An Automated Design Method for RF Antennas Based on State-Space Reduced-Order Model and Level Set Topology Optimization

Abstract

This application discloses an automated design method for radio frequency antennas based on a state-space reduced-order model and level set topology optimization. The method includes: constructing a level set function; initializing the level set function using a signed distance function to obtain an initial level set function; converting partial differential equations into a finite ordinary differential equation system through semi-discretization; using the physical residuals of Maxwell's equations as a self-supervised loss function to converge the state-space reduced-order model to a local electromagnetic reduced-order model; obtaining the gradient velocity field of the level set function based on the local electromagnetic reduced-order model; and continuously evolving the level set function based on the gradient velocity field to obtain the final level set function. This application combines high-degree-of-freedom model reconstruction with electromagnetic physics analysis, efficiently optimizing the antenna's topology and parameters through multiple granular stages, and achieving the automatic generation of high-performance complex topology antennas with limited computational resources.

Description

Technical Field

[0001] This application relates to the fields of electronic design automation and microwave radio frequency technology, and in particular to an automated design method for radio frequency antennas based on a state-space reduced-order model and level set topology optimization. Background Technology

[0002] With the continuous expansion of wireless communication, radar sensing, and high-precision sensing technologies, the evolution of devices to higher frequency bands places increasingly stringent demands on the performance of electromagnetic devices such as antennas, filters, and metamaterials. Traditional on-chip antenna design methods mainly rely on the designer's intuition and repeated trial-and-error parameter scanning, which is not only time-consuming and labor-intensive but also prone to getting trapped in local optima.

[0003] To overcome these limitations, automated design, particularly methods utilizing machine learning, has emerged. Current automated design methods mainly fall into two categories: The first is optimization methods based on predefined geometric templates, which restrict the device topology to a fixed geometric configuration and achieve this by optimizing a small number of parameters. While computationally efficient, this approach cannot escape the initial geometric assumptions and struggles to discover superior non-traditional structures. The second category is pixel-based design methods, which discretize the design domain into high-resolution pixel units. Theoretically, this provides extremely high degrees of freedom in topology generation, but the resulting extremely high-dimensional design space leads to a severe "curse of dimensionality" during optimization. In high-frequency on-chip device design, full-wave electromagnetic simulation is extremely time-consuming, and acquiring high-fidelity data is computationally very expensive. Furthermore, the performance sensitivity of electromagnetic structures is often unevenly distributed, making a globally uniform blind search strategy inherently inefficient and wasting significant computational resources. Currently, there are two core bottlenecks in the field of automated design of high-frequency electromagnetic devices: first, the underlying algorithms of commercial electromagnetic field simulation software (such as HFSS and ADS) are not differentiable, and cannot directly provide efficient analytical gradients; second, existing AI proxy models are often black-box structures, lacking physical consistency and highly dependent on simulation data. How to construct a differentiable electromagnetic physics simulator that can converge quickly while ensuring physical rigor is key to achieving high-performance automated antenna design. Summary of the Invention

[0004] The purpose of this application is to provide an automated design method for radio frequency antennas based on a state-space reduced-order model and level set topology optimization, in order to solve the technical problem that existing technologies are highly dependent on simulation data. The various technical effects of the preferred solutions among the many technical solutions provided in this application are detailed below.

[0005] To achieve the above objectives, this application provides the following technical solutions: This application provides an automated design method for radio frequency antennas based on a state-space order reduction model and level set topology optimization. The method includes: constructing a level set function to characterize the antenna topology; initializing the level set function using a signed distance function to obtain an initial level set function; converting the partial differential equations describing the electromagnetic field distribution into a finite ordinary differential equation system through semi-discretization; performing spatiotemporal dimensionality reduction modeling on the finite ordinary differential equation system using the state-space order reduction model; using the physical residuals of Maxwell's equations as a self-supervised loss function to drive the state-space order reduction model to undergo self-supervised training based on the initial level set function, causing the state-space order reduction model to converge to a local electromagnetic order reduction model; obtaining the normal gradient velocity field of the level set function based on the local electromagnetic order reduction model; continuously evolving the level set function based on the normal gradient velocity field to obtain a final level set function; and using the final level set function for automated antenna design to obtain the final antenna topology.

[0006] In some embodiments, obtaining the gradient velocity field of the horizontal set function based on the local electromagnetic order reduction model includes: representing the antenna performance target as a functional that depends on the electromagnetic field distribution output by the local electromagnetic order reduction model, and obtaining the topological gradient of the performance target with respect to the horizontal set function using the adjoint state method, as the normal gradient velocity field.

[0007] In some embodiments, the continuous evolution of the level set function based on the normal gradient velocity field includes: substituting the normal gradient velocity field into the Hamilton-Jacobi equation to drive the level set function to continuously evolve on a fixed grid in accordance with the Hamilton-Jacobi equation.

[0008] In some embodiments, the performance target is the antenna's return loss S. 11 .

[0009] In some embodiments, the level set function determines the metallic region, dielectric region, and boundary of the antenna based on the symbol, and the level set function is expressed as: in, Indicates the metallic area of ​​the antenna, Indicates the medium region, It represents the boundary between the metallic region and the dielectric region.

[0010] In some embodiments, initializing the level set function using the symbolic distance function includes: obtaining the symbolic distance function values ​​of each sub-geometry in the antenna topology, and merging the symbolic distance function values ​​using a polynomial smooth minimization operation.

[0011] In some embodiments, the finite ordinary differential equation system is expressed as: Among them, the full state vector Includes global electric field components and global magnetic field components , For system incentive terms, It is the spatial discrete differential operator matrix determined by the parameterization of the level set function.

[0012] In some embodiments, the spatiotemporal dimensionality reduction modeling of the finite ordinary differential equation system using the state-space reduced-order model is expressed as follows: Where A, B, C, and D are the learnable parameters of the state-space reduced-order model. It is a low-dimensional latent space state vector. The predicted electromagnetic field vector output by the reduced-order state-space model.

[0013] In some embodiments, the self-supervised loss function is calculated using the following formula: in, Represents the curl operator, Spatial permeability, The global steady-state electric field vector predicted by the reduced-order state-space model. Angular frequency, For the current level set function The spatial permittivity is determined. Here, j represents the port excitation current density in the frequency domain, and j is the imaginary unit. This represents the squared L2 norm of the residual energy calculation.

[0014] In some embodiments, the automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization further includes: extracting the zero level set contour from the final level set function, converting the zero level set contour into an explicit polygon, submitting it to 3D full-wave electromagnetic simulation software for verification, and exporting the verified explicit polygon as a GDSII format layout file.

[0015] Implementing one of the technical solutions described above in this application has the following advantages or beneficial effects: In this application, the antenna topology is implicitly expressed using a level set function, followed by spatiotemporal dimensionality reduction modeling using a state-space reduction model. Through self-supervised training using physical residuals, it converges to a high-precision local electromagnetic reduction model. Finally, the level set function is continuously evolved using the local electromagnetic reduction model to obtain the final level set function. This application's embodiment achieves zero-sample topology optimization without requiring a large amount of simulation data, solving the problems of poor physical consistency in existing AI models and low optimization efficiency caused by the non-differentiability of commercial software.

[0016] This application combines high-degree-of-freedom model reconstruction with electromagnetic physics analysis, and efficiently optimizes the antenna topology and parameters through multiple granular stages, realizing the automatic generation of high-performance complex topology antennas with limited computing resources. Attached Figure Description

[0017] To more clearly illustrate the technical solutions of the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1 This is a flowchart illustrating the automated design method for radio frequency antennas based on a state-space reduced-order model and level set topology optimization, according to an embodiment of this application. Detailed Implementation

[0018] To make the objectives, technical solutions, and advantages of this application clearer, various exemplary embodiments described below will be referenced to the accompanying drawings, which form part of the exemplary embodiments and depict various exemplary embodiments that may be adopted to implement this application. Unless otherwise indicated, the same numbers in different drawings represent the same or similar elements. The embodiments described in the following exemplary embodiments do not represent all embodiments consistent with this disclosure. It should be understood that they are merely examples of processes, methods, and apparatuses consistent with some aspects of this application disclosed as detailed in the appended claims, and other embodiments may be used, or structural and functional modifications may be made to the embodiments listed herein without departing from the scope and spirit of this application.

[0019] In the description of this application, it should be understood that the terms "center," "longitudinal," "lateral," etc., indicate the orientation or positional relationship based on the accompanying drawings, and are only for the convenience of describing this application and simplifying the description, and do not indicate or imply that the referred element must have a specific orientation, or be constructed and operated in a specific orientation. The terms "first," "second," etc., are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of indicated technical features. The term "multiple" means two or more. The terms "connected" and "linked" should be interpreted broadly, for example, they can be fixed connections, detachable connections, integral connections, mechanical connections, electrical connections, communication connections, direct connections, indirect connections through an intermediate medium, and can be the internal connection of two elements or the interaction relationship between two elements. The term "and / or" includes any and all combinations of one or more of the related listed items. Those skilled in the art can understand the specific meaning of the above terms in this application according to the specific circumstances.

[0020] To illustrate the technical solutions described in this application, specific embodiments are provided below, showing only the parts related to the embodiments of this application.

[0021] like Figure 1 As shown, this application provides an automated design method for radio frequency antennas based on a state-space reduced-order model and level set topology optimization, including the following steps (steps S1 to S3): S1. Construct a horizontal set function to characterize the antenna topology, and initialize the horizontal set function using the symbol distance function to obtain the initial horizontal set function.

[0022] Specifically, the antenna design area can be viewed as a continuous two-dimensional or three-dimensional space. Unlike existing methods that use discrete pixels or predefined geometric templates, this application introduces a high-order level set function to implicitly and continuously express the antenna topology mathematically. In some embodiments, the level set function can determine the metallic region, dielectric region, and boundaries of the antenna based on its sign. It can be represented as: in, Indicates the metallic area of ​​the antenna, Indicates the medium region, This represents the boundary between the metallic and dielectric regions. Using the zero isosurface of the level set function, the physical boundary between the metallic and dielectric regions of the antenna can be precisely and unambiguously defined. This transforms the complex topology optimization problem into the evolution problem of a smooth function on a fixed background mesh, thus converting the topology optimization process into finding the optimal level set function. .

[0023] In some embodiments, initializing the level set function using the symbolic distance function may include: obtaining the symbolic distance function values ​​of each sub-geometry in the antenna topology, and merging the symbolic distance function values ​​using a polynomial smooth minimization operation.

[0024] During the initialization phase, the initial topology, also known as the initial level set function, can be constructed using the symbolic distance function (SDF). Specifically, for a center coordinate of... A single rectangular patch with length L and width W, at any point in its space The SDF parsing calculation formula at the location is: Meanwhile, during the topology initialization phase, directly merging geometries using the standard minimum operation without any processing will result in sharp, non-differentiable bends at intersections or close proximity. Therefore, this application employs a polynomial smooth minimization operation to merge the SDFs of each geometry. Specifically, given the signed distance field function of two sub-geometries... , And parameters that control smoothness The merging process is as follows: First, calculate the local smoothing factor h: This leads to the merged level set function. : This polynomial smoothing minimization operation eliminates gradient discontinuities in the space, ensuring that the merged initial level set function strictly satisfies the Eikonal equation globally. Satisfying the Eikonal equation ensures that the level set function maintains a uniform distance field characteristic, that is, the gradient magnitude is always 1. This avoids the level set function becoming too steep or flat in space, thus completely eliminating the amplification of truncation error caused by finite difference calculation when solving complex topological evolution equations in the future, and maintaining the absolute numerical stability of the entire automated design calculation process.

[0025] The antenna design area in this embodiment can be one. square area Subsequently, a continuous level set function defined on this square region is introduced. The antenna topology can be a simple dipole antenna, which consists of two phase-separated... All dimensions are The rectangular patches are then used to precisely initialize the level set function using the minimum SDF of the two rectangular patches.

[0026] In some embodiments, initializing the level set function using the signed distance function can be expressed as: , in, and These represent two rectangular patches at points in space. The sign distance function value at that point. Then, to avoid standard minimum operation... The resulting gradients are discontinuous. In this specific embodiment, a polynomial smoothing minimization operation can be used to merge the SDFs of the rectangular patches.

[0027] The specific merging and calculation process is as follows: S2. The partial differential equations (PDEs) describing the electromagnetic field distribution are transformed into a finite ordinary differential equation system (ODE) through semi-discretization. A state-space reduced-order model (SSM) is then used to perform spatiotemporal dimensionality reduction modeling on the ODE system. The physical residuals of Maxwell's equations are used as a self-supervised loss function to drive the state-space reduced-order model to undergo self-supervised training based on the initial level set function, causing the state-space reduced-order model to converge to a local electromagnetic reduced-order model. The partial differential equations describing the electromagnetic field distribution can be Maxwell's partial differential equations.

[0028] Specifically, the antenna design region can first be semi-discretized using a finite difference grid, transforming the high-dimensional electromagnetic partial differential equations into a set of equivalent ODE descriptions. To address the computationally intensive problem of directly solving high-dimensional ODE systems, a state-space reduction model can be introduced for spatiotemporal dimensionality reduction modeling. This spatiotemporal dimensionality reduction modeling essentially maps the high-dimensional physical space to a low-dimensional implicit state space, resulting in a set of learnable system evolution matrices. The input to the state-space reduction model consists of the spatial medium distribution parameters determined by the current level set topology and the excitation source signal; the output is the predicted electromagnetic field vector reconstructed onto the global spatial grid.

[0029] The input to a state-space reduced-order model can include the current topology and the excitation source signal. The current topology can refer to the topology defined by the level set function. The spatial permittivity / permeability distribution is determined, and the excitation source signal can be a current source at the antenna port. wait.

[0030] The output of the state-space reduced-order model is the predicted electromagnetic field vector after the state-space reduced-order model is reconstructed back into the high-dimensional physical space, which is also the state vector. Or the final global steady-state electric field vector .

[0031] The training process of the state-space reduced-order model in this application is a self-supervised process of guessing, verifying, and correcting. The state-space reduced-order model first outputs a predicted global steady-state electric field vector based on the input; then, it substitutes this predicted global steady-state electric field vector into Maxwell's equations, and the difference between the left and right sides of the calculated equations is the physical residual; this physical residual is used as a self-supervised loss function, and the A, B, C, and D parameters of the system evolution matrix are updated in reverse using the AdamW optimizer until the physical residual approaches 0, at which point the state-space reduced-order model converges to the local electromagnetic reduced-order model.

[0032] Relying on the powerful sequence and ODE processing capabilities of SSM, the state-space reduced-order model can quickly converge to an effective local electromagnetic reduced-order model under a given topology, thereby achieving high-fidelity, fully differentiable electromagnetic field response prediction without the need for external simulation data.

[0033] For solving the electromagnetic field at a center frequency of 140 GHz in the D band, since the time-domain Maxwell's curl equation cannot be directly input into a conventional neural network, this embodiment first performs a central finite difference approximation on a fixed spatial grid to transform the infinite-dimensional PDE into a large-scale ordinary differential equation system with respect to time evolution, i.e., a finite ordinary differential equation system. The finite ordinary differential equation system can be expressed as: Among them, the full state vector Includes global electric field components and global magnetic field components , In this embodiment, the term "system excitation term" specifically refers to the port current source of the antenna. For level set function The parameterized spatial discrete differential operator matrix contains the spatial permittivity. and permeability distribution.

[0034] In some embodiments, a state-space reduced-order model is used to perform spatiotemporal dimensionality reduction modeling of a finite ordinary differential equation system, mapping the high-dimensional state to a low-dimensional latent space. Its dynamic evolution process can be represented as follows: Where A, B, C, and D are the learnable parameters of the state-space reduced-order model, which are also the aforementioned system evolution matrices. It is a low-dimensional latent space state vector. The predicted electromagnetic field vector output by the reduced-order state-space model contains the global steady-state electric field vector predicted by the model. And the corresponding magnetic field vector. Utilizing the continuous-time representation capability of the state-space reduced-order model, the discretized representation is transformed into efficient convolution operations or global recursion.

[0035] Subsequently, the self-supervised training phase of the state-space reduced-order model begins. The predicted electromagnetic field vector output from the state-space reduced-order model... Extract the predicted global steady-state electric field vector. Substituting these values ​​into the actual physical equations, the physical residuals of Maxwell's equations are used as the self-supervised loss function. This self-supervised loss function is used to measure whether the global steady-state electromagnetic field predicted by the state-space reduced-order model satisfies the physical constraints of the steady-state Helmholtz equations.

[0036] Let be the total state vector of the entire finite ordinary differential equation system. In the discretization of Maxwell's equations, to fully describe the electromagnetic field, this total state vector simultaneously includes both electric and magnetic field components, i.e. . It is the electric field vector, it is Part of this large collection.

[0037] In some embodiments, the self-supervised loss function can be calculated using the following formula: in, Represents the curl operator, Spatial permeability, The global steady-state electric field vector predicted by the reduced-order state-space model. Angular frequency, For the current level set function The spatial permittivity is determined. The port excitation current density in the frequency domain. The imaginary unit, This represents the squared L2 norm of the residual energy calculation.

[0038] In summary, this application constructs a self-supervised loss function at sampling points within the design domain, using the steady-state Helmholtz equation residuals, port excitation conditions, and absorbing boundary conditions. The AdamW optimizer drives the SSM for self-supervised learning, continuously updating the learnable parameters A, B, C, and D through backpropagation. Leveraging the powerful temporal and ODE processing capabilities of the state-space reduced-order model, it can quickly converge to an effective local electromagnetic reduced-order model under a given topology, thus achieving high-fidelity, fully differentiable global steady-state electromagnetic field response prediction without requiring any external simulation data labels.

[0039] S3. Obtain the gradient velocity field of the horizontal set function based on the local electromagnetic order reduction model. Continuously evolve the horizontal set function based on the gradient velocity field to obtain the final horizontal set function. The final horizontal set function is used for the automated design of the antenna to obtain the final antenna topology.

[0040] In some embodiments, obtaining the normal gradient velocity field of the level set function based on the local electromagnetic order reduction model may include: representing the antenna performance target as a functional that depends on the electromagnetic field distribution output by the local electromagnetic order reduction model, and using the adjoint state method to obtain the topological gradient of the performance target with respect to the level set function as the normal gradient velocity field.

[0041] Specifically, the antenna's performance metrics can be expressed as a complex functional that depends on the solution of a local electromagnetic reduced-order model. In some embodiments, the performance target can be the antenna's return loss S. 11 Because of S 11 It is not directly and explicitly determined by spatial coordinates, but rather by the distribution of the steady-state electromagnetic field in space. According to Maxwell's equations in the frequency domain, the steady-state magnetic field in space can be uniquely determined by the curl of the steady-state electric field, i.e., the global steady-state electric field vector. It is sufficient to completely and equivalently characterize the entire steady-state electromagnetic field distribution.

[0042] Furthermore, this electric field distribution is physically strictly controlled by the level set function characterizing the microscopic topological structure. Based on the above physical equivalence, S can be... 11 Represented as the global steady-state electric field vector extracted from the SSM output. functionals By constructing a functional, a mathematically precise differentiable mapping relationship between macroscopic performance indicators and microscopic topological structures is established, thus providing a rigorous theoretical basis for obtaining topological gradients using the adjoint state method (which only requires calculation of the electric field).

[0043] To find the update direction of the level set function that drives performance optimization, the adjoint state method can be used to calculate the normal gradient velocity field of the performance objective with respect to the level set function. Specifically, the adjoint Helmholtz equation corresponding to the steady-state Helmholtz equation is constructed and solved to obtain the adjoint electromagnetic field distribution. Since the SSM simulator is fully differentiable, solving the adjoint equations is practically equivalent to solving the functional equations along the feedback path. Perform an automatic differentiation backpropagation calculation for the objective function.

[0044] Subsequently, the global steady-state electric field vector predicted by SSM was used. and the accompanying electromagnetic field distribution obtained by backpropagation The spatial dot product is used to derive the performance objective for the level set function at the boundary. Normal gradient velocity field : in, To take the real part of a complex number, This represents the derivative of the spatial permittivity with respect to the horizontal set function. The normal gradient velocity field... Accurately quantified the effect of minute displacements of the physical boundary on the whole. The magnitude and direction of the impact on performance.

[0045] In some embodiments, the continuous evolution of the level set function based on the normal gradient velocity field may include: substituting the normal gradient velocity field into the Hamilton-Jacobi equation to drive the level set function to continuously evolve on a fixed grid according to the Hamilton-Jacobi equation. The theoretical expression of the Hamilton-Jacobi equation is: In the actual numerical solution and continuous evolution process, in order to ensure the smoothness of the generated topology, constrain the geometric complexity, and meet manufacturing process rules (such as preventing the generation of tiny holes or sharp angles), a curvature penalty term is introduced in the evolution. In the level set method, the curvature penalty is equivalent to regularizing the perimeter of the antenna boundary. The specific discrete iterative formula for updating the level set function numerically is as follows: in To provide a pseudo-time step that follows the CFL (Courant-Friedrichs-Lewy) stability condition, This is the curvature penalty weighting coefficient.

[0046] In each iteration where the topological boundary undergoes a minor evolution, the local electromagnetic order reduction model will be based on a new... Boundary conditions are fine-tuned in a very small number of steps under self-supervised guidance to quickly adapt to new boundary conditions and output updated gradients to guide the next evolution step. After a certain number of evolution steps, the level set function is reinitialized to restore its signed distance function property. This process iterates until the performance target meets the preset design specifications or the current iteration count reaches the maximum iteration count, resulting in the final level set function.

[0047] In some embodiments, the automated design method for radio frequency antennas based on state-space order reduction model and level set topology optimization may further include: extracting the zero level set contour from the final level set function, converting the zero level set contour into an explicit polygon, submitting it to 3D full-wave electromagnetic simulation software for verification, and exporting the verified explicit polygon as a GDSII format layout file.

[0048] Specifically, the zero-isosurface profile can be extracted from the ultimately converged level set function. This profile represents the precise geometric boundary of the optimal antenna, and morphological filtering is applied to ensure it meets the minimum feature size requirements of the 65nm CMOS process. This profile is then transformed into an explicit polygonal geometric entity. This geometric entity is imported into commercial full-wave electromagnetic simulation software for high-precision physical verification, and the finally verified geometry is exported as an industry-standard GDSII layout file, completing the entire automated design process.

[0049] This process generates a smooth and physically consistent topology, fundamentally avoiding the checkerboard and mesh dependency problems caused by pixelation methods.

[0050] In this application, the antenna topology is implicitly represented using a level set function. Subsequently, a state-space reduced-order model is used for spatiotemporal dimensionality reduction modeling. Through self-supervised training using physical residuals, the model converges to a high-precision local electromagnetic reduced-order model. Finally, the level set function is continuously evolved using the local electromagnetic reduced-order model to obtain the final level set function. This application's embodiment achieves zero-sample topology optimization without requiring a large amount of simulation data, solving the problems of poor physical consistency in existing AI models and low optimization efficiency caused by the non-differentiability of commercial software.

[0051] This application combines high-degree-of-freedom model reconstruction with electromagnetic physics analysis, and efficiently optimizes the antenna topology and parameters through multiple granular stages, realizing the automatic generation of high-performance complex topology antennas with limited computing resources.

[0052] Those skilled in the art will understand that all or part of the features / steps of the above-described method embodiments can be implemented by methods, data processing systems, or computer programs. These features may be implemented without hardware, entirely in software, or in a combination of hardware and software. The aforementioned computer program may be stored in one or more computer-readable storage media. When the computer program is executed (e.g., by a processor), it performs the steps of the above-described embodiments of the automated RF antenna design method based on a state-space reduced-order model and level set topology optimization.

[0053] The aforementioned storage media capable of storing program code include: static hard disks, solid-state hard disks, random access memory (SRAM), electrically erasable programmable read-only memory (EEPROM), erasable programmable read-only memory (EPROM), programmable read-only memory (PROM), read-only memory (ROM), optical storage devices, magnetic storage devices, flash memory, magnetic disks or optical disks, and / or combinations of the above devices, that is, they can be implemented by any type of volatile or non-volatile storage devices or combinations thereof.

[0054] This application also provides a processing device embodiment, including one or more processors and a memory; wherein the memory is used to store one or more computer programs, and the one or more processors are used to execute the one or more computer programs stored in the memory, so that the processors execute the features / steps of the above-described embodiment of the automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization.

[0055] The above description is merely a preferred embodiment of this application. Those skilled in the art will understand that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of this application. Furthermore, under the teachings of this application, these features and embodiments can be modified to adapt to specific situations and materials without departing from the spirit and scope of this application. Therefore, this application is not limited to the specific embodiments disclosed herein, and all embodiments falling within the scope of the claims of this application are within the protection scope of this application.

Claims

1. An automated design method for radio frequency antennas based on a state-space reduced-order model and level set topology optimization, characterized in that, include: A horizontal set function is constructed to characterize the antenna topology, and the horizontal set function is initialized using the symbol distance function to obtain the initial horizontal set function; The partial differential equations describing the electromagnetic field distribution are transformed into a finite ordinary differential equation system through semi-discretization. The state-space reduced-order model is used to perform spatiotemporal dimensionality reduction modeling on the finite ordinary differential equation system. The physical residuals of Maxwell's equations are used as a self-supervised loss function to drive the state-space reduced-order model to perform self-supervised training based on the initial level set function, so that the state-space reduced-order model converges to the local electromagnetic reduced-order model. The normal gradient velocity field of the horizontal set function is obtained based on the local electromagnetic order reduction model. The horizontal set function is continuously evolved based on the normal gradient velocity field to obtain the final horizontal set function. The final horizontal set function is used for the automated design of the antenna to obtain the final antenna topology.

2. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 1, characterized in that, The step of obtaining the normal gradient velocity field of the horizontal set function based on the local electromagnetic order reduction model includes: representing the antenna performance target as a functional that depends on the electromagnetic field distribution output by the local electromagnetic order reduction model, and obtaining the topological gradient of the performance target with respect to the horizontal set function using the adjoint state method, as the normal gradient velocity field.

3. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 2, characterized in that, The step of continuously evolving the level set function based on the normal gradient velocity field includes: substituting the normal gradient velocity field into the Hamilton-Jacobi equation to drive the level set function to continuously evolve on a fixed grid in accordance with the Hamilton-Jacobi equation.

4. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 2, characterized in that, The performance target is the antenna's return loss S. 11 .

5. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 1, characterized in that, The horizontal set function determines the metallic region, dielectric region, and boundary of the antenna based on the sign. The horizontal set function is expressed as: in, Indicates the metallic area of ​​the antenna, Indicates the medium region, It represents the boundary between the metallic region and the dielectric region.

6. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 1, characterized in that, The initialization of the horizontal set function using the symbolic distance function includes: obtaining the symbolic distance function values ​​of each sub-geometry in the antenna topology, and merging the symbolic distance function values ​​using a polynomial smooth minimization operation.

7. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 1, characterized in that, The finite ordinary differential equation system is expressed as: Among them, the full state vector Includes global electric field components and global magnetic field components , For system incentive terms, It is the spatial discrete differential operator matrix determined by the parameterization of the level set function.

8. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 1, characterized in that, The spatiotemporal dimensionality reduction modeling of the finite ordinary differential equation system using the state-space reduced-order model is expressed as follows: Where A, B, C, and D are the learnable parameters of the state-space reduced-order model. It is a low-dimensional latent space state vector. The predicted electromagnetic field vector output by the reduced-order state-space model.

9. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 1, characterized in that, The self-supervised loss function is calculated using the following formula: in, Represents the curl operator, Spatial permeability, The global steady-state electric field vector predicted by the reduced-order state-space model. Angular frequency, For the current level set function The spatial permittivity is determined. The port excitation current density in the frequency domain. The imaginary unit, This represents the squared L2 norm of the residual energy calculation.

10. The automated design method for radio frequency antennas based on state-space reduced-order model and level set topology optimization according to claim 1, characterized in that, The automated design method for radio frequency antennas based on state-space order reduction model and level set topology optimization further includes: extracting the zero level set contour from the final level set function, converting the zero level set contour into an explicit polygon, submitting it to 3D full-wave electromagnetic simulation software for verification, and exporting the verified explicit polygon as a GDSII format layout file.

Images