Operator learning based low-pressure plasma particle simulation method and system

Abstract

The application discloses a low-pressure plasma particle simulation method and system based on operator learning, and relates to the technical field of low-pressure plasma. The application comprises the following steps: constructing a plasma particle model, giving a training task set and a task target set of the plasma particle model; constructing an operator neural network based on operator learning based on a field equation of the plasma particle model, designing corresponding constraint conditions and a loss function, and selecting appropriate neural network parameters; training the constructed operator neural network, ending the training after the loss function value gradually converges to a set value; and taking the trained operator neural network as a field equation solver of the plasma particle model to calculate and output simulation results of the plasma particle model. The application can significantly improve the simulation efficiency of the particle model under the condition of the same model structure and different parameters, and overcomes the defects of the traditional particle simulation method, such as dependence on a large number of iterations for field equation solving and high calculation cost.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of low-pressure plasma, and particularly relates to a low-pressure plasma particle simulation method and system based on operator learning. BACKGROUND

[0002] Plasma is a complex system composed of a large number of electrons, ions and neutral particles, and is the fourth state of matter. As a kind of plasma, low-pressure plasma contains high-energy electrons, ions and various excited states and free radicals, and is widely used in semiconductor processing. There is a strong coupling relationship between plasma and electromagnetic field, and in industrial applications, electromagnetic field is needed to control plasma. Therefore, it is crucial to study the response of plasma to electromagnetic field.

[0003] Due to the serious non-collision heating phenomenon at low pressure, particle simulation has become a reliable simulation means for low-pressure plasma. Particle simulation needs to calculate the field coupling relationship in space from the first principle, and strongly depends on partial differential equations to analyze the spatial electromagnetic field. However, when facing complex geometric structures, boundary conditions and multi-physical field coupling, the traditional solver needs to perform a large number of iterative calculations, which may take several days or even weeks to simulate a single physical parameter. This huge computational cost seriously restricts the practical application of particle simulation technology in engineering design and parameter optimization. SUMMARY

[0004] In view of the shortcomings of the prior art, the purpose of the present application is to provide a low-pressure plasma particle simulation method and system based on operator learning, which overcomes the shortcomings of the traditional particle simulation method that the field equation solving depends on a large number of iterations and has high computational cost, and can realize high-precision simulation only through limited training samples, and has good generalization ability and practical value.

[0005] The purpose of the present application can be achieved by the following technical solutions:

[0006] According to the first aspect of the present application, in order to achieve the above purpose, the present application provides the following technical solutions: a low-pressure plasma particle simulation method based on operator learning, comprising the following steps:

[0007] S1. receiving physical parameters of plasma particles including particle number, particle charge, particle coordinates, particle adjacent grid point coordinates, boundary conditions and shape functions;

[0008] Based on the physical parameters of the plasma particles, a cloud midpoint interpolation method is used to construct a plasma particle model, and a training task set and a task target set of the plasma particle model are given;

[0009] S2. Based on the field equations of the plasma particle model in S1, construct an operator neural network based on operator learning. The operator neural network includes a branch network and a backbone network. The branch network takes the dimensionality reduction representation of the source function of the training task set as input, and the backbone network takes the spatial coordinates of the source function of the task target set as input. The outputs of the branch network and the backbone network are multiplied to generate the final prediction result of the operator neural network.

[0010] S3. Design a loss function to train the operator neural network constructed in S2. The training ends when the loss function value gradually converges to the set value, and the trained operator neural network is obtained.

[0011] S4. Use the operator neural network trained in S3 as the solver for the field equations of the plasma particle model, and calculate and output the simulation results of the plasma particle model.

[0012] Furthermore, based on the physical parameters of plasma particles, a plasma particle model is constructed using the cloud midpoint interpolation method, and the training task set and task target set of the plasma particle model are given as follows:

[0013] S1.1. Establishing the particle model field equations based on cloud midpoint interpolation and Poisson's equation:

[0014]

[0015] The boundary conditions are as follows:

[0016]

[0017]

[0018]

[0019] In the formula, It is the Laplace operator. It is the reference potential. It is a two-dimensional spatial coordinate. t It is time. The spatial coordinates are 、 Time is t The potential function value, p It is the number of particles. It is the particle charge. W It is a shape function. and These are the particle coordinates and the coordinates of the grid points adjacent to the particle, respectively. The vacuum permittivity, , , and are the electric potentials at the spatial coordinates , , and , and are given boundary potential values;

[0020] S1.2 takes the boundary potential values as variable parameters , gives a training task set , each parameter of the task set constructs a corresponding plasma particle model, gives a task target set , each parameter of the task set corresponds to a plasma particle model that needs to be calculated, and the parameters are specifically the number of particles, the initial particle distribution or the boundary conditions of the plasma particle simulation.

[0021] Further, based on the field equation of the plasma particle model in S1, an operator neural network based on operator learning is constructed, and the operator neural network includes a branch network and a trunk network, and specifically includes the following steps:

[0022] S2.1. uses a dimension reduction module to reduce the dimension of the source function of the plasma field equation;

[0023] S2.2. takes the dimension-reduced source function as the input quantity of the operator neural network, and takes the solution quantity u of the equation as the output of the neural network;

[0024] S2.3. adds geometric symmetry constraints or regularization constraints to the operator neural network framework in the form of hard coding or soft constraints.

[0025] Further, the dimension reduction module in step S2.1 specifically includes:

[0026] S2.1.1. manifold sampling is performed on all source functions of the given training task set , and is divided into k groups according to the particle conditions corresponding to the source functions, and forms a decentralized snapshot matrix A k ;

[0027] S2.1.2. singular value decomposition is performed on the snapshot matrix to obtain a left singular vector matrix and a singular value matrix ;

[0028] S2.1.3. gives the percentage of energy to be preserved , and according to the relative information content, the left singular vectors corresponding to the first singular values form a modal matrix ;

[0029] S2.1.4. Project the input source function according to its belonging particle condition group to the corresponding modal matrix to obtain the dimensionality reduction representation of the source function k . .

[0030] Further, the operator neural network takes a branch network and a trunk network as an encoder and a decoder, and the branch network and the trunk network are both composed of a feedforward neural network.

[0031] Further, step S3 trains the constructed operator neural network by designing a loss function, and the training is ended when the loss function value gradually converges to a set value, and a trained operator neural network is obtained, and the loss function is as follows:

[0032]

[0033] In the formula, L is a loss function, is a potential predicted by the operator neural network, is a reference potential.

[0034] Further, step S4 uses the trained operator neural network as a field equation solver of the plasma particle model to calculate the simulation result of the plasma particle model, and the specific steps are as follows:

[0035] S4.1. Constructing a plasma particle model of a target task;

[0036] S4.2. Using the trained operator neural network to solve the physical field distribution of the plasma particle model of the target task until the simulation time of the model reaches a set value;

[0037] S4.3. Obtaining the output of the operator neural network, that is, the simulation result of the corresponding plasma particle model.

[0038] According to the second aspect of the present application, the present application provides a low-pressure plasma particle simulation system based on operator learning, which is used to realize the low-pressure plasma particle simulation method based on operator learning described in the first aspect, and comprises:

[0039] A first construction module is configured to receive physical parameters of plasma particles including particle number, particle charge, particle coordinates, particle adjacent grid point coordinates, boundary conditions, and shape functions;

[0040] Based on the physical parameters of the plasma particles, a cloud midpoint interpolation method is used to construct a plasma particle model, and a training task set and a task target set of the plasma particle model are given;

[0041] The second construction module is configured to construct an operator neural network based on operator learning based on a field equation of a plasma particle model, the operator neural network comprising a branch network and a trunk network, wherein the branch network takes a dimension-reduced representation of a source function of a training task set as input, the trunk network takes spatial coordinates of a source function of a target task set as input, and the outputs of the branch network and the trunk network are point multiplied to generate a final prediction result of the operator neural network.

[0042] The training module is configured to train the constructed operator neural network by designing a loss function, and the training is ended when the loss function value gradually converges to a set value, so as to obtain a trained operator neural network.

[0043] The result output module is configured to take the trained operator neural network as a field equation solver of the plasma particle model to calculate and output a simulation result of the plasma particle model.

[0044] According to a third aspect of the present application, a terminal device is provided, comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, the memory stores a computer program capable of running on the processor, and when the processor loads and executes the computer program, the low-pressure plasma particle simulation method based on operator learning described in the first aspect is adopted.

[0045] According to a fourth aspect of the present application, a storage medium containing computer executable instructions is provided, the computer executable instructions are used to execute the low-pressure plasma particle simulation method based on operator learning described in the first aspect when executed by a computer processor.

[0046] The present application has the following beneficial effects:

[0047] The present application can significantly improve the simulation efficiency of the particle model under the condition of the same model structure and different parameters, and is especially suitable for complex and high-dimensional geometric scenes. Compared with the traditional particle simulation method, the present application overcomes the shortcomings of dependence on a large number of iterations for solving the field equation and high calculation cost, and can realize high-precision simulation only by limited training samples, and has good generalization ability and practical value. BRIEF DESCRIPTION OF DRAWINGS

[0048] In order to more clearly illustrate the technical solutions in the embodiments of the present application or the prior art, the drawings needed to be used in the embodiments or prior art description will be briefly introduced as follows, and obviously, other drawings can also be obtained by those skilled in the art without creative labor.

[0049] Figure 1 is a flowchart of the method described in the present application;

[0050] Figure 2It is the operator neural network framework schematic diagram of the electron extractor particle model solution in the application;

[0051] Figure 3 It is the two-dimensional distribution result comparison diagram of the method and the ordinary particle simulation solver in the application;

[0052] Figure 4 It is the particle trajectory comparison diagram of the method and the ordinary particle simulation solver in the application;

[0053] Figure 5 It is the mean and maximum result comparison diagram of the method and the ordinary particle simulation solver in the application.

[0054] Figure 6 It is the precision and time comparison diagram of the method and the ordinary particle simulation solver in the application. DETAILED DESCRIPTION

[0055] The technical solutions in the embodiments of the application will be clearly and completely described below with reference to the drawings in the embodiments of the application. Obviously, the described embodiments are only part of the embodiments of the application, rather than all the embodiments of the application. Based on the embodiments in the application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the application.

[0056] Embodiment one:

[0057] In this embodiment, the electron extractor is taken as the research object, and the electrostatic particle model is taken as the research sample, and the simulation result of the electrostatic particle model is obtained by batch training.

[0058] Please refer to Figures 1-6 The application provides a technical solution: a low-pressure plasma particle simulation method based on operator learning, which comprises the following steps:

[0059] Step 1, receiving physical parameters of plasma particles including particle number, particle charge amount, particle coordinates, particle adjacent grid point coordinates, boundary conditions, and shape functions, establishing a plasma particle model based on the physical parameters, and giving a training task set and a task target set;

[0060] Step 1.1, establishing a particle model field equation based on the cloud midpoint interpolation method and the Poisson equation:

[0061]

[0062] The boundary condition is:

[0063]

[0064]

[0065]

[0066] where, is the Laplacian operator, is the electric potential, is the two-dimensional spatial coordinate, t is time, is the spatial coordinate, 、 is the electric potential function value at time t is the particle number, p is the particle charge amount, is the shape function, W and are the particle coordinate and the coordinate of the particle's adjacent grid point, respectively, is the vacuum permittivity, , , , and are the electric potentials at the spatial coordinates , , and , and are the given boundary potential values;

[0067] Step 1.2, set the boundary potential values as variable parameters , give a training task set , each parameter of the task set corresponds to a plasma particle model that needs to be calculated, and each parameter corresponds to the solution of about seventy field equations;

[0068] Step 1.3, give a task target set , each parameter of the task set corresponds to a plasma particle model that needs to be calculated, and each parameter corresponds to the solution of about seventy field equations;

[0069] Step 2, based on the plasma particle model field equations of step 1, construct an operator learning-based neural network framework, the operator neural network includes a branch network and a trunk network, as shown in Figure 2 , detailed as follows;

[0070] Step 2.1, use a dimension reduction module to perform dimension reduction representation on the plasma field equation source function ;

[0071] Step 2.1.1, manifold sampling is performed on all source functions of the given training task set , which is divided into k= 10 groups according to the particle conditions corresponding to the source functions, and a decentralized snapshot matrix is formedA k ;

[0072] Step 2.1.2, singular value decomposition is used on the snapshot matrix to get the left singular vector matrix , singular value matrix ;

[0073] Step 2.1.3, given the percentage of energy that needs to be preserved , the left singular vectors corresponding to the first singular values are composed into a modal matrix according to the relative information content;

[0074] Step 2.1.4, the input source function is projected to the corresponding modal matrix according to the particle condition group to which it belongs k , to get the dimensionality reduction representation of the source function ;

[0075] Step 2.2, the dimensionality reduction representation of the source function is taken as the input quantity of the operator neural network, and the solution quantity of the equation is taken as the output of the neural network;

[0076] Step 2.2.1, two feedforward neural networks are used as the main network and branch network of the operator neural network respectively, and the branch network and the main network are used as the encoder and the encoder respectively;

[0077] Step 2.2.2, set the hidden layer of the two feedforward neural networks to 4 layers, each layer has 125 neurons, randomly initialize the weights, set the learning rate to , and set the training times to 1000000 times;

[0078] Step 2.3, the geometric symmetry constraint is added to the operator network in a hard-coded manner;

[0079]

[0080] Step 2.3.1, set the loss function as , where L is the loss function, is the potential predicted by the operator neural network, is the benchmark potential;

[0081] Specifically, as shown in Figure 2 , given a set of training tasks to form a snapshot matrix, and form a modal through singular value decomposition, the source function f of the target task set is projected to the modal to get the corresponding coefficient ), and as the input of the branch network in the operator neural network, the spatial coordinates of the task target set source function are used as the input of the trunk network in the operator neural network, finally, the branch network and the trunk network of the operator neural network are point multiplied to obtain the output function as the simulation result of the corresponding plasma particle model;

[0082] Step 3, training the operator neural network framework constructed in step 2, so that the loss function value gradually converges to a set value, and the training is ended, thereby completing the efficient approximation of the field solving equation;

[0083] Step 4, using the trained operator neural network framework in step 3 as a particle model field equation solver for fast simulation calculation of the target task , and finally outputting the simulation result of the plasma particle model.

[0084] At this time, the comparison chart of the results of the low-pressure plasma particle simulation method based on operator learning and the potential two-dimensional distribution, particle trajectory, mean and extreme value of the potential and electric field time evolution of the ordinary particle simulation is shown in Figure 3 , 4 , 5; as shown in Figure 3 , the potential two-dimensional distribution solved by the finite difference method FDM in the ordinary particle simulation is basically the same as the potential two-dimensional distribution solved by the method, the relative L2 error distribution of the results of the two methods is uniform, and the error is less than ; as shown in Figure 4 , the particle trajectories in the model are pushed by the electric field solved by the finite difference method FDM and the method respectively, and the trajectories are almost the same; as shown in Figure 5 , the mean and extreme values of the potential and electric field on the central axis always maintain consistency in trend and value under the time evolution.

[0085] It can be seen that first, the low-pressure plasma particle simulation method based on operator learning can accurately solve the plasma characteristics. In the calculation of the potential field, the error distribution is relatively uniform, and there is no obvious error concentration area. In addition, all particle trajectories can also be accurately solved under the neural network framework based on operator learning, and complex periodic boundary conditions can be handled.

[0086] The comparison of the neural network framework based on operator learning and the finite difference solver of ordinary particle simulation with different precisions is shown in Figure 6 , the precision of the field solving of the embodiment based on the operator learning neural network framework is to Between, while the Poisson solution time is greatly reduced, the calculation period required by the particle simulation is greatly reduced under the same precision solution, so that the operator network framework designed in the embodiment can well simulate the electron extraction process of the extractor, and obtain a relatively accurate equation numerical solution.

[0087] In summary, the application can significantly improve the simulation efficiency of the particle model under the same model structure and different parameter conditions, and is especially suitable for complex and high-dimensional geometric scenes. Compared with the traditional particle simulation method, the application overcomes the shortcomings of dependence on a large number of iterations and high calculation cost in solving the field equation, and can realize high-precision simulation only through limited training samples, and has good generalization ability and practical value.

[0088] Embodiment two:

[0089] The embodiment provides a low-pressure plasma particle simulation system based on operator learning, which is used for realizing the low-pressure plasma particle simulation method based on operator learning described in embodiment one, and comprises:

[0090] The first construction module is used for receiving physical parameters of plasma particles including particle number, particle charge, particle coordinates, particle adjacent grid point coordinates, boundary conditions and shape functions;

[0091] Based on the physical parameters of the plasma particles, a cloud midpoint interpolation method is used to construct a plasma particle model, and a training task set and a task target set of the plasma particle model are given;

[0092] The second construction module is used for constructing an operator neural network based on operator learning based on a field equation of the plasma particle model, the operator neural network comprising a branch network and a trunk network, wherein the branch network takes a dimension reduction representation of a training task set source function as input, the trunk network takes spatial coordinates of a task target set source function as input, and the outputs of the branch network and the trunk network are point multiplied to generate a final prediction result of the operator neural network;

[0093] The training module is used for training the constructed operator neural network by designing a loss function, ending the training after the loss function value gradually converges to a set value, and obtaining a trained operator neural network;

[0094] The result output module is used for taking the trained operator neural network as a field equation solver of the plasma particle model to calculate and output simulation results of the plasma particle model.

[0095] Embodiment three:

[0096] The application provides a terminal device, including a memory, a processor and a computer program stored in the memory and capable of running on the processor, the memory stores the computer program capable of running on the processor, and when the processor loads and executes the computer program, the operator learning-based low-pressure plasma particle simulation method described in embodiment one is adopted.

[0097] It should be noted that the terminal device can adopt a computer device such as a desktop computer, a notebook computer or a cloud server, and the terminal device includes but is not limited to a processor and a memory, for example, the terminal device can also include an input / output device, a network access device and a bus, etc.

[0098] Further, the processor can adopt a central processing unit (CPU), of course, according to the actual use, other general-purpose processors, digital signal processors (DSP), application-specific integrated circuits (ASIC), ready-to-program gate arrays (FPGA) or other programmable logic devices, discrete gates or transistor logic devices, discrete hardware components, etc. can also be adopted, the general-purpose processor can adopt a microprocessor or any conventional processor, etc., and the present application does not make any limitation.

[0099] Embodiment four:

[0100] The application provides a storage medium containing computer executable instructions, which are used to execute the operator learning-based low-pressure plasma particle simulation method described in embodiment one when executed by a computer processor.

[0101] Wherein, the computer program can be stored in a computer readable medium, the computer program includes computer program code, the computer program code can be in the form of source code, object code, executable file or some middleware form, etc., the computer readable medium includes any entity or device capable of carrying computer program code, recording medium, U disk, mobile hard disk, magnetic disk, optical disk, computer memory, read-only memory (ROM), random access memory (RAM), electric carrier signal, telecommunication signal and software distribution medium, etc., it should be noted that the computer readable medium includes but is not limited to the above components.

[0102] In the description of the present application, the description of the terms "one embodiment", "example", "specific example" and the like means that the specific features, structures, materials or characteristics described in conjunction with the embodiment or example are contained in at least one embodiment or example of the present application. In the present application, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner.

[0103] The above shows and describes the basic principles, main features and advantages of the present application. Those skilled in the art should understand that the present application is not limited to the above-mentioned embodiments, and the above-mentioned embodiments and descriptions in the specification are only to illustrate the principles of the present application. Without departing from the spirit and scope of the present application, various changes and improvements can be made to the present application, and these changes and improvements all fall within the scope of the claimed present application.

Claims

1. An operator learning-based low-pressure plasma particle simulation method, characterized by, Comprising: S1. receiving the physical parameters of the plasma particles including the number of particles, the amount of particle charge, the particle coordinates, the coordinates of the particle adjacent grid points, the boundary conditions, and the shape functions; Based on the physical parameters of the plasma particles, a cloud midpoint interpolation method is used to construct a plasma particle model, and a training task set and a task target set of the plasma particle model are given; S2. Based on the field equation of the plasma particle model in S1, an operator neural network based on operator learning is constructed, the operator neural network includes a branch network and a backbone network, wherein the branch network takes the dimension reduction representation of the training task set source function as input, the backbone network takes the spatial coordinates of the task target set source function as input, and the outputs of the branch network and the backbone network are point multiplied to generate the final prediction result of the operator neural network; S3. Design a loss function to train the operator neural network constructed in S2, and end the training when the loss function value gradually converges to a set value, to obtain a trained operator neural network; S4. The trained operator neural network in S3 is used as a field equation solver of the plasma particle model to calculate and output the simulation results of the plasma particle model; Based on the physical parameters of the plasma particles, a cloud midpoint interpolation method is used to construct a plasma particle model, and a training task set and a task target set of the plasma particle model are given, as follows: S1.

1. Based on the cloud midpoint interpolation method and the Poisson equation, the field equation of the particle model is established: Wherein, the boundary condition is: wherein, is the Laplace operator, is the reference potential, is the two-dimensional spatial coordinate, t is the time, is the spatial coordinate, 、 is the time, t is the potential function value, p is the particle number, is the particle charge amount, W is the shape function, and are the particle coordinate and the coordinate of the particle's neighboring grid point, respectively, is the vacuum permittivity, , , and are the potentials at the spatial coordinates, , , and , and are the given boundary potential values; S1.2 constructing a boundary potential value as a variable parameter , given a training task set each parameter of this task set constructs a corresponding plasma particle model, given a task target set each parameter of this task set corresponds to a plasma particle model that needs to be calculated, and the parameters are specifically the particle number, initial particle distribution or boundary condition of the plasma particle simulation; Based on the field equation of the plasma particle model in S1, an operator neural network based on operator learning is constructed, the operator neural network includes a branch network and a backbone network, and the specific steps include: S2.

1. using a dimensionality reduction module to reduce dimensionality of the plasma field equation source function to a reduced dimensionality representation; S2.

2. The source function represented by the reduced dimension is taken as the input quantity of the operator neural network, and the solving quantity of the equation is taken as the output of the neural network. the neural network S2.

3. Add geometric symmetry constraints or regularization constraints to the operator neural network framework in the form of hard coding or soft constraints; The dimension reduction module in step S2.1 specifically includes: S2.1.

1. Manifold sampling is performed on all source functions of a given training task set , which are divided into groups according to the particle conditions corresponding to the source functions, and a decentralized snapshot matrix is formed k A k ;​​ S2.1.

2. Use singular value decomposition on the snapshot matrix to obtain the left singular vector matrix , the singular value matrix ; S2.1.

3. Given the percentage of energy that needs to be preserved , the left singular vectors corresponding to the first singular values form the modal matrix ; S2.1.

4. Group the input source functions according to their particle condition k Project to the corresponding modal matrix to get the reduced representation of source functions .

2. The operator learning based low-pressure plasma particle simulation method according to claim 1, wherein The operator neural network takes the branch network and the backbone network as the encoder and the encoder, and the branch network and the backbone network are both composed of feedforward neural networks.

3. The operator learning based low-pressure plasma particle simulation method according to claim 2, wherein Step S3 designs a loss function to train the operator neural network constructed, and ends the training when the loss function value gradually converges to a set value, to obtain a trained operator neural network, and the loss function is as follows: wherein L is a loss function, is an operator neural network prediction potential, is a reference potential.

4. The operator learning based low-pressure plasma particle simulation method according to claim 3, wherein Step S4 uses the trained operator neural network as a field equation solver of the plasma particle model to calculate and output the simulation results of the plasma particle model, as follows: S4.

1. Construct the plasma particle model of the target task; S4.

2. Use the trained operator neural network to solve the physical field distribution of the plasma particle model of the target task until the simulation time of the model reaches a set value; S4.

3. Get the output of the operator neural network, which is the simulation result of the corresponding plasma particle model.

5. An operator learning-based low-pressure plasma particle simulation system for implementing the operator learning-based low-pressure plasma particle simulation method according to any one of claims 1 to 4, characterized by Comprising: A first construction module for receiving the physical parameters of the plasma particles including the number of particles, the amount of particle charge, the particle coordinates, the coordinates of the particle adjacent grid points, the boundary conditions, and the shape functions; Based on the physical parameters of the plasma particles, a cloud midpoint interpolation method is used to construct a plasma particle model, and a training task set and a task target set of the plasma particle model are given; The second construction module is configured to construct an operator neural network based on operator learning based on a field equation of a plasma particle model, the operator neural network comprising a branch network and a trunk network, wherein the branch network takes a dimension-reduced representation of a source function of a training task set as input, the trunk network takes spatial coordinates of a source function of a target task set as input, and the outputs of the branch network and the trunk network are point multiplied to generate a final prediction result of the operator neural network. The training module is configured to train the constructed operator neural network by designing a loss function, and the training is ended after the loss function value gradually converges to a set value, and a trained operator neural network is obtained. The result output module is configured to take the trained operator neural network as a field equation solver of the plasma particle model to calculate and output a simulation result of the plasma particle model.

6. A terminal device comprising a memory, a processor, and a computer program stored in the memory and capable of running on the processor, characterized in that, The processor loads and executes the computer program, and a low-pressure plasma particle simulation method based on operator learning according to any one of claims 1 to 4 is adopted.

7. A storage medium containing computer-executable instructions, wherein: The computer executable instructions, when executed by the computer processor, are used to perform the low-pressure plasma particle simulation method based on operator learning according to any one of claims 1 to 4.

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