Application Method and System for Intelligent Electromagnetic Simulation Data

Abstract

The present invention discloses an application method and system for intelligent electromagnetic simulation data, relating to the technical field of data processing. The method described includes: Step 1: Construct a virtual mirror electromagnetic space of a multi-source electromagnetic space; in the virtual mirror electromagnetic space, calculate the difference between the eigen-decomposition result and the simulation eigen-decomposition result; Step 2: Place a test object in the multi-source electromagnetic space, and with the center of the test object as the center, set multiple layers of electromagnetic scattering interfaces around the test object; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space according to the electromagnetic scattering characteristics; Step 3: Calculate the spatio-temporal electromagnetic field tensor corrected at each time and each position in the multi-source electromagnetic space. The present invention generates a high-precision spatio-temporal electromagnetic field tensor through technologies such as constructing a virtual mirror electromagnetic space, eigen-decomposition correction, and multi-layer interface propagation modeling.

Description

Technical Field

[0001] The present invention relates to the technical field of data processing, and particularly to an application method and system for intelligent electromagnetic simulation data. Background Art

[0002] The dynamic distribution characteristics of electromagnetic fields are the core content of research in the field of modern electromagnetic technology, involving multiple directions such as communication, radar, electronic countermeasure, radio wave propagation, antenna design, and imaging. Especially in a complex multi-source electromagnetic environment, the distribution of electromagnetic fields is not only affected by the characteristics of field sources but also jointly restricted by the spatial environment, medium properties, and the interaction between field sources. Therefore, how to accurately describe and dynamically update the spatio-temporal distribution of electromagnetic fields, and then obtain a spatio-temporal electromagnetic field tensor that can uniformly characterize the spatial position and time evolution law, has become a key scientific issue in electromagnetic simulation and optimization. However, the existing technologies have obvious deficiencies in computing efficiency, accuracy, and dynamic adaptability, and cannot meet the requirements of complex application scenarios.

[0003] Currently, the methods for describing the spatio-temporal distribution of electromagnetic fields mainly use numerical calculation methods based on physical modeling. The numerical calculation methods based on physical modeling rely on solving the basic theoretical models of electromagnetic fields, such as Maxwell's equations, and combine specific numerical algorithms to simulate the distribution of electromagnetic fields. Typical methods include the finite element method (FEM), the finite-difference time-domain method (FDTD), and the multilevel fast multipole method (MLFMM). The finite element method (FEM) discretizes the electromagnetic field space, divides the continuous medium into finite small elements, and uses the variational method to solve the distribution of the electric and magnetic fields. This method has high accuracy in regular geometric shapes and homogeneous media, but when dealing with complex geometric structures or multi-source field environments, it is necessary to refine the grid, resulting in a significant increase in computational complexity. The finite-difference time-domain method (FDTD) directly performs numerical solutions to Maxwell's equations in the time domain and can describe the time evolution law of electromagnetic fields. However, the FDTD method is limited by the grid size in terms of spatial resolution, and the computational efficiency drops sharply with the increase in the number of field sources and spatial complexity. In addition, for high-frequency electromagnetic waves or long-time simulations, the limitation of the time step further aggravates the computational burden. The multilevel fast multipole method (MLFMM) reduces the spatial complexity of calculations through the multipole expansion of electromagnetic fields. This method has good computational efficiency for the far-field propagation of a single field source, but still faces limitations in the scattering calculations of multi-field sources and complex media. Summary of the Invention

[0004] In view of this, the present invention provides a method and system for applying intelligent electromagnetic simulation data. By constructing a virtual mirror electromagnetic space, eigen-decomposition correction, multi-layer interface propagation modeling and other technologies, a high-precision spatio-temporal electromagnetic field tensor is generated. This tensor realizes the unified description of the spatial distribution and temporal evolution law of the electromagnetic field in a complex multi-source electromagnetic environment, and significantly improves the simulation accuracy through a dynamic correction mechanism. Compared with the prior art, the present invention overcomes problems such as non-linear coupling of multi-source fields, poor adaptability to dynamic changing environments, and insufficient spatio-temporal consistency.

[0005] The technical solution adopted by the present invention is as follows:

[0006] A method for applying intelligent electromagnetic simulation data, the method comprising:

[0007] Step 1: Construct a virtual mirror electromagnetic space of a multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate mirror electromagnetic field sources corresponding one by one to each electromagnetic field source in the multi-source electromagnetic space; obtain the electromagnetic field components generated by the electromagnetic field sources at each sampling point at each time in the multi-source electromagnetic space, and construct a spatio-temporal electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct a corresponding simulated spatio-temporal electromagnetic field tensor in the virtual mirror electromagnetic space; perform eigen-decomposition on the spatio-temporal electromagnetic field tensor and the simulated spatio-temporal electromagnetic field tensor respectively to obtain an eigen-decomposition result and a simulated eigen-decomposition result; calculate the difference between the eigen-decomposition result and the simulated eigen-decomposition result;

[0008] Step 2: Place a test object in the multi-source electromagnetic space, and around the center of the test object, set multiple layers of electromagnetic scattering interfaces, and the distance between each layer of electromagnetic scattering interface and the adjacent electromagnetic scattering interface is equal; calculate the electromagnetic scattering characteristics of the test object in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space according to the electromagnetic scattering characteristics.

[0009] Step 3: Calculate the corrected spatio-temporal electromagnetic field tensor at each time and each position in the multi-source electromagnetic space according to the difference between the eigen-decomposition result and the simulated eigen-decomposition result, and the interface propagation characteristic coefficient of the multi-source electromagnetic space.

[0010] Further, in step 1, the electromagnetic field components include: electric field, magnetic field and magnetic induction intensity.

[0011] Further, in step 1, the spatio-temporal electromagnetic field tensor is represented by the following formula.

[0012]

[0013] Wherein, represents the spatio-temporal electromagnetic field tensor at position at time t; N represents the number of electromagnetic field sources in the multi-source electromagnetic space; i is an integer subscript index; Vi represents the radiation spatial range of the i-th electromagnetic field source; V' is the spatial integration microelement; represents the position of the i-th electromagnetic field source at time t and the electric field generated in the X-axis direction at this position. represents the position of the i-th electromagnetic field source at time t and the electric field generated in the Y-axis direction at this position. represents the position of the i-th electromagnetic field source at time t and the electric field generated in the Z-axis direction at this position. represents the position of the i-th electromagnetic field source at time t and the magnetic field generated in the X-axis direction at this position. represents the position of the i-th electromagnetic field source at time t and the magnetic field generated in the Y-axis direction at this position. represents the position of the i-th electromagnetic field source at time t and the magnetic field generated in the Z-axis direction at this position. represents the position of the i-th electromagnetic field source at time t and the time rate of change of the magnetic induction intensity generated in the X-axis direction at this position. represents the position of the i-th electromagnetic field source at time t and the time rate of change of the magnetic induction intensity generated in the Y-axis direction at this position. represents the position of the i-th electromagnetic field source at time t and the time rate of change of the magnetic induction intensity generated in the Z-axis direction at this position. μ 0 is the vacuum magnetic permeability; j is the imaginary symbol; k is the wave number; assume that the corresponding simulation space-time electromagnetic field tensor is constructed in the virtual mirror electromagnetic space as

[0014] Furthermore, in step 1, the eigenvalue decomposition result Λ is obtained through the following formula EM :

[0015]

[0016] where assume has the dimension of m×n; U is an m×m orthogonal matrix; Σ is an m×n diagonal matrix; V is an n×n orthogonal matrix; T is the transpose operator; represents the divergence of the electric field at the position at time t. represents the divergence of the magnetic field at the position at time t. represents the curl of the electric field of the i-th electromagnetic field source at the position at time t. Denote the curl of the magnetic field at the position of the \(i\)-th electromagnetic field source at time \(t\). ; \(\|\cdot\|\) 2 Denote the calculation of the square of the modulus. Denote the variance of the divergence. Denote the variance of the curl; Let the simulation eigen - decomposition result be \(\Lambda\). SIM .

[0017] Furthermore, in step 1, calculate the difference \(\Delta\) between the eigen - decomposition result and the simulation eigen - decomposition result through the following formula: ES :

[0018]

[0019] where \(\|\cdot\|\) F is the Frobenius norm.

[0020] Furthermore, in step 2, calculate the electromagnetic scattering characteristics \(\sigma\) of the test object in the multi - source electromagnetic space through the following formula: RCS :

[0021]

[0022] where \(R\) is the distance from the surface of the test object; \(l\) is a surface distance threshold, which is a set value; is the scattered electric field generated by the \(i\) - th electromagnetic field source on the surface of the test object; is the incident electric field generated by the \(i\) - th electromagnetic field source on the surface of the test object; \(\in\) r is the relative permittivity corresponding to the test object; \(\mu\) r is the relative permeability corresponding to the test object; \(\alpha\) loss is the material loss coefficient of the test object, which is a set value; \(\theta\) i is the azimuth angle of the scattered electric field generated by the \(i\) - th electromagnetic field source on the surface of the test object; \(\beta\) i is the azimuth angle of the incident electric field generated by the \(i\) - th electromagnetic field source on the surface of the test object; \(\varphi\) i is the elevation angle of the scattered electric field generated by the \(i\) - th electromagnetic field source on the surface of the test object; \(\alpha\) i is the elevation angle of the incident electric field generated by the \(i\) - th electromagnetic field source on the surface of the test object; \(|\cdot|\) represents the determinant operation of the matrix.

[0023] Furthermore, in step 2, calculate the interface propagation characteristic coefficient of the multi - source electromagnetic space through the following formula:

[0024]

[0025] where \(M\) is the number of electromagnetic scattering interfaces; \(P\) iis the power of the i-th electromagnetic field source; D is the average distance from all electromagnetic field sources to the test object; d is the distance between the electromagnetic scattering interface and the adjacent electromagnetic scattering interface; α(s) is the attenuation function; k is an integer subscript index; Γ k is the interface scattering coefficient of the k-th electromagnetic scattering interface; s is the attenuation function variable, with a value range from 0 to d; ds is the integration element.

[0026] Furthermore, the attenuation function α(s) is an exponential attenuation function or a Gaussian attenuation function.

[0027] Furthermore, in step 3, through the following formula, calculate the corrected spatio-temporal electromagnetic field tensor at each time and each position in the multi-source electromagnetic space

[0028]

[0029] where represents the position is the average distance from all electromagnetic field sources.

[0030] An application system for intelligent electromagnetic simulation data, the system includes: a mirror simulation difference calculation part, used to construct a virtual mirror electromagnetic space of the multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate mirror electromagnetic field sources corresponding one by one to each electromagnetic field source in the multi-source electromagnetic space; obtain the electromagnetic field components generated by the electromagnetic field sources at each time and each sampling point in the multi-source electromagnetic space, and construct the spatio-temporal electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct the corresponding simulation spatio-temporal electromagnetic field tensor in the virtual mirror electromagnetic space; perform eigenvalue decomposition on the spatio-temporal electromagnetic field tensor and the simulation spatio-temporal electromagnetic field tensor respectively, and obtain the eigenvalue decomposition result and the simulation eigenvalue decomposition result respectively; calculate the difference between the eigenvalue decomposition result and the simulation eigenvalue decomposition result; a propagation characteristic calculation part, used to place a test object in the multi-source electromagnetic space, set multiple layers of electromagnetic scattering interfaces around the test object with the center of the test object, and the distance between each layer of electromagnetic scattering interface and the adjacent electromagnetic scattering interface is equal; calculate the electromagnetic scattering characteristics of the test object in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space according to the electromagnetic scattering characteristics; a correction part, used to calculate the corrected spatio-temporal electromagnetic field tensor at each time and each position in the multi-source electromagnetic space according to the difference between the eigenvalue decomposition result and the simulation eigenvalue decomposition result, and the interface propagation characteristic coefficient of the multi-source electromagnetic space.

[0031] Adopting the above technical solutions, the present invention has the following beneficial effects: By constructing a virtual mirror electromagnetic space and a space-time electromagnetic field tensor, the present invention successfully solves the problem of insufficient description of the multi-source field coupling effect in the prior art. A multi-source electromagnetic space usually has a complex field source distribution and dynamic space-time evolution characteristics. The traditional linear superposition model is difficult to reflect the non-linear interaction between field sources. However, the present invention generates mirror field sources corresponding to real field sources in the mirror space, and constructs a complete mapping relationship of the multi-source electromagnetic space based on the symmetry and equivalence of the mirror field. The introduction of this virtual mirror electromagnetic space not only reduces the difficulty of dealing with the non-linear complexity in the actual electromagnetic field environment, but also provides a more intuitive and mathematically rigorous tool for the coupling analysis of multi-source fields. Through mathematical modeling and optimization design, the present invention significantly improves the calculation efficiency of electromagnetic simulation data. The construction of the virtual mirror space reduces the calculation complexity of multi-source non-linear interaction, and the dynamic correction method based on eigenvalue decomposition avoids the repeated solution of the full-space tensor. This distributed correction mechanism can quickly respond to changes in the local environment while ensuring the consistency of global characteristics. In addition, the integral and accumulation operations used in the formula can flexibly adapt to various electromagnetic field distribution patterns, such as uniform distribution, multi-field source superposition, and local heterogeneity environment, so that the present invention can achieve efficient calculation in different scenarios.. By introducing eigenvalue decomposition technology to dynamically correct the space-time electromagnetic field tensor, the present invention solves the problem of deviation between the electromagnetic field model and the actual distribution in a complex environment. The eigenvalue decomposition technology can extract the main mode information contained in the tensor, and quantitatively calculate the difference between the actual eigenvalue decomposition result and the simulation eigenvalue decomposition result. This difference quantity is further combined with the interface propagation characteristic coefficient of the multi-source electromagnetic space to correct the initial tensor point by point, so as to effectively compensate for the errors caused by non-ideal field sources, noise, and dynamic environmental changes. This dynamic correction method based on feature differences significantly improves the accuracy of the space-time electromagnetic field tensor, enabling it to maintain high adaptability and consistency in a complex and changing electromagnetic environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 FIG. is a schematic flowchart of the application method of intelligent electromagnetic simulation data in an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0033] All features disclosed in this specification, or all steps in any disclosed method or process, except mutually exclusive features and / or steps, can be combined in any manner.

[0034] Any feature disclosed in this specification (including any additional claims, abstract) can be replaced by other equivalent or similar-purpose alternative features unless specifically stated. That is, unless specifically stated, each feature is only an example of a series of equivalent or similar features.

[0035] Example 1, reference Figure 1 : Application method of intelligent electromagnetic simulation data, the method comprising:

[0036] Step 1: Construct a virtual mirror electromagnetic space of a multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate mirror electromagnetic field sources corresponding one by one to each electromagnetic field source in the multi-source electromagnetic space; obtain the electromagnetic field components generated by the electromagnetic field sources at each sampling point at each time in the multi-source electromagnetic space, and construct a spatio-temporal electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct a corresponding simulation spatio-temporal electromagnetic field tensor in the virtual mirror electromagnetic space; perform eigen-decomposition on the spatio-temporal electromagnetic field tensor and the simulation spatio-temporal electromagnetic field tensor respectively to obtain an eigen-decomposition result and a simulation eigen-decomposition result; calculate the difference between the eigen-decomposition result and the simulation eigen-decomposition result;

[0037] The basic principle of the virtual mirror electromagnetic space is to establish a symmetric relationship through the mirror theory, so that there is a corresponding mirror field source for each real electromagnetic field source in the mirror space. This mirror relationship is not a simple geometric symmetry, but the result of precise calculation according to the boundary conditions and field distribution laws in electromagnetic theory. Physically, this mirror process can be regarded as a virtual field extension, so that the originally complex field distribution problem can be processed by simplified mathematical methods in a larger symmetric space. In this process, the characteristics of the field sources in the real electromagnetic space, such as intensity, direction, phase, etc., will be mapped into the mirror space according to preset rules to form mirror field sources. This mapping not only retains the basic properties of the field sources in the real space, but also introduces a mathematical supplement, making the joint analysis of the two spaces possible. While constructing the virtual mirror electromagnetic space, the system needs to perform data sampling on the actual multi-source electromagnetic space. This process discretizes the time and space dimensions of the electromagnetic field, decomposing the dynamic changes of the electromagnetic field into a series of discrete spatio-temporal points. At each sampling point, the spatial components and time variations of the electromagnetic field are completely recorded. The advantage of this sampling method is that it can capture the detailed information of the electromagnetic field at different positions and times simultaneously, providing a basis for subsequent modeling and analysis. After sampling, these data will be integrated into a multi-dimensional data structure to represent the electromagnetic field distribution in the entire multi-source electromagnetic space.

[0038] Meanwhile, in the virtual mirror electromagnetic space, the system generates a set of corresponding data based on the simulation model, and these data have a one-to-one correspondence with the data in the real space. In this way, the field distribution in the mirror space becomes a mapping of the real space, thus providing the possibility for subsequent comparison and analysis. After the data preparation in both the real and mirror spaces is completed, the system will perform feature extraction on them. The core of this feature extraction lies in finding the main patterns and laws in the field distribution through mathematical methods, thereby simplifying the complexity of the original data. To achieve feature extraction, the system will adopt a decomposition method to decompose multi-dimensional data into several relatively independent feature patterns. These feature patterns can be regarded as the main components of the field distribution, and each pattern reflects the variation law of the electromagnetic field in a specific direction, frequency, or time scale. Through this decomposition method, the originally complex electromagnetic field data is transformed into several feature patterns with clear physical meanings. The data in the virtual mirror space will undergo the same processing to obtain a set of corresponding feature patterns. The extraction and decomposition of this pair of feature patterns enable the distribution law of the complex electromagnetic field to be represented in a simpler and clearer manner. After completing the feature extraction, the system will compare the feature results of the real space and the mirror space. Since the mirror space is constructed based on the theoretical model, its field distribution characteristics should be highly consistent with the real space under ideal conditions. However, in the actual electromagnetic environment, due to factors such as non-linear interference between field sources and external noise, the feature results of the real space often have certain differences from those of the mirror space. By calculating and analyzing this difference, the system can identify the main factors affecting the electromagnetic field distribution and provide a basis for subsequent correction. The key principle of the entire step is that by introducing the virtual mirror electromagnetic space, the system effectively simplifies the complex multi-source electromagnetic field distribution problem in the real space into two sub-problems with a symmetric relationship. In the mirror space, the field distribution generated using the theoretical model and simulation methods can provide a reference at a relatively low computational cost, while the field distribution in the real space reflects the actual state of the electromagnetic field through actual sampling and feature extraction. After comparing the two, the complexity part introduced by the actual environment can be effectively separated, and the subsequent electromagnetic field distribution can be corrected based on these differences.

[0039] Step 2: Place a test object in the multi-source electromagnetic space. With the center of the test object as the center, set multiple layers of electromagnetic scattering interfaces around the test object, and the distance between each layer of electromagnetic scattering interface and the adjacent electromagnetic scattering interface is equal; calculate the electromagnetic scattering characteristics of the test object in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space according to the electromagnetic scattering characteristics;

[0040] The purpose of placing a test target in a multi-source electromagnetic space is to introduce a physical entity that can interact with the external electromagnetic field and thus affect the surrounding field distribution. The test target can be any object with electromagnetic scattering capabilities, such as a metal ball, a dielectric body with a complex shape, or a target object in other application scenarios. By studying the response of the target to the electromagnetic field, the electromagnetic scattering characteristics of the object can be extracted, and the electromagnetic scattering characteristics are an important physical manifestation of the object under the action of electromagnetic waves, which can reflect information such as the material, geometric structure, and position of the target. After placing the target, in order to more comprehensively describe the electromagnetic scattering effect, the system designs a series of equidistantly distributed multi-layer electromagnetic scattering interfaces around the target. The role of these interfaces is to capture the scattering laws of electromagnetic waves at different distances in a layered manner, so that the electromagnetic effect of the target in the entire space can be more accurately quantified. The mutual position relationship between the multi-layer electromagnetic scattering interfaces and the target is carefully designed, and the distance between each layer and its adjacent interface is kept consistent, which ensures the consistency and comparability of the sampling of the scattering effect at different distances. During the interaction between electromagnetic waves, the test target, and the scattering interfaces, different electromagnetic phenomena such as reflection, refraction, and scattering will occur at the interfaces. These phenomena essentially stem from the change in boundary conditions when electromagnetic waves encounter physical interfaces during propagation, such as the discontinuity of the refractive index of the medium or the wavefront distortion caused by the geometric characteristics of the target. By analyzing the electromagnetic field distribution on the scattering interfaces, the response characteristics of the target to incident waves of different bands, directions, and intensities can be extracted. These response characteristics are directly related to the physical properties of the target and are also closely related to the mutual interference of other field sources in the multi-source electromagnetic space.

[0041] After the scattering characteristics are calculated, the system further derives the interface propagation characteristic coefficient, which is the core parameter describing the propagation law of electromagnetic waves between interfaces. The interface propagation characteristic coefficient is a comprehensive index containing various information. It not only includes the attenuation effect of electromagnetic waves during propagation, but also complex phenomena such as phase shift and mode conversion. The attenuation effect describes the law that the energy of electromagnetic waves gradually weakens as the propagation distance increases. This attenuation may stem from free-space propagation loss, interface absorption, and scattering loss of the target. The phase shift is the phase change caused by the propagation path length, medium characteristics, or scattering effect of the target. The mode conversion is reflected in that electromagnetic waves may change from one field mode (such as a plane wave) to another mode (such as a spherical wave or a cylindrical wave) during propagation. Through in-depth analysis of the interface propagation characteristic coefficient, the propagation law of the electromagnetic environment around the target can be comprehensively understood, which is crucial for electromagnetic simulation in complex scenarios. The entire process of step 2 is a detailed modeling of the electromagnetic environment around the target, which not only describes the interaction between electromagnetic waves and the target from a physical level, but also provides an accurate quantitative description of the interface propagation characteristics from a mathematical level. The significance of this process lies in that it provides the core environmental parameters for subsequent simulation correction. Especially in a multi-source electromagnetic space, the interference between field sources, the scattering of the target, and the propagation characteristics between interfaces jointly determine the actual distribution of the electromagnetic field, and these factors are analyzed and quantified one by one in step 2. By calculating the scattering characteristics of the target and the interface propagation characteristic coefficient, the system can provide accurate inputs for the correction model in step 3, which ensures that the final correction result can reflect the true characteristics of the actual electromagnetic environment.

[0042] Step 3: According to the difference between the eigen-decomposition result and the simulation eigen-decomposition result, and the interface propagation characteristic coefficient of the multi-source electromagnetic space, calculate the corrected spatio-temporal electromagnetic field tensor at each time and each position in the multi-source electromagnetic space.

[0043] The calibration process first relies on the results of the eigenvalue decomposition in Step 1. These results can be regarded as an abstract representation of the electromagnetic field distribution characteristics in the multi-source electromagnetic space. Through eigenvalues and eigenvectors, the complex multi-dimensional electromagnetic field distribution is compressed into a set of mathematical expressions that can best characterize its core characteristics. The simulation eigenvalue decomposition results, on the other hand, are idealized reference models constructed based on the virtual mirror electromagnetic space. Therefore, the difference between the two essentially reflects the deviations existing in the actual electromagnetic environment, including the non-linear effects of field sources, environmental noise, and other non-negligible dynamic factors. The analysis of the eigenvalue decomposition differences provides the key calibration direction, which guides the system to focus on which characteristics and patterns during the subsequent adjustment process. At the same time, the interface propagation characteristic coefficients obtained in Step 2 play a bridging role in calibration. These coefficients record the propagation laws of electromagnetic waves when passing through the test object and its surrounding multi-layer scattering interfaces, reflecting the energy transfer and phase change characteristics of the electromagnetic field in space at different times and positions. These laws are not limited to the local scattering region of the object, but also capture the propagation dynamics in a wider space through the multi-layer interfaces. Therefore, the interface propagation characteristic coefficients become an important basis for adjusting the electromagnetic field distribution during the calibration process. During calibration, these coefficients are used to quantitatively compensate for the problems revealed by the eigenvalue decomposition differences, so as to ensure that the calibration results can not only eliminate the deviations, but also be compatible with the actual propagation characteristics in the complex electromagnetic environment. Specifically for the execution of the calibration calculation, the system uses a dynamic adjustment mechanism to process the electromagnetic field components at each time point and each spatial position. This adjustment mechanism fully considers the problems reflected by the eigenvalue decomposition differences and makes point-by-point corrections in combination with the interface propagation characteristic coefficients. During the calibration process, the adjustment in the time dimension aims to capture the dynamic change characteristics of the electromagnetic field and ensure that the simulation results can accurately reflect the time-varying behavior of the real field source. The adjustment in the spatial dimension, on the other hand, pays more attention to the distribution laws of the electromagnetic field at different positions, especially the interference and superposition effects between field sources in the multi-source electromagnetic space. Through the joint calibration in the time and space dimensions, the system can generate a comprehensive and accurate spatio-temporal electromagnetic field tensor.

[0044] A multi-source electromagnetic space is usually a dynamic system formed by multiple different field sources in a complex environment. The electromagnetic field distribution is affected by the characteristics of the field sources themselves, the interactions between the field sources, and the properties of the surrounding medium. Therefore, simple static or linear models are difficult to truly reflect the spatio-temporal evolution law in this system. An accurate spatio-temporal electromagnetic field tensor can comprehensively characterize the field component distribution of the electromagnetic field at each moment and each spatial position. This description not only captures the local change characteristics of the electromagnetic field but also reveals the global cooperative effects between multi-source fields. Its value lies in providing a physically accurate and dynamically updated basic framework, enabling complex electromagnetic field behaviors to be effectively understood and predicted. The direct use of this tensor is to support a variety of complex electromagnetic simulation applications. For example, in electromagnetic environment assessment, it can be used to analyze electromagnetic compatibility issues in a specific area, identify potential interference sources or risk areas by accurately predicting the field strength distribution. In antenna design and optimization, the spatio-temporal electromagnetic field tensor can help engineers simulate and optimize the radiation characteristics of antennas, ensuring their performance stability in complex environments. In the field of communication, it provides an accurate data basis for wireless channel modeling, thereby improving the design accuracy and reliability of communication systems. In addition, in the electromagnetic shielding design of electronic devices, this tensor can accurately characterize the propagation path and scattering behavior of electromagnetic waves, providing a scientific basis for the design of shielding structures. More importantly, the role of the spatio-temporal electromagnetic field tensor is not limited to the traditional electromagnetic simulation field. In an intelligent electromagnetic simulation system, the accuracy of this tensor provides the possibility for further application of artificial intelligence and machine learning algorithms. By inputting the corrected electromagnetic field data into intelligent algorithms, the system can automatically learn the field distribution patterns in complex environments and further optimize the simulation accuracy. This ability to combine with artificial intelligence means that the spatio-temporal electromagnetic field tensor is not only a data output but also the core input of the intelligent system, and its accuracy directly affects the feedback and optimization effects of intelligent simulation. In addition, the accurate spatio-temporal electromagnetic field tensor also has unique advantages in dynamic environments. Many electromagnetic field applications need to deal with non-static scenarios, such as real-time channel changes in mobile communication devices, environmental perception of autonomous vehicle sensors, and dynamic electromagnetic environment assessment in the aerospace field. In these scenarios, the electromagnetic field distribution shows highly complex dynamic characteristics with changes in time and spatial position, and traditional methods often cannot provide real-time and high-precision simulation results. However, the model based on the accurate spatio-temporal electromagnetic field tensor can be updated in real time to ensure that the simulation in dynamic application scenarios is highly consistent with the actual situation.

[0045] Example 2: In step 1, the electromagnetic field components include: electric field, magnetic field, and magnetic induction intensity.

[0046] First, the electric field is one of the core components of the electromagnetic field, which describes the electric force acting on charges at each position in space. The existence of the electric field directly determines the propagation characteristics of electromagnetic waves. Because in a time-varying electromagnetic field, a changing electric field will induce a magnetic field, thus forming mutually coupled electromagnetic waves. The components of the electric field not only contain intensity information but also direction characteristics, and its spatial distribution can intuitively reflect the layout and interaction of multi-source field sources. In a multi-source electromagnetic space, the electric field distribution may exhibit complex interference and superposition effects. By precisely sampling and modeling the electric field components, the system can capture these details, providing important support for the construction of the spatio-temporal electromagnetic field tensor. The magnetic field is another important component of the electromagnetic field and is closely related to the electric field. The magnetic field describes the magnetic force acting on electric currents or magnets in space. Especially in a multi-source electromagnetic space, due to the complex magnetic field superposition effects that may be generated by different field sources, its distribution and variation laws are often difficult to intuitively predict. By collecting the magnetic field components, the system can identify the magnetic force characteristics of different field sources and their influence on the surrounding space. This information is crucial in many application scenarios. For example, when analyzing the efficiency of a wireless charging system, the magnetic field components can directly reflect the magnetic coupling strength in the electric energy transfer path, thus providing a basis for optimizing the design. The magnetic induction intensity is an important parameter describing the characteristics of the magnetic field. It reflects the magnetic flux generated by the magnetic field per unit area and directly reflects the spatial intensity distribution of the magnetic field. The introduction of the magnetic induction intensity enables the system to more comprehensively describe the intensity characteristics of the magnetic field. Especially in a complex electromagnetic environment, different materials and structures may have a significant impact on the magnetic induction intensity. By introducing this component, the system can more meticulously analyze the magnetic response characteristics at different positions, providing more accurate input data for subsequent calibration steps.

[0047] Embodiment 3: In step 1, the spatio-temporal electromagnetic field tensor is represented by the following formula.

[0048]

[0049]

[0050] Wherein, represents the spatio-temporal electromagnetic field tensor at position at time t; N represents the number of electromagnetic field sources in the multi-source electromagnetic space; i is an integer subscript index; V i represents the radiation spatial range of the i-th electromagnetic field source; V' is a spatial integration infinitesimal; represents the electric field generated by the i-th electromagnetic field source at position along the X-axis direction at time t; represents the electric field generated by the i-th electromagnetic field source at position along the Y-axis direction at time t; represents the electric field generated by the i-th electromagnetic field source at position at time t At, the electric field generated in the Z-axis direction; Represents the position of the i-th electromagnetic field source at time t At, the magnetic field generated in the X-axis direction; Represents the position of the i-th electromagnetic field source at time t At, the magnetic field generated in the Y-axis direction; Represents the position of the i-th electromagnetic field source at time t At, the magnetic field generated in the Z-axis direction; Represents the position of the i-th electromagnetic field source at time t At, the time rate of change of the magnetic induction intensity generated in the X-axis direction; Represents the position of the i-th electromagnetic field source at time t At, the time rate of change of the magnetic induction intensity generated in the Y-axis direction; Represents the position of the i-th electromagnetic field source at time t At, the time rate of change of the magnetic induction intensity generated in the Z-axis direction; v 0 is the vacuum magnetic permeability; j is the imaginary symbol; k is the wave number; assume that the corresponding simulation space-time electromagnetic field tensor is constructed in the virtual mirror electromagnetic space as

[0051] Specifically, the core of the formula uniformly describes the electromagnetic field distribution at each position and moment through spatial integration and multi-source accumulation. The space-time electromagnetic field tensor in the formula Represents the comprehensive expression of the field strength at the position and time t, where the contribution of each field source i is accumulated through the integral term to form a global description of the electromagnetic field. The variable in the integral represents an arbitrary position within the radiation range of each field source, and the integral operation reflects the continuous influence of the field source on the entire space. This description method fully reflects the superposition effect of the field strength in space, that is, the radiation characteristics of each field source will affect the space field distribution with different intensities and directions within its action range, and the combined action of the multi-source fields is shown through superposition. In the formula, the distance term in the denominator describes the attenuation law of the field source radiation intensity with the spatial distance, and this design strictly follows the inverse attenuation characteristic of point source radiation in classical electromagnetic theory. As the distance increases, the field strength will show a decreasing trend, thus reflecting the energy dispersion effect of the radiation field in the far-field region. By introducing this distance factor, the formula can effectively simulate the distribution characteristics of the field strength in the multi-source electromagnetic space and ensure the physical rationality of the calculation results. The exponential term in the formula is the key part describing the phase change of the electromagnetic wave. During the propagation of the electromagnetic wave, not only the intensity decays, but also there is a periodic change in the phase. The exponential term includes the imaginary symbol j and the propagation path length It fully characterizes the dynamic propagation behavior of the wave. This description form can reflect the interference and phase superposition effects between multi-source fields, which is an important supplement to the propagation characteristics of electromagnetic waves. By combining the exponential term and the distance factor, the formula can express the amplitude and phase information of the field strength simultaneously within the same framework, providing a highly accurate tool for the dynamic description of the spatio-temporal electromagnetic field.

[0052] When describing the electromagnetic field components, the formula adopts a matrix form, unifying the time derivatives of the electric field, magnetic field, and magnetic induction intensity as multi-dimensional components. Each column of the matrix corresponds to the time derivatives of the electric field strength, magnetic field strength, and magnetic induction intensity in a certain direction respectively, and these components reflect the spatial distribution and time variation law of the electromagnetic field. For example, the three components of the electric field describe the electric force effects generated by the field source in different directions, while the corresponding components of the magnetic field reflect the magnetic force effects. The time derivative of the magnetic induction intensity captures the core characteristics of the dynamic changes in the electromagnetic field. The combined expression of these components enables the spatio-temporal electromagnetic field tensor to comprehensively reflect the complex change characteristics of the field strength in different directions, different times, and different positions. The summation term in the formula further reflects the comprehensive effect of the multi-source electromagnetic field. The electromagnetic radiation of each field source is calculated separately through independent integral terms, and the total contribution of the multi-source field is integrated through summation. This hierarchical calculation method can well adapt to the multi-source distribution characteristics in the actual complex electromagnetic environment. For example, in a multi-antenna system, the radiation characteristics of different antennas may vary significantly. The formula can model the characteristics of each antenna separately and then superimpose the effects of all antennas to generate a global electromagnetic field distribution.

[0053] Example 4: In step 1, the eigenvalue decomposition result Λ is obtained through the following formula EM :

[0054]

[0055] where Let have a dimension of m×n; U is an m×m orthogonal matrix; Σ is an m×n diagonal matrix; V is an n×n orthogonal matrix; T is the transpose operator; represents the divergence of the electric field at position at time t; represents the divergence of the magnetic field at position at time t; represents the curl of the electric field of the i-th electromagnetic field source at position at time t; represents the curl of the electric field of the i-th electromagnetic field source at position The curl of the magnetic field at; ||·|| 2 Denotes the square of the calculated modulus; Denotes the variance of the divergence; Denotes the variance of the curl; Let the simulation eigenvalue decomposition result be Λ SIM .

[0056] Specifically, the formula is first based on the classical eigenvalue decomposition theory, expressing the spatio-temporal electromagnetic field tensor as the product form of three matrices U, Σ, and V T . Among them, U and V are orthogonal matrices, corresponding to the row and column eigenvectors of the spatio-temporal tensor respectively, and Σ is a diagonal matrix containing the eigenvalues of the tensor. This decomposition form enables complex tensor data to be represented in a more concise manner. At the same time, the extraction of eigenvalues and eigenvectors provides tools for further analyzing the local and global characteristics of the electromagnetic field. To describe the physical characteristics of the electromagnetic field in more depth, the formula introduces weighted factors for divergence and curl. The divergence of the electric field and the divergence of the magnetic field respectively reflect the influence intensity of the field source on the electromagnetic field. According to Gauss's law, the divergence of the electric field is directly related to the charge density of the field source, while the divergence of the magnetic field is always zero in classical electromagnetic theory. This relationship provides physical constraints for the continuity and consistency of the field distribution. In the formula, the divergence is used as a weight factor to correct the eigenvalues through an exponential decay function. The exponential denominator of the correction term contains the variance of the divergence . This design aims to balance the contribution of divergence data in global and local characteristics. Specifically, when the divergence changes little, the influence of the weighted factor on the eigenvalues is small; conversely, when the divergence changes significantly, the influence of the weight will be significantly enhanced, thus highlighting the dominant role of the field source in the electromagnetic field distribution. Similarly, the curl characteristics are introduced through another part of the correction term. The curl of the electric field and the curl of the magnetic field are important parameters describing the dynamic characteristics of electromagnetic waves, and they are closely related to the rate of change of the magnetic field and the rate of change of the electric field respectively. In the formula, the square of the modulus of the curl is used to measure the non-uniformity of the field distribution, and the curl variance in the exponential term plays a smoothing role. When the change amplitude of the curl component is small, the system tends to maintain the stability of the eigenvalues; when the curl changes significantly, the system adjusts the eigenvalues to emphasize the local perturbation characteristics of the electromagnetic wave. By multiplying the curls of all field sources, the formula can capture the coupling and interference effects between multi-source fields, thus revealing the internal laws of the complex field environment more comprehensively.

[0057] In the formula, by combining the weighted correction of divergence and curl with eigenvalue decomposition, a deep integration of physical meaning and mathematical expression is achieved. This method plays an important role in the intelligent electromagnetic simulation system. On the one hand, it provides higher accuracy and reliability for the feature extraction of the spatio-temporal electromagnetic field tensor, enabling the eigenvalue decomposition result to not only characterize the main characteristics of the electromagnetic field but also reflect the detailed changes in its local area; on the other hand, through the variance analysis of divergence and curl, it dynamically adjusts the weights of eigenvalues, enabling the system to adapt to the dynamic changes of complex field sources and environments. The finally obtained eigenvalue decomposition result Λ EM is a multi-level expression of the spatio-temporal electromagnetic field. It contains both global information, such as the overall distribution characteristics of the field source and the field strength trend, and local detail information, such as interference, superposition, and dynamic change laws. This result not only provides a key basis for feature comparison in subsequent correction steps but also can be directly used in application scenarios such as electromagnetic environment assessment, wireless communication modeling, and complex electromagnetic system optimization. At the same time, the introduction of the simulation eigenvalue decomposition result Λ SIM provides a reference for the difference analysis between the actual features and the theoretical model. By comparing the two, the system can accurately identify the error sources and perform dynamic correction, thereby improving the accuracy and applicability of the entire intelligent electromagnetic simulation system.

[0058] Example 5: In step 1, the difference Δ ES between the eigenvalue decomposition result and the simulation eigenvalue decomposition result is calculated through the following formula:

[0059]

[0060] where, ‖·|| F is the Frobenius norm.

[0061] Specifically, the first part of the formula ||Λ EM -Λ SIM || F is the core of the difference calculation, using the Frobenius norm to quantify the global difference between the two eigenvalue decomposition results. The Frobenius norm, also known as the Frobenius norm, is the square root of the sum of the squares of all elements of the matrix and is used to measure the overall deviation between matrices. In this formula, ||Λ EM -Λ SIM || F reflects the deviation degree of the actual electromagnetic field eigenvalue decomposition result from the simulation result in the overall feature space. This part of the calculation ensures that the formula can capture the global consistency difference of the eigenvalue decomposition result, thereby providing basic data for subsequent correction. The second part of the formula conducts a refined analysis of the difference through the weights of curl and divergence. The curl weight term Describes the dynamic change characteristics of the field source. The curls of the electric and magnetic fields are key parameters reflecting the dynamic characteristics of electromagnetic waves. Especially in a multi-source electromagnetic space, the interaction between field sources will significantly affect the magnitude of the curl components. By multiplying the curl weights of each field source, the formula can identify the dynamic differences in local regions of the multi-source electromagnetic field. This approach ensures that the deviation analysis is not limited to global characteristics but can also delve into the local behavior of field sources, thus revealing the source of problems in more detail. The divergence term corresponding to the curl term describes the static characteristics of the field source distribution. The divergence of the electric field is directly related to the charge density, while the divergence of the magnetic field is usually zero in classical electromagnetic theory. Therefore, the divergence deviation can be an important indicator for measuring whether the field distribution conforms to physical constraints. By introducing divergence weights, the formula can identify the deviations caused by abnormal or discontinuous field source distributions and incorporate them as part of the overall difference analysis. This design is of great significance for the physical consistency analysis in a multi-source electromagnetic space. Through the comparison of the curl weight term and the divergence weight term, the formula further differentiates the effects of dynamic and static deviations. The curl weight term reflects the dynamic change characteristics of local regions by multiplying the contributions of all field sources, while the divergence weight term describes the global static distribution characteristics through a single exponential function. The difference between the two is used in the formula to correct the overall deviation measurement, ensuring that the deviation analysis can not only reflect the overall differences in the eigen-decomposition results but also, through the comparison of dynamic and static characteristics, reveal deeper sources of problems. This design provides higher sensitivity and adaptability for the intelligent electromagnetic simulation system, enabling the system to achieve more accurate calibration in complex electromagnetic environments. The finally calculated Δ ES is a comprehensive difference quantification index between the actual eigen-results and the simulated eigen-results. This result provides key data input for the calibration of the spatio-temporal electromagnetic field tensor in subsequent steps. By combining the global eigen-differences, dynamic characteristic deviations, and static characteristic deviations, the system can accurately analyze the non-ideality in the actual environment and then adjust the simulation model to improve its applicability and accuracy. This deviation calculation method is not only applicable to traditional electromagnetic simulation scenarios but also provides theoretical support for real-time calibration and optimization in dynamic electromagnetic environments, enabling the intelligent electromagnetic simulation system to more efficiently adapt to complex application requirements.

[0062] Example 6: In step 2, the electromagnetic scattering characteristic σ of the test object in the multi-source electromagnetic space is calculated through the following formula RCS :

[0063]

[0064] where, R is the distance from the surface of the test object; l is a surface distance threshold, which is a set value; is the scattered electric field generated by the i-th electromagnetic field source on the surface of the test object; is the incident electric field generated by the i-th electromagnetic field source on the surface of the test object; ∈ r is the relative permittivity corresponding to the test object; μ r is the relative permeability corresponding to the test object; α loss is the material loss coefficient of the test object, which is a set value; θ i is the azimuth angle of the scattered electric field generated by the i-th electromagnetic field source on the surface of the test object; β i is the azimuth angle of the incident electric field generated by the i-th electromagnetic field source on the surface of the test object; φ i is the elevation angle of the scattered electric field generated by the i-th electromagnetic field source on the surface of the test object; α i is the elevation angle of the incident electric field generated by the i-th electromagnetic field source on the surface of the test object; |·| represents the determinant operation of the matrix.

[0065] Specifically, the basic framework of the formula uses 4πR 2 as the scale normalization factor, which is directly related to the growth law of the radiation spherical surface area. According to classical electromagnetic theory, when electromagnetic waves propagate in the form of spherical waves, their energy distribution spreads uniformly to a larger spherical surface as the distance increases. Through this normalization design, the formula ensures that the calculation result of the scattering cross-sectional area can exclude the distance effect caused by spatial propagation, thereby reflecting the inherent scattering characteristics of the object. This part lays the theoretical foundation for the formula, enabling it to maintain the consistency and reliability of the results within different distance ranges. The core content of the formula is the ratio relationship between the scattered electric field and the incident electric field, that is For the i-th field source, this ratio reflects the response ability of the object surface to the incident electric field. The scattered electric field is the reflected wave or scattered wave generated after the interaction between the incident electric field and the object, and its intensity and direction are jointly affected by the material properties, geometric shape, and surface electromagnetic properties of the object. This ratio indicates the scattering efficiency of the object to the incident wave. The larger the value, the stronger the scattering ability of the object in this direction. By accumulating the contributions of all field sources, the formula can comprehensively reflect the global scattering characteristics of the object in a multi-field source environment. This design makes the formula applicable not only to simple scattering analysis of a single field source but also to accurately characterize the scattering behavior in a multi-source complex environment. In the geometric description of the scattering direction, the formula uses a matrix containing the relationship between the azimuth angle and the elevation angle, and the determinant |·| reflects the degree of deviation between the scattering and incident directions in space. The matrix is composed of θ i , φ i , α i , β iIt consists of equal-angle parameters that respectively describe the angular characteristics of the scattered electric field and the incident electric field in specific directions. The geometric characteristics of the target directly affect these angular relationships. For example, a smooth curved surface usually results in a smaller deviation between the scattering direction and the incident direction, while a rough surface or a complex geometric shape may lead to significant changes in the scattering direction. By calculating the magnitude of the determinant, the formula can quantify the impact of this angular relationship on the scattering intensity, further revealing the role of the target surface characteristics in the scattering behavior. This part is particularly important because the stealth design of the target often depends on the control of the scattering direction, and the formula provides a mathematical description of this key characteristic.

[0066] The material properties are incorporated into the formula through ∈ r , μ r , α loss and other parameters, reflecting the influence of the dielectric properties, magnetic permeability properties, and material loss properties of the target on the scattering behavior. The relative permittivity ∈ r indicates the polarization ability of the material to the electric field, while the relative permeability μ r reflects the response degree of the material to the magnetic field. The square roots of both describe the modulation effect of the material on the propagation speed of electromagnetic waves, which directly affects the scattering pattern of the target. The loss coefficient α loss is the core parameter for evaluating the ability of the material to absorb electromagnetic wave energy. The formula quantifies these material properties as a modulation factor of the scattering intensity through the exponential decay term . When the loss of the material is high, more electromagnetic wave energy is absorbed rather than reflected, resulting in a significant reduction in the scattering cross-section; conversely, for low-loss materials, more energy returns in the form of scattering, thus increasing the scattering cross-section. The design of this part enables the formula to distinguish the scattering characteristics of different materials, providing a theoretical basis for material selection and optimization design. The limit operation lim R→l in the formula is a limitation on the calculation range of the scattering cross-section. The set distance threshold l is usually selected as a fixed radius outside the target surface to ensure that the evaluation of the scattered field strength is concentrated in a range with greater practical significance. This setting not only avoids the abnormal increase in the local field strength caused by too close a distance but also eliminates the error influence caused by the weakening of the scattered field strength at too far a distance, thus ensuring the physical meaning and accuracy of the calculation results. Generally speaking, the formula forms a comprehensive quantitative analysis of the scattering behavior of the target through the comprehensive description of multi-source field effects, directional geometric characteristics, and material properties.

[0067] Example 7: In step 2, calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space through the following formula:

[0068]

[0069] where M is the number of electromagnetic scattering interfaces; P i is the power of the i-th electromagnetic field source; D is the average distance from all electromagnetic field sources to the test target; d is the distance between the electromagnetic scattering interface and the adjacent electromagnetic scattering interface; α(s) is the attenuation function; k is an integer subscript index; Γ k is the interface scattering coefficient of the k-th electromagnetic scattering interface; s is the attenuation function variable, with a value range from 0 to d; ds is the integration element.

[0070] Specifically, the core idea of the formula is to decompose the propagation characteristics of electromagnetic waves into multiple independent but interrelated physical factors, and express them as an overall propagation coefficient through the cumulative effect. First, through this part, the formula combines the power distribution of the multi-source field with the distance characteristics, reflecting the energy contributions of different field sources around the test target. The field source power P i is the direct factor determining the intensity of electromagnetic waves, while the average distance D reflects the uniformity of the spatial distribution. When the field sources are densely distributed and have a large power, this term will significantly increase P rec , and vice versa. This design ensures that the formula can adapt to the energy distribution characteristics under different field source configurations. Subsequently, the formula introduces the inverse square relationship between the wavelength λ and the path distance d, and through expresses the spatial propagation law of electromagnetic waves. This part strictly follows the classical radiation theory, that is, the intensity of point source radiation decreases inversely with the square of the propagation distance, and the increase in wavelength will reduce the attenuation degree of radiation energy. This description method ensures the physical rationality of the formula in practical applications, especially when dealing with the propagation of high-frequency or long-wave electromagnetic waves, it can give practical predictions. The electromagnetic scattering characteristic σ RCS is another key component of the formula, which is used to describe the scattering ability of the target to the incident wave. By incorporating the radar cross-sectional area of the target into the calculation of the propagation coefficient, the formula can reflect the significant influence of the test target on the propagation of electromagnetic waves. When the geometric shape of the target is complex or the surface material has strong reflection characteristics, σ RCS will increase significantly, thereby increasing the interface propagation characteristic coefficient. This part is closely related to the formula in Embodiment 6, further strengthening the adaptability of the system in the multi-layer scattering environment. The role of the multi-layer interface is precisely characterized through . The scattering coefficient Γ of each interface k describes the reflection ability of this interface to the incident wave, and represents the energy transfer efficiency through this interface. By multiplying the transfer efficiencies of all interfaces, the formula can comprehensively describe the overall loss characteristics of electromagnetic waves after multiple reflections and transmissions in a multi-layer interface. Such a design is particularly suitable for complex multi-layer structures, such as composite materials, stratified media, or multi-layer shields, etc., and can accurately quantify the contribution of each layer to the propagation of electromagnetic waves. In the formula, the exponential decay term describes the energy loss of electromagnetic waves along the propagation path. This term combines the absorption effect of the material medium, the path length, and the attenuation characteristics of the external environment. The attenuation function α(s) is a dynamic variable that can reflect the loss intensity of electromagnetic waves at different positions as the path s changes, and the integration operation accumulates the attenuation effect over the entire propagation path. The set value l serves as a benchmark, allowing the system to adjust the propagation coefficient according to different loss models. This part of the design ensures that the formula can flexibly adapt to various propagation environments. For example, in a high-loss medium, the exponential term will significantly reduce the propagation coefficient, while in a low-loss medium, a high energy transfer efficiency will be maintained.

[0071] Example 8: The attenuation function α(s) is an exponential decay function or a Gaussian decay function.

[0072] Specifically, when the attenuation function takes the exponential decay form, its expression can usually be written as α(s) = α 0 e -κs , where α 0 is the initial attenuation intensity, and κ is the attenuation rate. This form reflects the relationship that the energy loss in the medium decreases exponentially with the propagation path, and is widely applicable to highly absorptive media or the propagation of electromagnetic waves in strongly dissipative environments. For example, in a metal shield or a highly conductive material, the energy of electromagnetic waves will show a rapid decay characteristic as the propagation distance increases, and the exponential decay function can accurately capture this characteristic. In addition, when the absorption characteristics of the medium are uniform and there are no significant spatial variations, the exponential decay form can provide a simple and effective loss description. The advantage of this function form is high computational efficiency and good adaptation to common uniform medium attenuation models. In contrast, the Gaussian decay function is more suitable for describing local loss characteristics or the propagation characteristics of non-uniform media, and its expression can be written as where α 0 is the attenuation amplitude, s 0 is the central position, and σ is the standard deviation that controls the attenuation range. The characteristic of the Gaussian decay function is that its attenuation intensity is at the path center position (i.e., s 0) reaches its maximum and gradually weakens at positions far from the center. This form is particularly suitable for describing strongly localized energy loss phenomena, such as the most significant absorption of electromagnetic waves by a specific layer in a multi-layer medium, or energy dissipation caused by local scattering and interference in complex geometric structures. In practical applications, the Gaussian attenuation form can accurately capture the energy loss in certain key regions of the propagation path, providing a more refined analysis of propagation characteristics for intelligent electromagnetic simulation systems. The choice of the two attenuation function forms not only reflects the adaptability to different propagation environments but also provides the possibility for flexible system modeling. In an intelligent electromagnetic simulation system, the propagation environment is usually complex and variable. The medium may exhibit different uniformity characteristics, and there may even be regions with significant spatial variations. The combination of the simplicity of the exponential attenuation function and the locality characteristics of the Gaussian attenuation function enables the system to dynamically adjust the attenuation model according to the actual situation. For example, in some segments of the propagation path, electromagnetic waves may be dissipated by a homogeneous medium, and at this time, the exponential attenuation function can well describe the energy loss law; while in other segments, if the medium characteristics show obvious non-uniformity, the Gaussian attenuation function can be used to more precisely characterize the local characteristics. In addition, these two attenuation function forms also have different effects on the calculation of the integral term in the formula. When the exponential attenuation function is used, the integral result usually shows a simple exponential form, which makes the calculation efficiency of the propagation coefficient higher and is suitable for scenarios that require rapid evaluation of energy loss. When the Gaussian attenuation function is used, the integral result can reflect the influence of the attenuation center position and its range on the propagation coefficient, providing higher precision for local loss assessment in complex scenarios. This diversity design ensures that the system can achieve a dynamic balance between efficiency and precision.

[0073] Example 9: In step 3, through the following formula, calculate the corrected spatio-temporal electromagnetic field tensor at each time and each position in the multi-source electromagnetic space

[0074]

[0075] where represents the position and is the average distance from all electromagnetic field sources.

[0076] Specifically, the starting point of the formula is the initial spatio-temporal electromagnetic field tensor This tensor is constructed through the previous steps and represents the electromagnetic field distribution at each time and position in the multi-source electromagnetic space. However, non-ideal factors in the actual electromagnetic field environment, such as interference, noise, non-uniform medium characteristics, etc., may cause to not fully reflect the real field distribution. Therefore, the corrected spatio-temporal electromagnetic field tensor The calculation becomes a key step in the intelligent electromagnetic simulation system, aiming to minimize the deviation between the theoretical model and the actual environment by introducing a series of correction factors. In the formula, the correction factor P rec is the interface propagation characteristic coefficient of the multi-source electromagnetic space. Through the calculation of the previous steps, it integrates the energy loss, scattering characteristics, and transfer efficiency of the multi-layer interface into a comprehensive factor. By introducing P rec into the correction formula, the system can consider the specific influence of the multi-layer interface on the electromagnetic wave propagation at each position. For example, in a high-loss interface, the value of P rec will decrease significantly, thereby reducing the intensity of the correction tensor, which reflects the energy loss suffered by the electromagnetic wave during propagation. The addition of this factor makes the correction result closer to the multi-layer transmission characteristics in the real electromagnetic environment, ensuring the physical rationality of the correction process. The eigen-decomposition difference quantity Δ ES is another important correction factor in the formula, which is used to quantify the deviation between the initial tensor and the simulation tensor. This part reflects the eigenvalue deviation in the multi-source electromagnetic space due to the interaction between field sources, non-linear effects, or incomplete modeling. By incorporating Δ ES into the formula, the correction process can correct the initial tensor according to the direction and magnitude of the eigen-decomposition difference. For example, when the difference at certain positions is large, the formula will significantly adjust the correction value at that position, thereby enhancing the consistency of the corrected tensor in the spatial and temporal dimensions. This eigen-decomposition-based correction method improves the system's ability to analyze complex electromagnetic field characteristics, ensuring that the final correction result can more accurately reflect the actual characteristics of the field source. The integral term in the formula further considers the influence of spatial distance on the electromagnetic field distribution. represents the average distance between the target position and all field sources. This distance reflects the field source coverage of the target position and the overall length of the propagation path. During the integration process, the introduction of the variable c simulates the energy accumulation effect of the electromagnetic wave during propagation. By calculating the energy accumulation from the starting point to the target position, the formula can more precisely describe the spatial distribution law of the electromagnetic field. The design of this integral term is particularly suitable for the case where the field source distribution is uneven in a multi-source complex environment. For example, some positions may be strongly affected by multiple near-field sources, while other positions are mainly contributed by far-field sources. Through the adjustment of the integral term, the formula can better capture these spatial differences. Finally, the formula integrates the initial tensor, propagation characteristic coefficient, eigen-decomposition difference quantity, and spatial distance influence into a whole, and constructs the corrected spatio-temporal electromagnetic field tensor

[0077] Embodiment 10: An application system for intelligent electromagnetic simulation data, the system comprising: a mirror simulation difference calculation part, configured to construct a virtual mirror electromagnetic space of a multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space one by one; obtain the electromagnetic field components generated by the electromagnetic field sources at each sampling point at each time in the multi-source electromagnetic space, and construct a spatio-temporal electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct a corresponding simulated spatio-temporal electromagnetic field tensor in the virtual mirror electromagnetic space; perform eigenvalue decomposition on the spatio-temporal electromagnetic field tensor and the simulated spatio-temporal electromagnetic field tensor respectively, and obtain an eigenvalue decomposition result and a simulated eigenvalue decomposition result respectively; calculate the difference between the eigenvalue decomposition result and the simulated eigenvalue decomposition result; a propagation characteristic calculation part, configured to place a test object in the multi-source electromagnetic space, and around the center of the test object, set multiple layers of electromagnetic scattering interfaces, and the distance between each layer of electromagnetic scattering interface and the adjacent electromagnetic scattering interface is equal; calculate the electromagnetic scattering characteristics of the test object in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space according to the electromagnetic scattering characteristics; a correction part, configured to calculate the spatio-temporal electromagnetic field tensor corrected at each time and each position in the multi-source electromagnetic space according to the difference between the eigenvalue decomposition result and the simulated eigenvalue decomposition result, and the interface propagation characteristic coefficient of the multi-source electromagnetic space.

[0078] The present invention is not limited to the foregoing specific embodiments. The present invention extends to any new feature or any new combination disclosed in this specification, and any new method or process step or any new combination disclosed.

Claims

1. An application method of intelligent electromagnetic simulation data, characterized in that: The method comprises: Step 1: construct a virtual mirror electromagnetic space of the multi-source electromagnetic space; in the virtual mirror electromagnetic space, generate a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space; obtain the electromagnetic field components generated by the electromagnetic field source at each sampling point in the multi-source electromagnetic space at each time, and construct the space-time electromagnetic field tensor of the multi-source electromagnetic space; similarly, construct a corresponding simulated space-time electromagnetic field tensor in the virtual mirror electromagnetic space; perform eigendecomposition on the space-time electromagnetic field tensor and the simulated space-time electromagnetic field tensor, respectively, and obtain eigendecomposition results and simulation eigendecomposition results, respectively; calculate the difference between the eigendecomposition result and the simulation eigendecomposition result; Step 2: Place a test target in the multi-source electromagnetic space, with the test target as the center, and set multiple layers of electromagnetic scattering interfaces around the test target, with each layer of electromagnetic scattering interface being equidistant from the adjacent electromagnetic scattering interface; calculate the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficient of the multi-source electromagnetic space based on the electromagnetic scattering characteristics; Step 3: Based on the difference between the characteristic decomposition result and the simulation characteristic decomposition result, as well as the interface propagation characteristic coefficient of the multi-source electromagnetic space, calculate the corrected space-time electromagnetic field tensor at each time and each position in the multi-source electromagnetic space.

2. The application method of intelligent electromagnetic simulation data according to claim 1, characterized in that: In step 1, the electromagnetic field components include: electric field, magnetic field and magnetic induction intensity.

3. The application method of intelligent electromagnetic simulation data according to claim 2, characterized in that: In step 1, the space-time electromagnetic field tensor is expressed using the following formula: ； in, Indicates at time Time, Location The space-time electromagnetic field tensor at ; Indicates the number of electromagnetic field sources in the multi-source electromagnetic space; is an integer subscript index; Indicates The radiation spatial range of an electromagnetic field source; is the spatial integral differential element; Indicates The electromagnetic field source at time Time, Location At , the electric field is generated along the X-axis direction; Indicates The electromagnetic field source at time Time, Location At , the electric field is generated along the Y axis; Indicates The electromagnetic field source at time Time, Location At , the electric field is generated along the Z axis; Indicates The electromagnetic field source at time Time, Location At , the magnetic field generated along the X-axis direction; Indicates The electromagnetic field source at time Time, Location At , the magnetic field generated along the Y axis; Indicates The electromagnetic field source at time Time, Location At , the magnetic field generated along the Z axis; Indicates The electromagnetic field source at time Time, Location The time rate of change of the magnetic induction intensity generated along the X-axis direction; Indicates The electromagnetic field source at time Time, Location The time rate of change of the magnetic induction intensity generated along the Y-axis direction; Indicates The electromagnetic field source at time Time, Location The time rate of change of the magnetic induction intensity generated along the Z axis; is the vacuum permeability; is the imaginary number symbol; is the wave number; let the corresponding simulated space-time electromagnetic field tensor constructed in the virtual mirror electromagnetic space be .

4. The application method of intelligent electromagnetic simulation data according to claim 3, characterized in that: In step 1, the characteristic decomposition result is obtained by the following formula: : ； in, ;set up The dimension is ; for The orthogonal matrix of for The diagonal matrix of ; for The orthogonal matrix of is the transposition operator; Indicates at time Time, Location The divergence of the electric field at ; Indicates at time Time, Location The divergence of the magnetic field at ; Indicates The electromagnetic field source at time Time, Location The curl of the electric field at ; Indicates The electromagnetic field source at time Time, Location The curl of the magnetic field at ; Indicates the calculation of the square of the modulus; represents the variance of the divergence; represents the variance of the curl; let the simulation characteristic decomposition result be .

5. The application method of intelligent electromagnetic simulation data according to claim 4, characterized in that: In step 1, the difference between the characteristic decomposition result and the simulation characteristic decomposition result is calculated by the following formula: : ； in, is the F-norm.

6. The method for applying intelligent electromagnetic simulation data according to claim 5, characterized in that: In step 2, the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space are calculated by the following formula: : ； Among them, among them, is the distance from the surface of the test object; is a surface distance threshold, which is a set value; For the The scattered electric field generated by an electromagnetic field source on the surface of the test target; For the The incident electric field generated by an electromagnetic field source on the surface of the test target; is the relative dielectric constant corresponding to the test target; Relative magnetic permeability corresponding to the test target; is the material loss coefficient of the test target object, which is the set value; For the The azimuth of the scattered electric field generated by an electromagnetic field source on the surface of the test target; For the The azimuth of the incident electric field generated by an electromagnetic field source on the surface of the test target; For the The elevation angle of the scattered electric field generated by an electromagnetic field source on the surface of the test target; For the The pitch angle of the incident electric field generated by an electromagnetic field source on the surface of the test target; Represents the determinant operation of a matrix.

7. The method for applying intelligent electromagnetic simulation data according to claim 6, characterized in that: In step 2, the interface propagation characteristic coefficient of the multi-source electromagnetic space is calculated by the following formula: ； in, is the number of electromagnetic scattering interfaces; For the The power of an electromagnetic field source; is the average distance from all electromagnetic field sources to the test target; The distance between the electromagnetic scattering interface and the adjacent electromagnetic scattering interface; is the decay function; is an integer subscript index; For the The interface scattering coefficient of an electromagnetic scattering interface; is the decay function variable, ranging from 0 to ; is the integral differential element; is the wavelength.

8. The method for applying intelligent electromagnetic simulation data according to claim 7, characterized in that: Decay function is an exponential decay function or a Gaussian decay function.

9. The method for applying intelligent electromagnetic simulation data according to claim 8, characterized in that: In step 3, the corrected space-time electromagnetic field tensor at each time and each position in the multi-source electromagnetic space is calculated by the following formula: : ； in, Indicates location The average distance from all electromagnetic field sources.

10. An application system for intelligent electromagnetic simulation data for implementing the method according to any one of claims 1 to 9, characterized in that: The system comprises: a mirror simulation difference calculation part, which is used to construct a virtual mirror electromagnetic space of a multi-source electromagnetic space; in the virtual mirror electromagnetic space, a mirror electromagnetic field source corresponding to each electromagnetic field source in the multi-source electromagnetic space is generated; the electromagnetic field component generated by the electromagnetic field source at each sampling point in the multi-source electromagnetic space at each time is obtained to construct a space-time electromagnetic field tensor of the multi-source electromagnetic space; similarly, a corresponding simulation space-time electromagnetic field tensor is constructed in the virtual mirror electromagnetic space; characteristic decomposition is performed on the space-time electromagnetic field tensor and the simulation space-time electromagnetic field tensor respectively, and characteristic decomposition results and simulation characteristic decomposition results are obtained respectively; the characteristic decomposition results and the simulation characteristic decomposition results are calculated and compared. The method comprises the following steps: a propagation characteristic calculation part, which is used to place a test target in the multi-source electromagnetic space, set a plurality of electromagnetic scattering interfaces around the test target with the test target at the center, and each layer of electromagnetic scattering interface is equidistant from the adjacent electromagnetic scattering interface; calculate the electromagnetic scattering characteristics of the test target in the multi-source electromagnetic space; and calculate the interface propagation characteristic coefficients of the multi-source electromagnetic space based on the electromagnetic scattering characteristics; a correction part, which is used to calculate the space-time electromagnetic field tensor after correction at each time and each position in the multi-source electromagnetic space based on the difference between the characteristic decomposition result and the simulation characteristic decomposition result and the interface propagation characteristic coefficients of the multi-source electromagnetic space.

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