Digital twin accelerator beam modulation method based on Gaussian integrated belief propagation

Abstract

The invention provides a digital twin accelerator beam modulation method based on Gaussian integrated belief propagation. The method comprises the following steps: initializing parameters; constructing a prior factor graph; generating a sample set and constructing a condition graph; variable nodes and factor nodes in the condition graph are converted, and a posterior graph is constructed; calculating an accelerator operation parameter estimation value; and acquiring an accelerator beam modulation result. According to the method, efficient calculation is carried out by using a near-low-order Gaussian matrix generated by a sample set, conversion can be carried out among set statistics, various parameterization and effective operation on the parameters, sampling is carried out from the generation priori, the set statistics are converted into a standard form, belief propagation is carried out, and a set sample matched with an updated belief is recovered; and low-rank local information is transmitted on the condition graph to update integration, so that complex dependent structures and high-dimensional states and parameters can be processed, and the efficiency of the beam modulation process of the accelerator is improved.

Description

Technical Field

[0001] The present invention belongs to the field of digital twin technology and relates to an accelerator beam adjustment method, specifically to a digital twin accelerator beam adjustment method based on Gaussian integrated belief propagation, which can be used in the field of accelerator design simulation technology. Background Art

[0002] Particle accelerators are electromagnetic devices that use artificial methods to accelerate various types of charged particles to higher energies with the help of various forms of electric fields. Particle accelerators play an important role in basic scientific research, medical treatment and material processing.

[0003] Particle accelerator beam tuning refers to the process of adjusting and optimizing various parameters of the particle beam in the accelerator to meet the experimental or application requirements. Common beam tuning target parameters include beam intensity, beam quality, beam center position, energy distribution, transmission efficiency, pulse width, beam stability and radiation loss. The goal of beam tuning is to improve the performance and quality of the particle beam without affecting the safety and stability of the accelerator, thereby improving the overall output efficiency of the accelerator.

[0004] Digital twin technology is a technology that uses computer simulation technology to accurately replicate physical systems in digital space. The basic principle of digital twin accelerator beam adjustment is to digitally model the real particle accelerator, simulate the operating status and performance of the real accelerator, combine it with real-time sensor data feedback, perform virtual beam adjustment, and adjust the parameters of the actual accelerator through simulation result feedback.

[0005] The existing digital twin accelerator beam tuning method is implemented in the following steps: collect the real-time operation data of the digital twin accelerator to build a data set; use the collected data set to calibrate the digital twin model in a data-driven manner; and find the optimal operating parameters on the calibrated digital twin model through the nonlinear least squares method so that the output meets the desired beam characteristics. This method uses digital twin technology and nonlinear least squares method to find the most likely operating parameters given the beam distribution, but the YAG image generated by the actual accelerator contains complex components (such as the ring structure at the edge), and the size, shape and position of the beam spot vary greatly. Errors may occur during image data preprocessing and alignment, which in turn affects the accuracy of the beam tuning results. The nonlinear least squares method requires the calculation of the Jacobian matrix or the Hessian matrix at each step, which involves the inverse operation of the matrix, resulting in a high computational complexity of the algorithm, especially for high-dimensional parameter spaces or large data sets, the computational cost will increase dramatically. Summary of the invention

[0006] The purpose of the present invention is to overcome the defects of the above-mentioned prior art and propose a digital twin accelerator beam adjustment method based on Gaussian integrated belief propagation to solve the technical problems of low accuracy and efficiency in the prior art.

[0007] To achieve the above object, the technical solution adopted by the present invention includes the following steps:

[0008] (1) Initialization parameters:

[0009] Initialize the accelerator's operating parameter variable to X = {X d} 1≤d≤D , the set of generated processes is P = {P j} 1≤j≤J The beam tuning target parameter of the accelerator is Among them, X d represents the dth running parameter variable, D represents the total number of running parameter variables, P j represents the jth generation equation P describing the generation process j :X Ij →X Oj , J represents the number of generating equations, represents the kth beam adjustment target parameter value, K represents the number of beam adjustment target parameters, X Ij , X Oj They represent the input and output operating parameter variables in the j-th generation equation, X Ij ∈X,X Oj ∈X;

[0010] (2) Constructing a priori factor graph:

[0011] Constructs a variable X for each run d and X d The prior distribution p(X d ) is a variable node, and each generated equation P j Factor is a factor node, with X d and The lines between them are the prior factor graph G of the edges, where X d The prior distribution of X is Gaussian distribution, d ∈X Ij ∪X Oj , represents the dependent operating parameter variable described by the j-th generating equation;

[0012] (3) Generate a sample set and construct a conditional graph:

[0013] For the variable nodes corresponding to the ancestral variables in the prior factor graph G Perform O sampling and calculate the sampling value according to the sampling value. and the generation process set {P j} 1≤j≤J Calculate the remaining variable nodes Parameter value corresponding to the running parameter variable And calculate by and X *d The parameter set The contribution index of each parameter set to the accelerator boundary Then select N parameter sets with high contribution index to form a priori sample set At the same time, construct the factor adjacent to the variable node X corresponding to the beam state variable

[0014] A collection of child nodes For factor nodes in G Update and remove the variable node X corresponding to the beam state variable ε With edges, we get a conditional graph G including S variable nodes * ,in, represents the variable node corresponding to the qth ancestor variable, express The value of the oth sampling, represents the calculated value of the oth time of the dth remaining variable node, represents the parameter set consisting of the D operating parameter values ​​after the oth sampling and calculation,

[0015] (4) Transform the variable nodes and factor nodes in the conditional graph and construct the posterior graph:

[0016] For the conditional graph G * Each variable node X in s and factor nodes Convert to X s and The nearly low-order Gaussian standard form X sηP and f jηP , and uses a low-order information propagation algorithm from factor nodes To the adjacent variable node Propagate low-rank information and use it to update variable node X s The belief is obtained from the posterior graph G ** , where X sηP For variable node X s The Gaussian information parameter of the initial belief, f jηP is a factor node Gaussian information parameter of

[0017] (5) Calculate the estimated values ​​of the accelerator operating parameters:

[0018] Make sure to use XZ The corresponding sample is consistent with the belief The affine transformation T of the prior sample set X A Convert to the posterior sample set X post , and according to the posterior sample set X post Inference accelerator run parameter estimates

[0019] (6) Obtain accelerator beam adjustment results:

[0020] Estimating the accelerator parameters Load the digital twin accelerator as preset parameters and simulate the output beam state And judge Is it true? If so, estimate the value as the beam tuning parameter of the accelerator; otherwise, let N=N+1 and execute step (3).

[0021] Compared with the prior art, the present invention has the following advantages:

[0022] 1. The present invention generates a sample set and constructs a conditional graph, transforms the variable nodes and factor nodes in the conditional graph and constructs a posterior graph, calculates accelerator running parameter estimates, uses a near low-order Gaussian matrix generated by the sample set for efficient calculation, can convert between set statistics, various parameterizations and effective operations on these parameters, samples from the generated prior, converts the set statistics to a standard form, performs belief propagation, and recovers a posterior sample set that matches the belief, thereby reducing errors that may occur in the data collection process and improving the accuracy of the beam adjustment results.

[0023] 2. The present invention transforms the variable nodes and factor nodes in the conditional graph and constructs a posterior graph, and transmits low-rank local information on the conditional graph to update the integration, so that it can handle complex dependency structures and high-dimensional states and parameters, and improve the efficiency of the accelerator beam tuning process. BRIEF DESCRIPTION OF THE DRAWINGS

[0024] Figure 1 It is a flow chart for implementing the present invention. DETAILED DESCRIPTION

[0025] The present invention is further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0026] Reference Figure 1 , the present invention comprises the following steps:

[0027] Step 1) Initialize parameters:

[0028] Initialize the accelerator's operating parameter variable to X = {X d} 1≤d≤D, the set of generated processes is P = {P j} 1≤j≤J The beam tuning target parameter of the accelerator is Among them, X d represents the dth running parameter variable, D represents the total number of running parameter variables, P j represents the jth generation equation P describing the generation process j :X Ij →X Oj , J represents the number of generating equations, represents the kth beam adjustment target parameter value, K represents the number of beam adjustment target parameters, X Ij , X Oj They represent the input and output operating parameter variables in the j-th generation equation, X Ij ∈X,X Oj ∈X;

[0029] The operating parameter variables of the accelerator include control variables, equipment state variables and beam state variables. The control variables include the main bend magnet current, quadrupole magnet gradient, sextupole magnet gradient, RF frequency, acceleration voltage, power supply current stability and pulse power supply time synchronization; the equipment state variables include vacuum pressure, electron cooler current and cooling length; the beam state variables include beam intensity, beam quality, beam center position, energy distribution, transmission efficiency, pulse width, beam stability and radiation loss;

[0030] Beam tuning target parameter values: target values ​​of the beam state at the end of beam tuning, including beam intensity, beam quality, beam center position, energy distribution, transmission efficiency, pulse width, beam stability and radiation loss;

[0031] The generation process set is a set of generation equations that describe the direct dependency coupling relationship between the operating parameter variables. The generation equation P j An independent running parameter variable that does not depend on other running parameter variables is an ancestor variable;

[0032] Step 2) Construct a priori factor graph:

[0033] Constructs a variable X for each run d and X d The prior distribution p(X d ) is a variable node, and each generated equation P j Factor is a factor node, with X d and The lines between them are the prior factor graph G of the edges, where X d The prior distribution of X is Gaussian distribution, d ∈X Ij ∪X Oj , represents the dependent operating parameter variable described by the j-th generating equation;

[0034] The prior factor graph is a bipartite graph, including variable nodes and factor nodes. Variable nodes represent variables, and factor nodes represent the coupling dependency between variables. The corresponding variable nodes and factor nodes are connected according to the dependency between variable nodes and factor nodes. The prior distribution is set for the variables according to the prior knowledge. At this time, the joint distribution of all variable nodes in the prior factor graph is The factor node is express The dependencies between them.

[0035] Step 3) Generate a sample set and construct a conditional graph:

[0036] For the variable nodes corresponding to the ancestral variables in the prior factor graph G Perform O sampling and calculate the sampling value according to the sampling value. and the generation process set {P j} 1≤j≤J Calculate the remaining variable nodes Parameter value corresponding to the running parameter variable And calculate by and X *d The parameter set The contribution index of each parameter set to the accelerator boundary Then select N parameter sets with high contribution index to form a priori sample set At the same time, construct the factor adjacent to the variable node X corresponding to the beam state variable

[0037] A collection of child nodes For factor nodes in G Update and remove the variable node X corresponding to the beam state variable ε With edges, we get a conditional graph G including S variable nodes * ,in, represents the variable node corresponding to the qth ancestor variable, express The value of the oth sampling, represents the calculated value of the oth time of the dth remaining variable node, represents the parameter set consisting of the D operating parameter values ​​after the oth sampling and calculation,

[0038] According to the prior distribution of variable nodes on the prior factor graph, the variable nodes corresponding to the ancestor variables are sampled to obtain sampling values. According to the sampling values ​​and the generation process set, the parameter values ​​of all accelerator running variables can be calculated in turn to obtain the parameter set. Select a priori sample set to prepare for efficient calculation of the near-low-order Gaussian matrix generated by Gaussian ensemble belief propagation based on the sample set. The calculation formula is:

[0039]

[0040] in, express The number of directions that contribute to the accelerator's boundary performance, U represents The total number of directions contributing to the accelerator's boundary performance;

[0041] In the factor graph, X ε The observed value will affect the factor nodes directly connected to it. After the factor node is fixed by the observed value, the dimension of the original factor is reduced. is conditioned into the factor node. In this way, constructing the conditional graph can effectively reduce the computational complexity while retaining the dependency information between unobserved variables. The update formula is:

[0042]

[0043] in, express Time Factor Node Connect the conditional distribution of the remaining variables;

[0044] Step 4) Transform the variable nodes and factor nodes in the conditional graph and construct the posterior graph:

[0045] For the conditional graph G * Each variable node X in s and factor nodes Convert to X s and The nearly low-order Gaussian standard form X sηP and f jηP , and uses a low-order information propagation algorithm from factor nodes To the adjacent variable node Propagate low-rank information and use it to update variable node X s The belief is obtained from the posterior graph G ** , where X sηP For variable node X s The Gaussian information parameter of the initial belief, f jηP is a factor node Gaussian information parameter of

[0046] Due to the properties of Gaussian distribution, the conditional distribution of any subset of variables is still Gaussian. We represent complex variable dependencies through sparse matrices and low-rank approximations;

[0047] For the conditional graph G * The variable node X in s and factor nodes To perform the conversion, the steps are:

[0048] Step 4a) Set the prior sample set Variable node X s The sample set matrix composed of the corresponding samples And calculate the variable node X in the matrix s The corresponding sample mean m s and variance K s , X As The overall average is The population variance is expressed as Rewrite the mean and variance operations to describe the empirical moments of a set:

[0049]

[0050]

[0051]

[0052] Among them, C N :=I N -A N B N , I N is the N×N identity matrix, A N Each element is N-dimensional column vector, B N is an N-dimensional unit vector, EX As Represents X As The empirical mean of Var V X As Represents X As Cov(X,Y) represents the empirical variance of X As and the empirical covariance of Y, V is a matrix with elements σ 2 The diagonal matrix of , Y represents the sample set composed of samples corresponding to another variable node;

[0053] Step 4b) Calculate X s Information s =P s ·m s and precision Get X s The nearly low-order Gaussian standard form X sηP :η s ,P s =U s -[R s ][R s] T , where u s For variable X s The accuracy of U s =diag([u s ]) indicates that u s The diagonal matrix constructed for the elements, [R s ] represents the variable X s The associated low-rank matrix, [R s ] T Represents the matrix R s The transpose operation of

[0054] Step 4c) Combine the Gaussian belief propagation algorithm with the integrated Kalman filter to transform the conditional graph G * Middle Factor Node Set as Factor Neighborhood Set X j The experience distribution of in, Indicates the mean Covariance is Var V X j Gaussian density moment of

[0055] Step 4d) Calculate factor nodes The information vector and the precision matrix Get the nearly low-order Gaussian standard form of the factor η js Represents the information corresponding to the variable in the factor node, η jl Indicates the information of the remaining variable nodes connected to the factor node except the variable node to be transferred, u js is the corresponding variable node X in the factor node s The accuracy of u jl The precision matrix of the remaining variables in the factor node corresponding to the factor node connection except the variable node to be transferred, Indicates u jl and u js is a diagonal matrix of elements, [R js ] indicates the corresponding variable node X in the factor node s The associated low-rank matrix, [R jl ] represents the low-rank matrix related to the remaining variables connected to the factor node except the transfer variable node.

[0056] A low-order information propagation algorithm is used to propagate information from factor nodes To the adjacent variable node X s Propagate low-rank information and use it to update variable node X s The steps to achieve the belief are:

[0057] Step 4e) At the factor node The information vector and information from the variable η s Represented as joint information vector and the joint precision matrix in,

[0058] Step 4f) For the joint precision matrix P prod Inverse to get the joint covariance K prod ;

[0059] Step 4g) P prod and η prod Multiply them to get the joint mean vector m prod =P prod η prod ;

[0060] Step 4h) extracting m prod and K prod The marginal mean vector m obtained by the marginal components of l and marginal covariance K l ;

[0061] Step 4i) K l Singular value decomposition retains the first N largest singular values ​​and the corresponding singular vectors, and obtains a low-order matrix constrained to a rank of N. The inverse is obtained to obtain the reduced-dimensional marginal precision matrix P′ jls =K l -1 ;

[0062] Step 4j) For P′ jl and m l Multiply to get the information vector η' jl =P′ jl m l ;

[0063] Step 4k) Factor node f j To the adjacent variable node X s ∈X Ij ∪X Oj The low-order information transmitted is η' j→s =η' jl and P′ j→s =P′ jl , update variable node X s The Gaussian information parameter information vector η of the belief s for and precision P s for in Represents the variable node X s Adjacent factor nodes transmit information vector summation, Represents the variable node X s The precision matrices passed by adjacent factor nodes are summed;

[0064] Step 41) Calculate the information vector and the precision matrix The amount of change and judge Is it true? If so, get the posterior graph G ** ; Otherwise, execute step (4e).

[0065] Step 5) Calculate the estimated values ​​of the accelerator operation parameters:

[0066] Make sure to use X Z The corresponding sample is consistent with the belief The affine transformation T of the prior sample set X A Convert to the posterior sample set X post , and according to the posterior sample set X post Inference accelerator run parameter estimates

[0067] Gaussian belief propagation method uses the parameters of the normal distribution to summarize the inference x (n) ~φ M (x; m, K), is the moment of the Gaussian density, where x is the variable, m is the mean of the variable, and K is the covariance matrix of the variable. The integrated Kalman filter uses a collection of Monte Carlo samples to summarize the joint distribution, that is, the matrix X composed of N samples = [x (n) ] 1≤n≤N , the overall mean can be expressed as The population variance is expressed as Among them A N It is composed of N The column vector, B N is the row vector, C N :=I N -A N B N , I N is an N×N identity matrix, rewriting the mean and variance operations to describe the empirical moments of the sample set,

[0068]

[0069]

[0070]

[0071] Where V is the diagonal matrix entry, set to σ 2 I, Assumption Combining the Gaussian belief propagation algorithm with the integrated Kalman filter method, the following inferences can be obtained:

[0072]

[0073] The steps to calculate the estimated values ​​of the accelerator running parameters are:

[0074] (5a) In the prior sample set Select the variable node X corresponding to the ancestor variable Z The corresponding samples constitute the ancestral sample set {X Z n} 1≤n≤N ;

[0075] (5b) Based on the posterior graph G ** Query the variable node X corresponding to the ancestor variable Z The posterior belief b G** (X Z )=φ M (X Z ;m Z ,K Z );

[0076] (5c) Select an affine transformation to minimize the Frobenius norm distance

[0077]

[0078] where μ is the mean shift set to the posterior mean m Z , is a decentralized ancestral sample set, B is a column of N-dimensional unit vectors;

[0079] (5d) Transform the prior sample set X through affine transformation T A Convert to posterior sample set

[0080] (5e) According to the posterior sample set matrix Compute the estimated values ​​of the accelerator operating parameters The calculation formula is as follows:

[0081]

[0082] in, represents the beam state variable node X in the posterior sample ε Corresponding to a set of N samples, Represents the posterior graph G in the posterior sample **The S variable nodes correspond to a set of N samples;

[0083] Step 6) Obtain the accelerator beam adjustment result:

[0084] Estimating the accelerator parameters Load the digital twin accelerator as preset parameters and simulate the output beam state value And judge Is it true? If so, estimate the value as the beam tuning parameter of the accelerator; otherwise, let N=N+1 and execute step (3).

Claims

1. A digital twin accelerator beam adjustment method based on Gaussian integrated belief propagation, characterized in that: The steps include: (1) Initialization parameters: Initialize the accelerator's operating parameter variable to X = {X d } 1≤d≤D , the set of generated processes is P = {P j } 1≤j≤J The beam tuning target parameter of the accelerator is Among them, X d represents the dth running parameter variable, D represents the total number of running parameter variables, P j represents the jth generation equation P describing the generation process j :X Ij →X Oj , J represents the number of generating equations, represents the kth beam adjustment target parameter value, K represents the number of beam adjustment target parameters, X Ij , X Oj They represent the input and output operating parameter variables in the j-th generation equation, X Ij ∈X,X Oj ∈X; (2) Constructing a priori factor graph: Constructs a variable X for each run d and X d The prior distribution p(X d ) is a variable node, and each generated equation P j Factor is a factor node, with X d and The lines between them are the prior factor graph G of the edges, where X d The prior distribution of X is Gaussian distribution, d ∈X Ij ∪X Oj , represents the dependent operating parameter variable described by the j-th generating equation, (3) Generate a sample set and construct a conditional graph: For the variable nodes corresponding to the ancestral variables in the prior factor graph G Perform O sampling and calculate the sampling value according to the sampling value. and the generation process set {P j } 1≤j≤J Calculate the remaining variable nodes Parameter value corresponding to the running parameter variable And calculate by and X *d The parameter set The contribution index of each parameter set to the accelerator boundary Then select N parameter sets with high contribution index to form a priori sample set At the same time, construct the variable node X corresponding to the beam state variable ε The set of adjacent factor nodes For factor nodes in G Update and remove the variable node X corresponding to the beam state variable ε With edges, we get a conditional graph G including S variable nodes * ,in, represents the variable node corresponding to the qth ancestor variable, express The value of the oth sampling, represents the calculated value of the oth time of the dth remaining variable node, represents the parameter set consisting of the D operating parameter values ​​after the oth sampling and calculation, S = DK; (4) Transform the variable nodes and factor nodes in the conditional graph and construct the posterior graph: For the conditional graph G * Each variable node X in s and factor nodes Convert to X s and The nearly low-order Gaussian standard form X sηP and f jηP , and uses a low-order information propagation algorithm from factor nodes To the adjacent variable node Propagate low-rank information and use it to update variable node X s The belief is obtained from the posterior graph G ** , where X sηP For variable node X s The Gaussian information parameter of the initial belief, f jηP is a factor node Gaussian information parameter of (5) Calculate the estimated values ​​of the accelerator operating parameters: Make sure to use X Z The corresponding sample is consistent with the belief The affine transformation T of the prior sample set X A Convert to the posterior sample set X post , and according to the posterior sample set X post Inference accelerator run parameter estimates (6) Obtain accelerator beam adjustment results: Estimating the accelerator parameters Load the digital twin accelerator as preset parameters and simulate the output beam state And judge Is it true? If so, estimate the value as the beam tuning parameter of the accelerator; otherwise, let N=N+1 and execute step (3).

2. The method according to claim 1, characterized in that The accelerator operating parameter variable X described in step (1) and the beam tuning target parameter value in: X includes control variables, device state variables and beam state variables; Controlled variables include main bend magnet current, quadrupole magnet gradient, sextupole magnet gradient, RF frequency, accelerating voltage, power supply current stability, and pulse power supply time synchronization; Equipment state variables include vacuum pressure, electronic cooler current, and cooling length; Beam state variables include beam intensity, beam quality, beam center position, energy distribution, transmission efficiency, pulse width, beam stability and radiation loss; Beam adjustment target parameter value It is the target value of the beam state at the end of beam tuning, including beam intensity, beam quality, beam center position, energy distribution, transmission efficiency, pulse width, beam stability and radiation loss.

3. The method according to claim 1, characterized in that The accelerator generation process set P described in step (1) = {P j } 1≤j≤J , the set of generated processes is to describe the coupling between the main bending magnet current and the beam energy, to describe the coupling between the bending magnet current and the beam center position, to describe the coupling between the quadrupole magnet gradient and the beam emittance, to describe the coupling between the quadrupole magnet gradient and the beam stability, to describe the coupling between the sextupole magnet gradient and the beam brightness, to describe the coupling between the sextupole magnet gradient and the energy distribution, to describe the coupling between the RF frequency and the beam energy, to describe the coupling between the RF frequency and the beam stability, to describe the coupling between the acceleration voltage and the energy distribution, to describe the coupling between the acceleration voltage and the beam transmission efficiency, to describe the power supply current stability and the bending magnet current and the quadrupole magnet gradient The coupling between the pulse power supply time synchronization and the RF frequency, the coupling between the pulse power supply time synchronization and the RF frequency pulse width, the coupling between the vacuum pressure and the beam quality, the coupling between the vacuum pressure and the radiation loss, the coupling between the electron cooler current and the cooling length and the beam energy spread, the coupling between the electron cooler current and the cooling length and the beam emittance, the coupling between the beam intensity and the beam stability, the coupling between the beam intensity and the radiation loss, and the coupling between the beam center position and the main bending magnet current and the quadrupole magnet gradient; the generating equation P j An independent running parameter variable that does not depend on other running parameter variables is an ancestor variable.

4. The method according to claim 1, characterized in that: The variable nodes and factor nodes described in step (2), wherein: X d The prior distribution of Represents variable X d The mean of Represents variable X d Variance; The joint distribution of all variable nodes in the prior factor graph G is The factor node is express The dependencies between them.

5. The method according to claim 1, characterized in that Each parameter set described in step (3) Contribution index to the accelerator boundary The calculation formula is: in, express The number of directions that contribute to the accelerator's boundary performance, U represents Total number of directions contributing to the accelerator's boundary performance.

6. The method according to claim 1, characterized in that The variable node X corresponding to the beam state variable in G described in step (3) ε Factors of adjacent factor nodes Update, the update formula is: in, express Time Factor Node Connect the conditional distribution of the remaining variables.

7. The method according to claim 1, characterized in that The condition graph G described in step (4) * The variable node X in s and factor nodes To perform the conversion, the steps are: (4a) The prior sample set Variable node X s The sample set matrix composed of the corresponding samples And calculate the variable node X in the matrix s The corresponding sample mean m s and variance K s , X As The overall average is The population variance is expressed as Rewrite the mean and variance operations to describe the empirical moments of the set: Among them, C N :=I N -A N B N , I N is the N×N identity matrix, A N Each element is N-dimensional column vector, B N is an N-dimensional unit vector, EX As Represents X As The empirical mean of Var V X As Represents X As Cov(X,Y) represents the empirical variance of X As and the empirical covariance of Y, V is a matrix with elements σ 2 The diagonal matrix of , Y represents the sample set composed of samples corresponding to another variable node; (4b) Calculate X s Information s =P s ·m s and precision P s =K s -1 , we get X s The nearly low-order Gaussian standard form X sηP :η s ,P s =U s -[R s ][R s ] T , where u s For variable X s The accuracy of U s =diag([u s ]) indicates that u s The diagonal matrix constructed for the elements, [R s ] represents the variable X s The associated low-rank matrix, [R s ] T Represents the matrix R s The transpose operation of (4c) Combining Gaussian belief propagation algorithm with integrated Kalman filtering, the conditional graph G * Middle Factor Node Set as Factor Neighborhood Set X j The experience distribution of in, It means the mean Covariance is Var V X j Gaussian density moment of (4d) Calculation Factor Node The information vector and the precision matrix P j =,Var V X j -1 Get the nearly low-order Gaussian standard form of the factor f jηP : η js Represents the information corresponding to the variable in the factor node, η jl Indicates the information of the remaining variable nodes connected to the factor node except the variable node to be transferred, u js is the corresponding variable node X in the factor node s The accuracy of u jl The precision matrix of the remaining variables in the factor node corresponding to the factor node connection except the variable node to be transferred, Indicates u jl and u js is a diagonal matrix of elements, [R js ] indicates the corresponding variable node X in the factor node s The associated low-rank matrix, [R jl ] represents the low-rank matrix related to the remaining variables connected to the factor node except the transfer variable node.

8. The method according to claim 1, characterized in that The low-order information propagation algorithm described in step (4) is used to propagate information from the factor nodes To the adjacent variable node X s Propagate low-rank information and use it to update variable node X s The steps to achieve the belief are: (4e) At the factor node The information vector and information from the variable η s Represented as joint information vector and the joint precision matrix in, (4f) For the joint precision matrix P prod Inverse to get the joint covariance K prod ; (4g) Through P pro d and η prod Calculate the joint mean vector m prod =P prod η prod ; (4h) Extraction prod and K prod The marginal mean vector m obtained by the marginal components of l and marginal covariance K l ; (4i) K l Singular value decomposition retains the first N largest singular values ​​and the corresponding singular vectors, and obtains a low-order matrix constrained to a rank of N. The inverse is obtained to obtain the reduced-dimensional marginal precision matrix P' jls =K l -1 ; (4j) Through P' jl and m l Calculate the information vector η' jl =P' jl m l ; (4k) Factor Nodes To the adjacent variable node X s ∈X Ij ∪X Oj The low-order information transmitted is η' j→s =η' jl and P' j→s =P' jl , update the variable node X s The Gaussian information parameter information vector η of the belief s for and precision P s for in Represents the variable node X s Adjacent factor nodes transmit information vector summation, Represents the variable node X s The precision matrices passed by adjacent factor nodes are summed; (4l) Calculate the information vector and the precision matrix The amount of change and judge Is it true? If so, get the posterior graph G ** ; Otherwise, execute step (4e).

9. The method according to claim 1, characterized in that: The estimated values ​​of the computational accelerator operation parameters described in step (5) The implementation steps are: (5a) In the prior sample set {X A n } 1≤n≤N Select the variable node X corresponding to the ancestor variable Z The corresponding samples constitute the ancestral sample set {X Z n } 1≤n≤N ; (5b) Based on the posterior graph G ** Query the variable node X corresponding to the ancestor variable Z The posterior belief b G** (X Z )=φ M (X Z ;m Z ,K Z ); (5c) Select the affine transformation T to minimize the Frobenius norm distance μ,T : where μ is the mean shift set to the posterior mean m Z , is a decentralized ancestral sample set, B is a column of N-dimensional unit vectors; (5d) Transform the prior sample set X through affine transformation T A Convert to posterior sample set (5e) According to the posterior sample set matrix Compute the estimated values ​​of the accelerator operating parameters The calculation formula is as follows: in, represents the beam state variable node X in the posterior sample ε Corresponding to a set of N samples, Represents the posterior graph G in the posterior sample ** The S variable nodes correspond to a set of N samples.

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