Method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping

Abstract

The application belongs to the technical field of the intersection of laser physics, strong field optics and computational physics, and discloses a multi-parameter coupled physical system analysis method based on spatial weight-position mapping, which comprises constructing a local parameter box and generating sample points, for each sample point, acquiring a spatial response field distribution and discretizing it into a two-dimensional discrete grid matrix, performing standardization processing on each grid point to obtain a standard response value, establishing a linear weighting model for each grid point to obtain an influence weight coefficient of each key control parameter on the grid point, generating a weight matrix and a parameter dominance spatial distribution map, identifying the key control parameter with the maximum absolute value of the influence weight in different spatial regions according to the distribution map, and determining the parameter adjustment direction and priority based on the positive and negative signs of the weights of the parameters. The application realizes quantitative visualization of the parameter dominant region under the condition of a small sample, and provides interpretable technical support for precise regulation and control of a multi-parameter physical system.

Description

Technical Field

[0001] This application belongs to the interdisciplinary field of laser physics, strong field optics and computational physics, specifically involving a method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping. Background Technology

[0002] In fields such as strong-field laser-matter interactions, radiation source design, and particle dynamics analysis, parameter sensitivity analysis is a core technical means to reveal physical mechanisms and optimize system performance. As laser technology develops towards ultra-intense and ultra-short lasers, system outputs (such as radiation angular distribution, plasma density distribution, and beam phase spatial distribution) exhibit increasingly complex spatial structure characteristics, making it difficult for traditional analysis methods to meet the needs of refined research and engineering optimization.

[0003] Currently, there are four main technical solutions for parameter analysis of spatially distributed outputs:

[0004] 1. Global Quantity Analysis Method: This method characterizes system performance using single global indicators such as maximum radiated power, total radiated power, and collimation angle. However, it only reflects the overall characteristics of the system and cannot pinpoint the local origins of spatial structures. It also cannot distinguish the differentiated influences of different parameters on different angular regions of the radiation field, and cannot decompose the individual contributions when multiple parameters are coupled.

[0005] 2. Full-parameter scanning method: This method involves high-density sampling calculations in the parameter space. The computational load increases exponentially with the number of parameters, requiring more than 100,000 simulations, making it completely impractical for engineering applications and unsuitable for high-dimensional, multi-parameter systems.

[0006] 3. Global Sensitivity Analysis Methods: Represented by the Sobol exponent method, this method calculates the contribution of parameters to the global output through variance decomposition. However, this method only yields a single numerical result and provides no spatial resolution information. If Sobol analysis is forcibly performed on each spatial pixel individually, the computational load will increase by 2-3 orders of magnitude, making it unsuitable for applications requiring local optimization, such as directional radiometric modulation.

[0007] 4. Machine Learning Alternative Models: This method replaces numerical simulation with trained neural networks. However, it requires massive amounts of training data, and the model is a black box, unable to establish a physical relationship between parameters and spatial structure, thus failing to reveal physical mechanisms. Furthermore, the prediction results are uncertain and cannot guide high-precision engineering optimization.

[0008] In summary, existing technologies generally suffer from three core defects: inability to spatially locate objects, explosive computational demands, and lack of physical interpretability. There is still no universal technical solution capable of achieving pixel-level spatial parameter-dominant quantitative analysis under small sample conditions. This common industry challenge has become a key bottleneck restricting the leap from "phenomenon observation" to "precise control" in the field of strong-field physics. Summary of the Invention

[0009] To address the aforementioned technical issues, this application provides a method for analyzing multi-parameter coupled physical systems based on spatial weight-location mapping. This method constructs a three-in-one analysis framework of sampling, modeling, and mapping. The local parameter spatial sparse sampling module, the pixel-by-pixel linear weighted modeling module, and the spatial weight-location mapping analysis module are organically combined and work collaboratively to achieve the spatial pixel-level parameter-dominant quantitative analysis function that cannot be achieved by existing technologies. This solves the technical problems of existing technologies being unable to achieve pixel-level parameter sensitivity analysis of spatial distribution fields, having low computational efficiency, and lacking physical interpretability. It enables quantitative visualization of parameter-dominant regions under small sample conditions, providing interpretable technical support for the precise control of multi-parameter physical systems.

[0010] To achieve the above objectives, this application employs the following technical solution:

[0011] This application presents a method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping, specifically including the following steps:

[0012] Step 1: Based on pre-simulation or pre-experimental data, determine the spatial output field distribution that affects the multi-parameter coupled physical system. Each key control parameter and its effective value range are defined to construct... 3D local parameter box ,in The effective range of the key control parameter is defined as the relative change in the local response value of the spatial output field distribution exceeding a preset threshold when the key control parameter changes within this effective range. The continuous interval, the preset threshold Based on the numerical noise level or experimental measurement error of the multi-parameter coupled physical system;

[0013] Step 2, the one constructed in step 1 3D local parameter box Endogenous generation Representative sample points;

[0014] Step 3: For each representative sample point, obtain the corresponding spatial response field distribution through numerical simulation or experimental measurement, and discretize the spatial response field distribution as follows: A two-dimensional discrete grid matrix;

[0015] Step 4, for Each grid point in a two-dimensional discrete grid matrix of Each response value is processed Standardization process yields representative sample points at grid points. Standard response value at ;

[0016] Step 5: Establish a linear weighted model with regularization constraints for each grid point, and use analytical solutions to obtain the influence weight coefficients of each key control parameter on the grid point. To improve the computational stability under small sample conditions, a linear weighted model with regularization constraints (such as ridge regression, LASSO regression, elastic net regression) can be preferred. The regularization parameter can be determined by cross-validation or preset based on empirical values ​​according to system characteristics. Arrange the influence weight coefficients of all grid points according to their spatial positions to generate a weight matrix for each key control parameter.

[0017] Step 6: Perform maximum absolute value normalization on the weight matrix generated in Step 5 to generate a parameter dominance spatial distribution map. Based on the generated parameter dominance spatial distribution map, identify the key control parameters that have the greatest impact on the absolute value of the weights in different spatial regions. Based on the enhancement or suppression effect represented by the positive or negative sign of the weights of each parameter, determine the parameter adjustment direction and priority for different spatial regions to guide the performance optimization of the physical system.

[0018] A further improvement in this application is that: Step 1 specifically involves: based on pre-simulation single-parameter scanning or physical mechanism analysis, selecting key control parameters that satisfy the significance criterion from the candidate control parameters of the multi-parameter coupled physical system, wherein the significance criterion is: for the first... After a disturbance is applied to one of the candidate control parameters at the reference operating point, the relative change in the response value of at least one local region in the spatial output field distribution exceeds a preset threshold. For each key control parameter, the effective value range of the key control parameter is determined by pre-simulation single-parameter scanning. The effective value range is defined as the range in which the relative change in the response value of at least one local region in the spatial output field distribution continuously exceeds a preset threshold when the key control parameter changes within that range. Continuous intervals;

[0019] Depend on The key control parameters and their effective value ranges constitute the key control parameters. 3D local parameter box :

[0020] ,

[0021] in, For the first One key control parameter, , These are the minimum and maximum values ​​of the effective range of the key control parameters, respectively.

[0022] A further improvement of this application is that, in step 2, the material constructed in step 1... 3D local parameter box The internal generation method employs one of the following: Latin hypercube sampling, uniform design sampling, or sparse grid sampling. Representative sample points, among which .

[0023] A further improvement in this application is that step 3 specifically includes the following steps:

[0024] Step 3.1: For each representative sample point, obtain the corresponding spatial response field distribution through numerical simulation or experimental measurement, characterized as follows:

[0025] ,

[0026] in, For physical space coordinates, A vector of key control parameters. , For transpose;

[0027] Step 3.2: Characterize the spatial response field distribution Discretize into a two-dimensional discrete grid matrix:

[0028] ,

[0029] in, For grid height, For grid width, For the first Representative sample points at grid points The response value at that location.

[0030] A further improvement in this application is that step 4 specifically involves: […]. Each grid point in a two-dimensional discrete grid matrix of Each response value is processed Standardization process yields representative sample points at grid points. Standard response value at :

[0031] ,

[0032] in, For the first Representative sample points at grid points The response value at that location, For grid points The mean response across all samples. For grid points The standard deviation of the response.

[0033] A further improvement of this application is that, in step 5, when the linear weighted model with regularization constraints is adopted, the weight coefficient at the grid point is solved analytically using the following solution:

[0034] ,

[0035] in, For this grid point The standardized response vector at that point, To design the matrix, The standardized parameter matrix, For regularization parameters, regularization parameters according to The method of cross-validation can be used to determine the value, or it can be pre-set based on empirical values. for An identity matrix of order 1;

[0036] Linear weighted models with regularization constraints include ridge regression, LASSO regression, or elastic net regression.

[0037] When the ridge regression model is used, the weight coefficients are solved by the following objective function:

[0038] ,

[0039] When the LASSO regression model is used, the weight coefficients are solved using the following objective function:

[0040] ,

[0041] When using an elastic network regression model, the weight coefficients are solved using the following objective function:

[0042] ,

[0043] in, The weight coefficient vector obtained by solving the above objective function has the following components. For the first Key control parameters at grid points The influence weight coefficient at the location, and It shares the same technical feature as the aforementioned influence weighting coefficient;

[0044] Generate the weight matrix for each key control parameter:

[0045] .

[0046] A further improvement in this application is that step 6 specifically includes the following steps:

[0047] Step 6.1: Perform maximum absolute value normalization on the weight matrix of each key control parameter:

[0048] ,

[0049] The mapping relationship between the grid and physical space coordinates is as follows:

[0050] ,

[0051] in, and The mapping function from grid coordinates to physical space coordinates is used to transform grid coordinates to physical space coordinates. The normalized weight values ​​are used as color values ​​to draw a heat map on the physical coordinate plane and generate a parameter-dominant spatial distribution map.

[0052] Step 6.2: Based on the generated parameter dominance spatial distribution map, for any spatial region, compare the absolute values ​​of the weights of all key control parameters in that spatial region. The parameter with the largest absolute weight value is the dominant control parameter for that region. A positive weight indicates that increasing the dominant control parameter can enhance the response of that region, while a negative weight indicates that decreasing the dominant control parameter can suppress the response of that region.

[0053] This application provides a multi-parameter coupled physical system based on spatial weight-position mapping, the multi-parameter coupled physical system analysis system comprising:

[0054] Data acquisition unit: used to acquire the spatial response field distribution corresponding to different control representative sample points, and discretize the spatial response field distribution into a two-dimensional discrete grid matrix;

[0055] Local parameter spatial sparse sampling module: Communicatively connected to the data acquisition unit, used to determine the multi-parameter coupled physical system to be analyzed. Constructing key control parameters and their effective value ranges. A local parameter box is generated, and sparse uniform sampling is used within the local parameter box. A representative sample point is sent to the data acquisition unit.

[0056] Pixel-wise linear weighted modeling module: It is communicatively connected to the data acquisition unit and the local parameter space sparse sampling module, runs on a GPU accelerator card or FPGA chip, and is used to realize real-time calculation. It is used to standardize the response value of each grid point in the two-dimensional discrete grid matrix, and to establish a local linear weighted model with regularization constraints for each grid point, and solve for the influence weight coefficient of each key control parameter on the grid point.

[0057] Spatial weight-location mapping analysis module: Communicatively connected to the pixel-by-pixel linear weighted modeling module, used to arrange the influence weight coefficients of all grid points according to their spatial location to generate a weight matrix, normalize the weight matrix and generate a parameter-dominant spatial distribution map through physical coordinate mapping, and identify the dominant control parameters and parameter adjustment directions of different spatial regions based on the parameter-dominant spatial distribution map, and output the system optimization scheme.

[0058] A further improvement of this application is that the multi-parameter coupled physical system includes, but is not limited to, any one of the following: nonlinear Thomson scattering system, laser-plasma interaction system, laser-solid target interaction system, terahertz radiation generation system, or particle accelerator system.

[0059] The beneficial effects of this application are:

[0060] The pixel-wise linear weighted modeling module of this application adopts a GPU or FPGA hardware acceleration architecture. Utilizing its parallel computing characteristics, it can simultaneously process regression calculation tasks of thousands of grid points, improving computational efficiency by two orders of magnitude: the sample size is reduced from more than 1,000 in traditional full scan to 10-20, and the computation time is reduced from more than 40 GPU hours to less than 1 GPU hour. For the first time, it realizes fast spatial sensitivity analysis of multi-parameter systems.

[0061] This application achieves pixel-level spatial resolution for the first time: it can locate the parameter dominance of a single angle or pixel, which solves the fundamental defect of existing technologies that can only obtain global indicators;

[0062] This application is fully physically interpretable: the weight coefficients of the linear model directly correspond to the physical effects of the parameters, thus avoiding the black box problem of machine learning;

[0063] This application is highly versatile: it does not depend on a specific physical system and can be directly transferred to all multi-parameter coupled systems with spatially distributed output;

[0064] This application has the potential for real-time control: due to its extremely small computational load, it can be integrated into the online feedback system of high repetition rate laser facilities to achieve real-time adaptive adjustment of radiation source parameters.

[0065] This application utilizes a GPU / FPGA hardware acceleration architecture to increase the computational speed of pixel-by-pixel parameter sensitivity analysis by three orders of magnitude, achieving a leap from offline analysis to real-time control. This hardware system can be directly integrated into the online feedback control system of a high-repetition-rate laser device, enabling adaptive adjustment of radiation source parameters with a response time of less than one second, thus meeting the urgent need for dynamic control in strong-field physics experiments. Attached Figure Description

[0066] Figure 1 This is a schematic diagram of the multi-parameter coupled physical system of this application.

[0067] Figure 2 This is a schematic diagram of the application.

[0068] Figure 3 This is a schematic diagram of a nonlinear Thomson forward scattering (NTFS) system.

[0069] Figure 4 This is a schematic diagram of the spatial distribution of the dominant parameters generated by the method of this application.

[0070] Figure 5 This is a schematic diagram of the parameter-dominated spatial distribution when sparse grid sampling and ordinary linear regression modeling are used, and the system parameters are kept the same as in Example 1.

[0071] Figure 6 They are different A schematic diagram of the dominant spatial distribution of parameters within the sampling interval. Detailed Implementation

[0072] The embodiments of this application will be disclosed below with reference to the drawings. For clarity, many practical details will be described in the following description. However, it should be understood that these practical details should not be used to limit this application. That is, in some embodiments of this application, these practical details are not necessary. In addition, for the sake of simplicity, some conventional structures and components will be shown in the drawings in a simple schematic manner.

[0073] The analytical method presented in this application is particularly suitable for engineering and scientific research scenarios that require spatially resolved parameter-driven quantitative analysis, such as nonlinear Thomson scattering radiation modulation, laser-driven X / γ-ray source optimization, plasma physics evolution analysis, and particle accelerator beam tuning.

[0074] like Figure 1 As shown, this application provides a multi-parameter coupled physical system analysis system based on spatial weight-position mapping, the multi-parameter coupled physical system analysis system comprising:

[0075] Data acquisition unit: used to acquire the spatial response field distribution corresponding to different control representative sample points, and discretize the spatial response field distribution into a two-dimensional discrete grid matrix;

[0076] Local parameter spatial sparse sampling module: Communicatively connected to the data acquisition unit, used to determine the multi-parameter coupled physical system to be analyzed. Constructing key control parameters and their effective value ranges. A local parameter box is generated, and sparse uniform sampling is used within the local parameter box. A representative sample point is sent to the data acquisition unit.

[0077] Pixel-wise linear weighted modeling module: It is communicatively connected to the data acquisition unit and the local parameter space sparse sampling module, runs on a GPU accelerator card or FPGA chip, and is used to realize real-time calculation. It is used to standardize the response value of each grid point in the two-dimensional discrete grid matrix, and to establish a local linear weighted model with regularization constraints for each grid point, and solve for the influence weight coefficient of each key control parameter on the grid point.

[0078] Spatial weight-location mapping analysis module: Communicatively connected to the pixel-by-pixel linear weighted modeling module, used to arrange the influence weight coefficients of all grid points according to their spatial location to generate a weight matrix, normalize the weight matrix and generate a parameter-dominant spatial distribution map through physical coordinate mapping, and identify the dominant control parameters and parameter adjustment directions of different spatial regions based on the parameter-dominant spatial distribution map, and output the system optimization scheme.

[0079] The multi-parameter coupled physical systems of this application include, but are not limited to, any one of the following: nonlinear Thomson scattering systems, laser-plasma interaction systems, laser-solid target interaction systems, terahertz radiation generation systems, or particle accelerator systems.

[0080] like Figure 2 As shown, this application is a method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping. The method specifically includes the following steps:

[0081] Step 1: Based on pre-simulation or pre-experimental data, determine the spatial output field distribution that affects the multi-parameter coupled physical system. Each key control parameter and its effective value range are defined to construct... 3D local parameter box ,in The effective range of the key control parameter is defined as the relative change in the local response value of the spatial output field distribution exceeding a preset threshold when the key control parameter changes within this effective range. The continuous interval, the preset threshold The numerical noise level or experimental measurement error of the multi-parameter coupled physical system is predetermined. Step 1 specifically involves: based on pre-simulation single-parameter scanning or physical mechanism analysis, selecting key control parameters that meet the significance criterion from the candidate control parameters of the multi-parameter coupled physical system. The significance criterion is: for the first... After a disturbance is applied to one of the candidate control parameters at the reference operating point, the relative change in the response value of at least one local region in the spatial output field distribution exceeds a preset threshold. For each key control parameter, the effective value range of the key control parameter is determined by pre-simulation single-parameter scanning. The effective value range is defined as the range in which the relative change in the response value of at least one local region in the spatial output field distribution continuously exceeds a preset threshold when the key control parameter changes within that range. Continuous intervals;

[0082] Depend on The key control parameters and their effective value ranges constitute the key control parameters. 3D local parameter box :

[0083] ,

[0084] in, For the first One key control parameter, , These are the minimum and maximum values ​​of the effective range of the key control parameters, respectively.

[0085] Step 2, the one constructed in step 1 3D local parameter box The internal generation method employs one of the following: Latin hypercube sampling, uniform design sampling, or sparse grid sampling. Representative sample points, among which To minimize computational cost while ensuring representativeness of the samples;

[0086] Step 3: For each representative sample point, obtain the corresponding spatial response field distribution through numerical simulation or experimental measurement, and discretize the spatial response field distribution as follows: The two-dimensional discrete grid matrix is ​​obtained by the following steps:

[0087] Step 3.1: For each representative sample point, obtain the corresponding spatial response field distribution through numerical simulation or experimental measurement, characterized as follows:

[0088] ,

[0089] in, For physical space coordinates, A vector of key control parameters. , For transpose;

[0090] Step 3.2: Characterize the spatial response field distribution Discretize into a two-dimensional discrete grid matrix:

[0091] ,

[0092] in, For grid height, For grid width, For the first Representative sample points at grid points The response value at that location.

[0093] Step 4, for Each grid point in a two-dimensional discrete grid matrix of Each response value is processed Standardization process yields representative sample points at grid points. Standard response value at :

[0094] ,

[0095] in, For the first Representative sample points at grid points The response value at that location, For grid points The mean response across all samples. For grid points The standard deviation of the response.

[0096] Step 5: Establish a linear weighted model with regularization constraints for each grid point, and use analytical solutions to obtain the influence weight coefficients of each key control parameter on the grid point. To improve the computational stability under small sample conditions, linear weighted models with regularization constraints, such as ridge regression, LASSO regression, and elastic net regression, can be preferred. The regularization parameter can be determined by cross-validation or preset based on empirical values ​​according to system characteristics. Arrange the influence weight coefficients of all grid points according to their spatial positions to generate the weight matrix of each key control parameter.

[0097] In step 5, the linear weighted model with regularization constraints includes the ridge regression model, the LASSO regression model, or the elastic net regression model.

[0098] When using the linear weighted model with regularization constraints, the weight coefficients at this grid point are solved analytically as follows:

[0099] ,

[0100] in, For this grid point The standardized response vector at that point, To design the matrix, The standardized parameter matrix, For regularization parameters, regularization parameters according to The method of cross-validation can be used to determine the value, or it can be pre-set based on empirical values. for An identity matrix of order 1;

[0101] When the ridge regression model is used, the weight coefficients are solved by the following objective function:

[0102] ,

[0103] When the LASSO regression model is used, the weight coefficients are solved using the following objective function:

[0104] ,

[0105] When using an elastic network regression model, the weight coefficients are solved using the following objective function:

[0106] ,

[0107] in, The weight coefficient vector obtained by solving the above objective function has the following components. For the first Key control parameters at grid points The influence weight coefficient at the location, and It shares the same technical feature as the aforementioned influence weighting coefficient;

[0108] Generate the weight matrix for each key control parameter:

[0109] .

[0110] Step 6: Perform maximum absolute value normalization on the weight matrix generated in Step 5 to generate a parameter dominance spatial distribution map. Based on the generated parameter dominance spatial distribution map, identify the key control parameters that have the greatest impact on the absolute value of the weights in different spatial regions. Based on the enhancement or suppression effect represented by the positive or negative sign of each parameter's weight, determine the parameter adjustment direction and priority for different spatial regions to guide the performance optimization of the physical system. Based on the above identification results, determine the parameter adjustment direction and priority for different spatial regions to guide system performance optimization, including but not limited to: targeted enhancement of the response in specific regions, suppression of the spatial structure in unfavorable regions, or achieving coordinated parameter adjustment under multi-objective constraints. Specifically, this includes the following steps:

[0111] Step 6.1: Perform maximum absolute value normalization on the weight matrix of each key control parameter:

[0112] ,

[0113] The mapping relationship between the grid and physical space coordinates is as follows:

[0114] ,

[0115] in, and The mapping function from grid coordinates to physical space coordinates is used to transform grid coordinates to physical space coordinates. The normalized weight values ​​are used as color values ​​to draw a heat map on the physical coordinate plane and generate a parameter-dominant spatial distribution map.

[0116] Step 6.2: Based on the generated parameter dominance spatial distribution map, for any spatial region, compare the absolute values ​​of the weights of all key control parameters in that spatial region. The parameter with the largest absolute weight value is the dominant control parameter for that region. A positive weight indicates that increasing the dominant control parameter can enhance the response of that region, while a negative weight indicates that decreasing the dominant control parameter can suppress the response of that region.

[0117] The standard approach uses LHS sampling and ridge regression modeling.

[0118] To illustrate the implementation process of this application in detail, this embodiment uses a nonlinear Thomson forward scattering (NTFS) system as an example.

[0119] System Description:

[0120] like Figure 3 As shown, the initially stationary single electron is located at the origin of the Cartesian coordinate system. The system includes [a series of electrons] along [the coordinate system]. A Gaussian ellipticized laser pulse propagating in a specific direction, with a wavelength of... Normalized amplitude pulse width =5 Corresponding strength and the static linear magnetic field along the laser propagation direction. Electrons undergo relativistic motion under the influence of a composite field, producing nonlinear Thomson scattering radiation.

[0121] The three core control parameters are: magnetic field strength : Range of values Laser beam waist radius : Range of values Laser elliptic polarization The spatial output of the system, ranging from 0.6 to 0.9, is the angular distribution of the radiated power. Discretized into a 361×361 grid Specifically, the steps include the following:

[0122] S1: Construct a local parameter box and select a representative parameter range through pre-simulation: , , ;

[0123] S2: Ten uniformly distributed sample points are generated using Latin hypercube sampling (LHS);

[0124] S3: For each sample point, solve the electron relativistic dynamics equations using the 8th-9th order Runge-Kutta method, and then use the Liénard-Wiechert formula to calculate the far-field radiated power angular distribution, resulting in 10 361×361 response matrices.

[0125] S4: Perform processing on the 10 response values ​​for each angle grid point. Standardized processing:

[0126] S5: Build a ridge regression model for each grid point, and set the regularization parameter. (Determined through 5-fold cross-validation), the solution is obtained. The weighting coefficients of the three parameters;

[0127] The general expression for the locally linearly weighted model is: in: For control parameter vectors; For bias terms; For the first Each control parameter affects the grid points. The influence weights are represented by their absolute values, indicating the degree of influence, with positive or negative signs indicating enhancement or inhibition. To improve computational stability under small sample conditions, ridge regression with L2 regularization is used to solve for the weight coefficients. The general objective function is: Its analytical solution is: in: This is the standardized response vector of the grid point; To design the matrix, The standardized parameter matrix; This is the regularization parameter (recommended value: 0.1-0.2, determined through 5-fold cross-validation). for An identity matrix of order 1.

[0128] S6: Arrange the weight coefficients according to their spatial position to generate a weight matrix with three parameters;

[0129] S7: Employ maximum absolute value normalization: The weight matrix is ​​normalized to the [-1,1] interval to generate a parameter dominance spatial distribution map, such as... Figure 2 As shown.

[0130] Results analysis:

[0131] like Figure 4 As shown: Figure 4 b1 in The weighting plot shows a clear concentric ring distribution, with the positive weights corresponding perfectly to the peak values ​​of the radiation rings, indicating that the magnetic field dominates the contrast of the radiation ring structure. Figure 4 b2 in Weighted graph The high-weight regions are concentrated in the forward small corner region. This indicates that the waist radius dominates the collimation of forward radiation; Figure 4 b3 in The weighted graph shows obvious Axisymmetric distribution, highly sensitive areas are concentrated and The proximity indicates that the degree of polarization dominates the asymmetry of the azimuth direction.

[0132] The results are in complete agreement with the physical mechanism, demonstrating the accuracy and physical interpretability of the method presented in this application.

[0133] This embodiment uses sparse grid sampling and ordinary linear regression modeling, and compares different sampling and modeling methods.

[0134] In this embodiment, the system parameters remain the same as in Embodiment 1, only the following are replaced:

[0135] Sampling method: A 3×3×3 sparse grid was used for sampling, resulting in a total of 27 sample points;

[0136] Modeling method: Ordinary least squares linear regression is used, without regularization constraints.

[0137] Comparison results:

[0138] like Figure 5 As shown, the parameter dominance distribution diagrams obtained from the two schemes are basically the same, with the key feature being... ring structure, Forward concentration, of The axisymmetric properties match perfectly.

[0139] Comparative conclusion: The analytical framework of this application has high versatility and stability, and does not depend on specific sampling or modeling algorithms.

[0140] The dominant evolution of parameters under different degrees of elliptic polarization:

[0141] This embodiment verifies the applicability of this application under different physical regimes. (Selecting...) The analysis was performed on the three intervals [0.85, 0.90] and [0.95, 1.00], and the results are as follows: Figure 6 As shown.

[0142] The results show that, with Increase (approaching circular polarization). The weight gradually decreases, while and The weight distribution maintains its basic characteristics and is completely consistent with physical laws, proving that the method in this application has good robustness under different parameter regimes.

[0143] Hardware implementation examples:

[0144] This embodiment details the hardware implementation of the analysis system of this application, including two schemes: GPU acceleration and FPGA hardware implementation.

[0145] 1. GPU acceleration implementation scheme:

[0146] The NVIDIA A100 GPU is used as the computing core, and pixel-by-pixel parallel computation is achieved using the CUDA programming model. The specific implementation steps are as follows:

[0147] (1) Data preprocessing stage: indivual The response matrix and the standardized parameter matrix are copied from CPU memory to GPU global memory;

[0148] (2) Parallel computing phase: Startup Each CUDA thread independently processes a ridge regression calculation for one grid point. Each thread block contains 256 threads to fully utilize the GPU's SM (Streaming Multiprocessor) resources.

[0149] (3) Weight matrix generation stage: Assemble the weight coefficients calculated by all threads according to their spatial positions. indivual The weight matrix is ​​copied from GPU global memory back to CPU memory;

[0150] (4) Visualization and analysis stage: The normalization of the weight matrix and the generation of the parameter dominance spatial distribution map are completed on the CPU.

[0151] Performance test results show that for a 361×361 grid and 10 sample points, the computation time after GPU acceleration is about 0.8 seconds, which is about 1200 times faster than CPU single-core computation.

[0152] 2. FPGA hardware implementation scheme:

[0153] The ridge regression algorithm is hardware-based using a Xilinx Kintex UltraScale+ FPGA chip and a High-Level Synthesis (HLS) tool. The specific architecture is as follows:

[0154] (1) Input interface module: Receives response matrix data and parameter matrix data from the data acquisition unit through the PCIe 3.0 interface;

[0155] (2) Data caching module: Uses on-chip BRAM to store the response values ​​and parameter values ​​required for the current calculation;

[0156] (3) Linear regression solver module: It adopts a pipelined structure to realize matrix multiplication and matrix inversion operations, and can complete the weight coefficient calculation of one grid point in each clock cycle;

[0157] (4) Output interface module: The calculated weight coefficients are sent to the spatial weight-location mapping analysis module through the PCIe interface.

[0158] The FPGA implementation has a latency of approximately 10 microseconds per grid point and consumes only 1 / 10 the power of a GPU, making it particularly suitable for embedded and low-power applications.

[0159] 3. Inter-module communication methods:

[0160] The various modules of the system communicate with each other via Ethernet or PCIe interfaces.

[0161] The local parameter spatial sparse sampling module and the data acquisition unit transmit sample point parameters via Ethernet.

[0162] The data acquisition unit and the pixel-by-pixel linear weighted modeling module transmit response matrix data via a PCIe 3.0 interface, with a bandwidth of up to 8GB / s;

[0163] The pixel-wise linear weighted modeling module and the spatial weight-location mapping analysis module transmit the weight matrix number via a PCIe interface. This application presents a general spatial parameter sensitivity analysis framework that does not rely on the specific physical mechanisms of the NTFS system and can be directly transferred to various multi-parameter systems with spatially distributed outputs:

[0164] 1. Multi-electron plasma interaction system: Control parameters include laser intensity, plasma density, pulse length, etc., and spatial outputs include plasma density distribution, electron temperature distribution, radiation angle distribution, etc. This application can be used to analyze the local effects of various parameters on plasma evolution and radiation characteristics, and optimize the performance of laser fusion and plasma accelerators.

[0165] 2. Laser-solid interaction system: Control parameters include laser incident angle, target thickness, target composition, etc., and spatial output includes ion energy spectrum distribution, secondary electron emission distribution, X-ray radiation distribution, etc. This application can be used to improve ion acceleration efficiency and spatial uniformity of radiation dose.

[0166] 3. Terahertz radiation generation system: Control parameters include laser polarization, crystal orientation, pump power, etc., and the spatial output is the angular and spectral distribution of terahertz radiation. This application can be used to optimize the directionality and conversion efficiency of terahertz radiation.

[0167] 4. Particle accelerator system: Control parameters include magnet strength, radio frequency power, and initial beam parameters, while spatial outputs include beam phase spatial distribution, beam spot size, and emittance. This application can be used to rapidly optimize beam quality and shorten the accelerator commissioning cycle.

[0168] The above description is merely an embodiment of this application and is not intended to limit this application. Various modifications and variations can be made to this application by those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principle of this application should be included within the scope of the claims of this application.

Claims

1. A method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping, characterized in that: The multi-parameter coupled physics system is any one of a nonlinear Thomson scattering system, a laser-plasma interaction system, a laser-solid target interaction system, a terahertz radiation generation system, or a particle accelerator system. The analysis method for the multi-parameter coupled physics system specifically includes the following steps: Step 1: Based on pre-simulation or pre-experimental data, determine the spatial output field distribution that affects the multi-parameter coupled physical system. Each key control parameter and its effective value range are defined to construct... 3D local parameter box ,in ; Step 2, the one constructed in step 1 3D local parameter box Intrinsic generation Representative sample points; Step 3: For each representative sample point generated in Step 2, obtain the spatial response field distribution corresponding to each representative sample point through numerical simulation or experimental measurement, and discretize the spatial response field distribution as follows: A two-dimensional discrete grid matrix; Step 4, for Each grid point in a two-dimensional discrete grid matrix of Each response value is processed Standardization process yields representative sample points at grid points. Standard response value at ; Step 5: Establish a linear weighted model with regularization constraints for each grid point, and use analytical solutions to obtain the influence weight coefficient of each key control parameter on the grid point. Arrange the influence weight coefficients of all grid points according to their spatial location to generate the weight matrix of each key control parameter. Step 6: Perform maximum absolute value normalization on the weight matrix generated in Step 5 to generate a parameter dominance spatial distribution map. Based on the generated parameter dominance spatial distribution map, identify the key control parameters that have the greatest impact on the absolute value of the weights in different spatial regions. Based on the enhancement or suppression effect represented by the positive or negative sign of the weights of each key control parameter, determine the parameter adjustment direction and priority for different spatial regions to guide the performance optimization of the multi-parameter coupled physical system.

2. The method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping according to claim 1, characterized in that: Step 1 specifically involves: based on pre-simulation single-parameter scanning, selecting key control parameters that satisfy the significance criterion from the candidate control parameters of the multi-parameter coupled physical system. The significance criterion is: for the first... After a disturbance is applied to one of the candidate control parameters at the reference operating point, the relative change in the response value of at least one local region in the spatial output field distribution exceeds a preset threshold. For each key control parameter, the effective value range of the key control parameter is determined by pre-simulation single-parameter scanning. The effective value range is defined as the range in which the relative change in the response value of at least one local region in the spatial output field distribution continuously exceeds a preset threshold when the key control parameter changes within that range. Continuous intervals; Depend on The key control parameters and their effective value ranges constitute the key control parameters. 3D local parameter box : in, For the first One key control parameter, , These are the minimum and maximum values ​​of the effective range of the key control parameters, respectively.

3. The method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping according to claim 1, characterized in that: In step 2, the material constructed in step 1 3D local parameter box The internal generation method employs one of the following: Latin hypercube sampling, uniform design sampling, or sparse grid sampling. Representative sample points, among which .

4. The method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping according to claim 2, characterized in that: Step 3 specifically includes the following steps: Step 3.1: For each representative sample point, obtain the corresponding spatial response field distribution through numerical simulation or experimental measurement, characterized as follows: in, For physical space coordinates, A vector of key control parameters. , For transpose; Step 3.2: Characterize the spatial response field distribution Discretize into a two-dimensional discrete grid matrix: ， in, For grid height, For grid width, For the first Representative sample points at grid points The response value at that location.

5. The method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping according to claim 4, characterized in that: Step 4 specifically involves: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] Each grid point in a two-dimensional discrete grid matrix of Each response value is processed Standardization process yields representative sample points at grid points. Standard response value at : in, For the first Representative sample points at grid points The response value at that location, For grid points The mean response across all samples. For grid points The standard deviation of the response.

6. The method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping according to claim 5, characterized in that: In step 5, when the linear weighted model with regularization constraints is used, the weight coefficient at this grid point is solved analytically using the following solution: in, For this grid point The standardized response vector at that point, To design the matrix, The standardized parameter matrix, For regularization parameters, for An identity matrix of order 1; Linear weighted models with regularization constraints include ridge regression, LASSO regression, or elastic net regression. When the ridge regression model is used, the weight coefficients are solved by the following objective function: When the LASSO regression model is used, the weight coefficients are solved using the following objective function: When using an elastic network regression model, the weight coefficients are solved using the following objective function: in, The weight coefficient vector obtained by solving the above objective function has the following components. For the first Key control parameters at grid points The influence weight coefficient at the location, and It shares the same technical feature as the aforementioned influence weighting coefficient; Generate the weight matrix for each key control parameter: 。 7. The method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping according to claim 6, characterized in that: Step 6 specifically includes the following steps: Step 6.1: Perform maximum absolute value normalization on the weight matrix of each key control parameter to obtain the normalized weight values. : The mapping relationship between the grid and physical space coordinates is as follows: in, and This is a mapping function from mesh coordinates to physical space coordinates. It uses a physical coordinate mapping function to transform mesh coordinates to physical space coordinates, and then uses normalized weight values. For color values, a heatmap is plotted on the physical space coordinate plane to generate a parameter-dominant spatial distribution map; Step 6.2: Based on the generated parameter dominance spatial distribution map, for any spatial region, compare the absolute values ​​of the weights of all key control parameters in that spatial region. The parameter with the largest absolute weight value is the dominant control parameter for that region. A positive weight indicates that increasing the dominant control parameter can enhance the response of that region, while a negative weight indicates that decreasing the dominant control parameter can suppress the response of that region.

8. The method for analyzing multi-parameter coupled physical systems based on spatial weight-position mapping according to claim 1, characterized in that: The multi-parameter coupled physical system analysis method is implemented through a multi-parameter coupled physical system analysis system, which includes: Data acquisition unit: used to acquire the spatial response field distribution corresponding to different control representative sample points, and discretize the spatial response field distribution into a two-dimensional discrete grid matrix; Local parameter spatial sparse sampling module: Communicatively connected to the data acquisition unit, used to determine the multi-parameter coupled physical system to be analyzed. Constructing key control parameters and their effective value ranges. Dimensional local parameter boxes, and generate within the local parameter boxes. A representative sample point is sent to the data acquisition unit. Pixel-wise linear weighted modeling module: It is communicatively connected to the data acquisition unit and the local parameter space sparse sampling module, runs on a GPU accelerator card or FPGA chip, and is used to realize real-time calculation. It is used to standardize the response value of each grid point in the two-dimensional discrete grid matrix, and to establish a local linear weighted model with regularization constraints for each grid point, and solve for the influence weight coefficient of each key control parameter on the grid point. Spatial weight-location mapping analysis module: Communicatively connected to the pixel-by-pixel linear weighted modeling module, used to arrange the influence weight coefficients of all grid points according to their spatial location to generate a weight matrix, normalize the weight matrix and generate a parameter-dominant spatial distribution map through physical coordinate mapping, and identify the dominant control parameters and parameter adjustment directions of different spatial regions based on the parameter-dominant spatial distribution map, and output the system optimization scheme.

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