Beam adjustment method for digital twin accelerator based on Gaussian ensemble belief propagation

Abstract

The present invention proposes a digital twin accelerator beam tuning method based on Gaussian ensemble belief propagation, and the implementation steps are as follows: initializing parameters; constructing a priori factor graph; generating a sample set and constructing a conditional graph; converting the variable nodes and factor nodes in the conditional graph and constructing a posterior graph; calculating the estimated values ​​of the accelerator operation parameters; and obtaining the accelerator beam tuning results. The present invention uses a near-low-order Gaussian matrix generated by a sample set for efficient calculations, and is capable of converting between set statistics, various parameterizations, and effective operations on these parameters. It samples from the generated prior, converts the set statistics into a standard form, performs belief propagation, recovers the set samples that match the updated belief, improves the accuracy of the beam tuning, and transmits low-rank local information on the conditional graph to update the ensemble, so that it can handle complex dependency structures and high-dimensional states and parameters, thereby improving the efficiency of the accelerator beam tuning process.

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 artificially accelerate charged particles of various types to high energies using various forms of electric fields. Particle accelerators play a vital role in basic scientific research, medical treatment, and materials processing.

[0003] Particle accelerator beam tuning refers to the process of adjusting and optimizing various parameters of the particle beam within the accelerator to meet 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 compromising accelerator safety and stability, thereby increasing the overall output efficiency of the accelerator.

[0004] Digital twin technology uses computer simulation to precisely replicate physical systems in digital space. The fundamental principle of digital twin accelerator beam tuning is to digitally model a real particle accelerator, simulate its operating status and performance, and perform virtual beam tuning based on real-time sensor data. The simulation results are then used to adjust the actual accelerator's parameters.

[0005] Existing digital twin accelerator beam tuning methods implement the following steps: collect real-time operating data from the digital twin accelerator to construct a dataset; use the collected dataset to calibrate the digital twin model in a data-driven manner; and then use nonlinear least squares to find the optimal operating parameters on the calibrated digital twin model so that the output meets the desired beam characteristics. This method uses digital twin technology and nonlinear least squares to find the most likely operating parameters given a given beam distribution. However, the YAG images generated by actual accelerators contain complex components (such as annular structures at the edges), and the size, shape, and position of the beam spot vary significantly. Errors may occur during image data preprocessing and alignment, affecting the accuracy of the beam tuning results. The nonlinear least squares method requires the calculation of the Jacobian matrix or Hessian matrix at each step, involving matrix inversion operations, resulting in high computational complexity. The computational cost increases dramatically, especially for high-dimensional parameter spaces or large datasets. 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 tuning 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 generation process set is P = {P j} 1≤j≤J , the accelerator beam tuning target parameter value 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] Construct a variable X for each run d and X d The prior distribution p(X d ) is a variable node, and each generating equation P j Factor is a factor node, with X d and The lines between them are the edge prior factor graph G, 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 value of the sampling 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, the factor node adjacent to the variable node X corresponding to the beam state variable is constructed.

[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, Indicates the calculated value of the dth remaining variable node for the oth time, represents the parameter set consisting of 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 adopts 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;

[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 is transformed by T A Convert to 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] Run the accelerator to estimate the parameter values Load the preset parameters into the digital twin accelerator 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 operation parameter estimates, uses a near-low-order Gaussian matrix generated by the sample set for efficient calculations, and can convert between set statistics, various parameterizations, and effective operations on these parameters. It can sample from the generated prior, convert the set statistics to a standard form, perform belief propagation, and recover a posterior sample set with matching beliefs, thereby reducing errors that may occur during data acquisition 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, thereby improving 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 with reference to 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 accelerator beam tuning target parameter value 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, device 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 device 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 ancestral variable;

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

[0033] Construct a variable X for each run d and X d The prior distribution p(X d ) is a variable node, and each generating equation P j Factor is a factor node, with X d and The lines between them are the edge prior factor graph G, 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 them. The prior distribution is set for the variables based on 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 value of the sampling 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, the factor node adjacent to the variable node X corresponding to the beam state variable is constructed.

[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, Indicates the calculated value of the dth remaining variable node for the oth time, represents the parameter set consisting of D operating parameter values ​​after the oth sampling and calculation,

[0038] On the prior factor graph, according to the prior distribution of the variable nodes, the variable nodes corresponding to the ancestral variables are sampled to obtain the 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 a factor graph, X ε The observed value will affect the factor node directly connected to it. After the factor node is fixed by the observed value, the dimension of the original factor is reduced. Conditioned into factor nodes, in this way, constructing a conditional graph can effectively reduce 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 adopts 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;

[0046] Due to the properties of the 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 * 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 mean m of the corresponding sample 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 the element of σ 2 The diagonal matrix of , Y represents the sample set consisting of samples corresponding to another variable node;

[0053] Step 4b) Calculate X s Information η 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 is the 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;

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

[0055] Step 4d) Calculate factor nodes 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 precision of u jl The precision matrix of the remaining variables in the factor node 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] Adopt low-order information propagation algorithm 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 Expressed 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 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 corresponding singular vectors, and obtains a low-order matrix constrained to a rank of N. The inverse is obtained to obtain the marginal precision matrix P′ after dimensionality reduction 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 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;

[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 operating 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 is transformed by T A Convert to 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 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 composed of row vectors, 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 term, set to σ 2 I, Assumption Combining the Gaussian belief propagation algorithm with the integrated Kalman filter method, we can get the following inferences:

[0072]

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

[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 estimated values ​​of 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 results:

[0084] Run the accelerator to estimate the parameter values 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 tuning 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 accelerator beam tuning target parameter value 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: Construct a variable X for each run d and X d The prior distribution p(X d ) is a variable node, and each generating equation P j Factor is a factor node, with X d and The lines between them are the edge prior factor graph G, 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 value of the sampling 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, the variable node X corresponding to the beam state variable is constructed 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, Indicates the calculated value of the dth remaining variable node for the oth time, represents the parameter set consisting of 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 adopts 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; (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 is transformed by T A Convert to 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: Run the accelerator to estimate the parameter values Load the preset parameters into the digital twin accelerator 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 adjustment 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; The device 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 in step (1) is as follows: j } 1≤j≤J The generated process set is to describe the coupling between the main bending magnet current and the beam energy, describe the coupling between the bending magnet current and the beam center position, describe the coupling between the quadrupole magnet gradient and the beam emittance, describe the coupling between the quadrupole magnet gradient and the beam stability, describe the coupling between the sextupole magnet gradient and the beam brightness, describe the coupling between the sextupole magnet gradient and the energy distribution, describe the coupling between the RF frequency and the beam energy, describe the coupling between the RF frequency and the beam stability, describe the coupling between the acceleration voltage and the energy distribution, describe the coupling between the acceleration voltage and the beam transmission efficiency, describe the coupling between 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 are described; 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, wherein 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, wherein Each parameter set described in step (3) Contribution index to accelerator boundary The calculation formula is: 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.

6. The method according to claim 1, wherein 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) * 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 mean m of the corresponding sample 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 the element of σ 2 The diagonal matrix of , Y represents the sample set consisting of samples corresponding to another variable node; (4b) Calculate X s Information η s =P s ·m s and precision P s =K s -1 , 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 is the 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; (4c) Combining Gaussian belief propagation algorithm with integrated Kalman filter to transform the conditional graph G * Neutral Factor Node Set as factor neighborhood Set X j The empirical distribution of in, Indicates the mean Covariance is Var V X j Gaussian density moment of (4d) Calculation Factor Node 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 precision of u jl The precision matrix of the remaining variables in the factor node 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 Expressed 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 of m prod and K prod The marginal mean vector m obtained by the marginal components of l and marginal covariance K l ; (4i) K l The singular value decomposition retains the first N largest singular values ​​and the corresponding singular vectors, and the result is a low-order matrix constrained to a rank of N. The inverse is used 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 estimated values ​​of 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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