart of CF2CF2CN, (k) is a comparison chart of CF2CFCF3, and (l) is a comparison chart of CF2CFCN. Detailed Implementation

[0061] The technical solution of the present invention will be described in detail below with reference to specific embodiments.

[0062] This invention proposes a method for calculating the chemical kinetics of environmentally friendly gases based on a physical information neural network, which includes four steps;

[0063] Step 1: First, use quantum chemistry and transition state theory to determine the feasible reaction path of the environmentally friendly gas reaction system, calculate the reaction rate constant, determine the participating particles, establish a chemical reaction kinetic model of the environmentally friendly gas, and construct a set of chemical kinetic ordinary differential equations.

[0064] Step 2: Then, based on the chemical reaction kinetics model, construct the corresponding single-hidden-layer physical information neural network architecture, randomly initialize its hidden layer weights and biases and keep them unchanged, only set the output layer weights as learnable parameters, and embed the control equation residuals and initial conditions into the loss function.

[0065] Step 3: Next, after numerical transformation of the time domain, it is evenly divided into multiple subdomains. Different single-layer neural networks are used to solve different reaction particles in each subdomain, and the initial values ​​are hard-coded into the neural network. The final value after training of each subdomain is used as the initial value of the next subdomain. The training and solution are carried out in sequence.

[0066] Step 4: Finally, construct the total loss function of the network and iteratively update the weights of the output layer until the loss function value drops to a given threshold, thereby realizing the numerical calculation of the chemical kinetic equations of environmental gases.

[0067] Step 1 is detailed below:

[0068] Based on the specific problem, an environmental gas chemical kinetic model is established, and then the following set of ordinary differential equations is constructed to describe the evolution of the particles participating in the reaction over time under given initial conditions:

[0069]

[0070] In the formula, k is the particle number, i is the reaction number involved by the particle, and N is the total number of particles participating in the reaction. Let be the concentration of the k-th particle. These are stoichiometric coefficients. Let be the reaction rate of the i-th reaction;

[0071] The initial condition of the model is the initial concentration vector of the particles participating in the reaction:

[0072]

[0073] Solving this model yields the particle concentration vector at a specified time t:

[0074]

[0075] Step 2 is detailed below:

[0076] A single-hidden-layer neural network suitable for chemical kinetic models is constructed, with time t as input and particle concentration as output. The hidden layer weights and biases are randomly initialized and kept constant, while only the output layer weights are set as learnable parameters. The network's physical constraint layer includes only the governing equations and initial conditions, which must satisfy the following form:

[0077]

[0078]

[0079] In the formula, Y is the particle concentration vector. Let be the vector of the rate of change of particle concentration over time. and These are the operators for the governing equation and the initial condition equation, respectively. R is the chemical source term vector, and Y0 is the initial concentration vector of the reacting particles.

[0080] Construct the total loss function of the network based on the training task. It consists of two parts: the residual loss of the governing equations and the residual loss of the initial conditions.

[0081]

[0082]

[0083]

[0084] in It is the residual loss function for evaluation, N s It is the total number of time steps. This represents the residual loss function of the governing equations. The residual loss function represents the initial conditions. These are the weights of the loss function of the control equation. These are the weights of the initial conditional loss function.

[0085] Step 3 is detailed below:

[0086] First select parameters The following numerical transformations are performed on the time domain based on the value of :

[0087]

[0088] Then, the time domain is uniformly divided into multiple subdomains, and different single-layer neural networks are used to solve for different reaction particles in each subdomain. The initial values ​​of each segment are hard-coded into the neural network as shown in the following formula:

[0089]

[0090] In the formula Represents the subdomain in the k-th time segment The neural network used above to approximate the temporal distribution of the concentration of the j-th particle. This represents the final value vector of the (k-1)th segment, where n is the total number of neurons in the hidden layer. For the i-th neuron in the hidden layer, For the selectable nonlinear activation function, The weights from the i-th hidden layer neuron to the output layer;

[0091] Finally, the final value of each subdomain after training is used as the initial value of the next subdomain, and the training and solution are performed by connecting the subdomains one by one.

[0092] Step 4 is detailed below:

[0093] Step 4.1: After approximating all N types of particles using N independent neural networks, construct the total residual loss function of the neural network based on the chemical kinetic equations, as shown in the following formula:

[0094]

[0095] In the formula This represents the particle concentration vector composed of N particles in the k-th time subdomain, where M is the number of residual points in the time subdomain.

[0096] Then, the output layer weight parameters are adjusted according to the loss function. The update is performed iteratively, and the update formula is shown below:

[0097]

[0098]

[0099] in Based on Moore-Penrose generalized inverse calculation, It is the Jacobian matrix of the loss function. The L2 norm of the loss function is set to specify the error limit, so that the iteration process ends when the specified error threshold is reached. Finally, the simulation results of the evolution of the concentration of each particle in the reaction system over time are obtained.

[0100] Please see Figure 1 As shown, the chemical kinetics of the decomposition of pure C4F7N gas at 3000K is taken as the research object. The simulation results of the concentration evolution of the main reacting particles over time are calculated using the method proposed in this invention, including the following steps:

[0101] Step 1: Establish a kinetic model for the decomposition of pure C4F7N gas and construct a set of ordinary differential equations for chemical kinetics, as detailed below:

[0102] Step 1.1: First, based on quantum chemistry and transition state theory, it is determined that the pure C4F7N gas decomposition reaction system contains 50 main reaction pathways and 33 main reaction particles. At a given temperature T=3000K, the rate constants of each reaction are calculated using the Arrhenius formula.

[0103] Step 1.2: Based on the data of the pure C4F7N gas decomposition reaction system, establish an environmentally friendly gas chemical kinetic model, and construct the following set of ordinary differential equations to describe the evolution of the particles participating in the reaction over time under given initial conditions:

[0104]

[0105] In the formula, k is the particle number, i is the reaction number involved by the particle, and N is the total number of particles participating in the reaction. Let be the concentration of the k-th particle. These are stoichiometric coefficients. Let be the reaction rate of the i-th reaction;

[0106] Step 1.3: Set the initial concentration vector of the particles participating in the reaction as the initial condition:

[0107]

[0108] Step 2: Construct the corresponding single-hidden-layer physical information neural network architecture based on the chemical kinetic model in Step 1, such as... Figure 2 As shown, details are as follows:

[0109] Step 2.1: Construct a single-hidden-layer neural network with time t as input and particle concentration Y as output. Set the number of hidden layer neurons to 10 and use the tanh function as the activation function.

[0110] Step 2.2: Randomly initialize the hidden layer weights and biases and keep them unchanged; only set the output layer weights. It is the only learnable parameter;

[0111] Step 2.3: Construct the physical constraints, governing equations, and initial conditions of the network based on the set of ordinary differential equations of chemical kinetics, in the following form:

[0112]

[0113]

[0114] In the formula, Y is the particle concentration vector. Let be the vector of the rate of change of particle concentration over time. and These are the operators for the governing equation and the initial condition equation, respectively. R is the chemical source term vector, and Y0 is the initial concentration vector of the reacting particles.

[0115] Step 2.4: Construct the network loss function It consists of two parts: the residual loss of the governing equations and the residual loss of the initial conditions.

[0116]

[0117]

[0118]

[0119] in It is the residual loss function for evaluation, N s It is the total number of time steps. This represents the residual loss function of the governing equations. The residual loss function represents the initial conditions. These are the weights of the loss function of the control equation. These are the weights of the initial conditional loss function.

[0120] Step 3: After numerical transformation of the time domain, it is uniformly divided into multiple subdomains. Different single-layer neural networks are used to solve for different reaction particles in each subdomain. The subdomains are then connected segment by segment for training. Details are as follows:

[0121] Step 3.1: Set the time interval to [10 -20 10 0 ] seconds, parameters The value of is 0.01. The following numerical transformation is performed on the time domain:

[0122]

[0123] Step 3.2: Divide the time domain into 120 subdomains, with 10 residual points in each subdomain. Use a separate single-layer neural network to solve for different reaction particles in each subdomain.

[0124] Step 3.3: Hard-encode the initial values ​​into the neural network in each time subdomain as shown in the following equation:

[0125]

[0126] In the formula Represents the subdomain in the k-th time segment The neural network used above to approximate the temporal distribution of the concentration of the j-th particle. This represents the final value vector of the (k-1)th segment, where n is the total number of neurons in the hidden layer. For the i-th neuron in the hidden layer, The selected nonlinear activation function is... The weights from the i-th hidden layer neuron to the output layer;

[0127] Step 3.4: After training is completed in each time subdomain, the final value of that subdomain is used as the initial value of the next subdomain, and training is advanced segment by segment.

[0128] Step 4: Construct the total loss function of the network and iteratively update the output layer weights until the loss function value drops to a given threshold, as detailed below:

[0129] Step 4.1: After approximating all N types of particles using N independent neural networks, construct the total residual loss function of the neural network based on the chemical kinetic equations, as shown in the following formula:

[0130]

[0131] In the formula This represents the particle concentration vector composed of N particles in the k-th time subdomain, where M is the number of residual points in the time subdomain.

[0132] Step 4.2: Adjust the output layer weight parameters according to the loss function obtained in Step 4.1. The update is performed iteratively, and the update formula is shown below:

[0133]

[0134]

[0135] in Based on Moore-Penrose generalized inverse calculation, It is the Jacobian matrix of the loss function.

[0136] Step 4.3: Repeat steps 4.1-4.2 and observe whether the L2 norm of the neural network loss function reaches the specified error limit;

[0137] Step 4.4: Obtain the output of the neural network, which is the simulation result of the evolution of the concentration of each particle in the corresponding chemical kinetic reaction system over time.

[0138] The comparison charts between the neural network training results and the rigid ordinary differential equation solver training results are shown below. Figure 3 As shown, due to the large number of particles involved in the reaction, only the training results of some major particles are displayed. The figure reveals that the chemical kinetics of pure C4F7N gas exhibits significant rigidity, with large differences in the order of magnitude of different particles and extremely large differences in the reaction timescales of each particle, posing a significant challenge to the solution. Traditional non-rigid ordinary differential equation solvers require short step sizes and are prone to numerical divergence. The single-layer physical information neural network and its accompanying time-domain decomposition strategy proposed in this invention overcome the rigidity problem in the C4F7N chemical kinetics, capturing the changes of different particles at their corresponding timescales, and achieving accurate solutions for the evolution of different particles in the C4F7N chemical kinetics, achieving accuracy comparable to rigid ordinary differential equation solvers.

[0139] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0140] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0141] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0142] Although preferred embodiments of the invention have been described, those skilled in the art, upon learning the basic inventive concept, can make other changes and modifications to these embodiments. Therefore, the appended claims are intended to be interpreted as including both the preferred embodiments and all changes and modifications falling within the scope of the invention.

[0143] Obviously, those skilled in the art can make various modifications and variations to this invention without departing from its spirit and scope. Therefore, if these modifications and variations fall within the scope of the claims of this invention and their equivalents, this invention also intends to include these modifications and variations.

Claims

1. A method for calculating the chemical kinetics of environmentally friendly gases based on physical information neural networks, characterized in that... Includes the following steps: Step 1: Based on the feasible reaction pathways and reaction particles of the environmentally friendly gas reaction system, construct a chemical reaction kinetic model of the environmentally friendly gas, and construct a set of ordinary differential equations of chemical kinetics based on the chemical reaction kinetic model; Step 2: Based on the chemical kinetic ordinary differential equations, construct the corresponding single hidden layer physical information neural network architecture, randomly initialize its hidden layer weights and biases and keep them unchanged, set only the output layer weights as learnable parameters, and embed the control equation residuals and initial conditions into the loss function. Step 3: Divide the time domain of the chemical kinetic ordinary differential equation system into multiple subdomains. In each subdomain, use different single-layer neural networks to solve for different reaction particles. Hard-encode the initial values ​​into the neural network. Use the final value after training in each subdomain as the initial value for the next subdomain. Train and solve the subdomains one by one. Step 4: Construct the total loss function of the neural network, iteratively update the weights of the output layer until the loss function value drops to a given threshold, and obtain the result of the evolution of the concentration of each particle in the reaction system over time. In step 3, the specific process of dividing the time domain into multiple subdomains is as follows: According to parameters Based on the set values, the following numerical transformations are performed on the time domain. ， Where T is the time variable, These are time mapping coefficients; Then the time domain is evenly divided to obtain multiple subdomains; In step 3, different single-layer neural networks are used to solve for different reaction particles in each subdomain, and each initial value is hard-coded into the neural network as shown in the following formula. ， in, Represents the subdomain in the m-th time segment. The neural network used above to approximate the temporal distribution of the concentration of the j-th particle. This represents the final value vector of the (m-1)th segment, where n is the total number of neurons in the hidden layer. For the i-th neuron in the hidden layer, For the selectable nonlinear activation function, denoted as the weights from the i-th hidden layer neuron to the output layer.

2. The method as described in claim 1, characterized in that: The specific process of step 1 is as follows: The feasible reaction pathways of the environmentally friendly gas reaction system are determined using quantum chemistry and transition state theory. The reaction rate constants for each reaction at a given temperature are calculated, and the reaction particles are identified. The following chemical kinetic model is constructed to describe N types of microscopic particles and M types of reactions. ， in, Let be the chemical symbol for the k-th particle. and These are the stoichiometric coefficients of the reactants and products of the k-th particle in the i-th reaction, respectively. The following set of ordinary differential equations is constructed to describe the evolution of the particles participating in the reaction over time under given initial conditions. ， Where k is the particle number, i is the reaction number involved by the particle, and N is the total number of particles participating in the reaction. Let be the concentration of the k-th particle. These are stoichiometric coefficients. Let be the reaction rate of the i-th reaction.

3. The method as described in claim 1, characterized in that: The specific process of step 2 is as follows: Step 21: Construct a single-hidden-layer physical information neural network architecture corresponding to the chemical kinetic ordinary differential equation system, wherein the neural network takes time as input and the concentration of each particle as output; Step 22: Randomly initialize and keep the hidden layer weights and biases of the neural network unchanged, only setting the output layer weights as learnable parameters; the physical constraint layer of the neural network includes only the governing equations and initial conditions, which satisfy the following form, ， ， Where Y is the particle concentration vector. Let be the vector of the rate of change of particle concentration over time. and These are the operators for the governing equation and the initial condition equation, respectively. R is the chemical source term vector, and Y0 is the initial concentration vector of the reacting particles. Step 23: Construct the total loss function of the neural network based on the training task. It consists of two parts: the residual loss of the governing equations and the residual loss of the initial conditions. ， ， ， in, It is the residual loss function for evaluation, N s It is the total number of time steps. This represents the residual loss function of the governing equations. The residual loss function represents the initial conditions. These are the weights of the loss function of the control equation. These are the weights of the initial conditional loss function.

4. The method as described in claim 3, characterized in that: In step 22, the method for obtaining the particle concentration vector Y is as follows: Define the initial concentration vector of the particles participating in the reaction. ， in, This represents the initial concentration of the k-th type of reaction particles, where N is the total number of particles; Solve the aforementioned set of ordinary differential equations for chemical kinetics to obtain the particle concentration vector at a specified time t. ， in, This represents the particle concentration of the k-th reaction.

5. The method as described in claim 1, characterized in that: The specific process of step 4 is as follows: Step 41: After approximating all N types of particles using N independent neural networks, the total residual loss function of the neural network is constructed as shown in the following formula. ， in, Let R represent the particle concentration vector composed of N particles in the m-th time subdomain, where M is the number of residual points in the time subdomain, and R() is the chemical kinetic source term function. This represents the p-th time residual point; Step 42, adjust the output layer weight parameters according to the loss function. The update is performed iteratively, and the update formula is shown below. ， ， in, This represents the output layer weight vector of the l-th iteration. The update step size for this round is calculated using the Moore-Penrose generalized inverse. It is the Jacobian matrix of the loss function. The specified error limit of the L2 norm of the loss function is set so that the iteration process ends when the specified error threshold is reached, thereby obtaining the simulation results of the evolution of the concentration of each particle in the reaction system over time.

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