Artificial neural network microwave device wide-range modeling method based on multi-dimensional space division and dynamic adaptive sampling

Abstract

The invention discloses an artificial neural network microwave device wide-range modeling method based on multi-dimensional space division and dynamic adaptive sampling, and relates to the field of microwave device modeling. The invention provides a boundary smooth splicing method based on a Sigmoid function. And overlapping unit samples are shared by the adjacent sub-regions, so that rich data support is provided for the boundary region. And on the basis, a self-adaptive correction function is constructed by utilizing a Sigmoid function: according to the position of the sub-model on each dimension, single-side Sigmoid correction is adopted in a boundary partition, and double-side correction is adopted in a middle partition. Weighted fusion is only carried out in the boundary overlapping region in the correction, so that the outputs of adjacent sub-regions are in smooth transition, and the internal precision of each sub-model is not influenced. And finally, all the corrected sub-models are superposed to form a globally continuous and seamlessly spliced ANN model, so that the problem of boundary discontinuity in multi-dimensional and wide-range modeling is effectively solved.

Description

Technical Field

[0001] This invention relates to the field of microwave device modeling, and more particularly to wide-range modeling problems in multidimensional parameter spaces. Background Technology

[0002] In recent years, the rapid development of mobile communication technology has continuously driven the emergence of new processes, new materials, and new structures in microwave devices. To meet the ever-increasing demands of device design, modeling techniques based on Artificial Neural Networks (ANNs) have been widely applied in the microwave device design process. [1]-[5] ANNs (Abstract Neural Networks) simulate the information processing mechanism of the human brain's nervous system using mathematical methods. A well-trained neural network model can quickly and accurately represent the complex nonlinear relationship between input and output within the modeling space. Microwave device replacement models built based on ANNs can replace time-consuming full-wave electromagnetic simulations, enabling rapid optimization design and thus significantly improving design efficiency and shortening the development cycle.

[0003] However, in actual design processes, to meet diverse performance requirements, the geometric parameters of microwave devices often need to be optimized and adjusted over a wide range. [6]-[8] As the range of parameter variations expands, the nonlinearity between the device response and its geometric parameters increases significantly, posing a serious challenge to constructing a wide-range parameterized model that is both accurate and efficient. While theoretically feasible to use a single neural network to cover the entire parameter space, this requires a massive amount of training and testing samples, and sample generation is time-consuming, resulting in low overall modeling efficiency. Furthermore, this method often converges slowly, and the final model accuracy rarely meets expectations.

[0004] To alleviate the above problems, researchers proposed a parallel decomposition technique, which divides a wide-range parameter space into several sub-regions and builds sub-models for each, then combines them to form a complete model, thereby improving modeling speed. [9] However, this method still requires the pre-generation of a large number of uniformly distributed training samples throughout the modeling space for region division. Therefore, it is still limited by the bottleneck of large sample size and long sampling time, resulting in limited improvement in overall modeling efficiency.

[0005] Therefore, developing a new method capable of efficiently handling the parametric modeling of microwave devices with a wide range of parameters and high nonlinearity has become an urgent need. To this end, this invention proposes an artificial neural network modeling method based on multidimensional spatial partitioning and dynamic adaptive sampling. Through a systematic spatial decomposition and intelligent sampling strategy, it aims to achieve efficient and high-precision modeling of microwave devices across a wide range of parameter spaces.

[0006] References:

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[0008] [2]Feng F, Na W, Jin J, et al. ANNs for Fast Parameterized EMModeling: The State of the Art in Machine Learning for Design Automation ofPassive Microwave Structures[J]. IEEE Microwave Magazine, 2021, 22(10): 37-50.

[0009] [3]Y. Yu, Z. Zhang, Q. S. Cheng, B. Liu, Y. Wang, C. Guo, and T. T.Ye, “State-of-the-art: AI-assisted surrogate modeling and optimization formicrowave filters,” IEEE Transactions on Microwave Theory and Techniques,vol. 70, no. 11, pp. 4635–4651, 2022.

[0010] [4]Liu Z, Hu X, Liu T, et al. Attention-Based Deep Neural NetworkBehavioral Model for Wideband Wireless Power Amplifiers[J]. IEEE Microwaveand Wireless Components Letters, 2020, 30(1): 82-85.

[0011] [5]F. Feng, W. Na, J. Jin, J. Zhang, W. Zhang, and Q.-J. Zhang,“Artificial neural networks for microwave computer-aided design: The state ofthe art,” IEEE Transactions on Microwave Theory and Techniques, vol. 70, no.11, pp. 4597–4619, 2022.

[0012] [6]H. Kabir, V. Shilimkar, L. Zhang and K. Kim, "Large space RFICspiral inductor parametric modeling technique," 2015 IEEE MTT-S InternationalConference on Numerical Electromagnetic and Multiphysics Modeling andOptimization (NEMO), Ottawa, ON, Canada, 2015, pp. 1-3.

[0013] [7]P. Barmuta, G. Avolio, F. Ferranti, A. Lewandowski, L. Knockaertand D. M. M. . -P. Schreurs, "Hybrid Nonlinear Modeling Using AdaptiveSampling," in IEEE Transactions on Microwave Theory and Techniques, vol. 63,no. 12, pp. 4501-4510, Dec. 2015.

[0014] [8]H. Kabir, L. Zhang and K. Kim, "Automatic parametric modeldevelopment technique for RFIC inductors with large modeling space," 2017IEEE MTT-S International Microwave Symposium (IMS), Honololu, HI, USA, 2017,pp. 551-554.

[0015] [9]W. Zhang, F. Feng, J. Zhang, Z. Zhao, J. Ma and Q. -J. Zhang, "Parallel Decomposition Approach to Wide-Range Parametric Modeling WithApplications to Microwave Filters," in IEEE Transactions on Microwave Theoryand Techniques, vol. 68, no. 12, pp. 5288-5306, Dec. 2020. Summary of the Invention

[0016] This invention proposes a wide-range modeling method for microwave devices based on multidimensional spatial partitioning and dynamic adaptive sampling of artificial neural networks (ANN). This method achieves efficient non-uniform sampling and high-precision continuous modeling in a wide-range, high-dimensional parameter space by combining a systematic spatial decomposition strategy with dynamic adaptive sampling and boundary smoothing stitching technology based on the Sigmoid function. This effectively solves the core problems of traditional methods in terms of sampling efficiency, model accuracy and boundary continuity. The invention specifically includes the following: (1) In view of the problem of high sample generation cost and unreasonable distribution leading to low modeling efficiency in high-dimensional wide-range modeling space, this invention proposes a systematic spatial partitioning strategy based on key boundary points and minimum units, and designs a dynamic adaptive sampling mechanism on this basis. The mechanism first generates training sub-regions by equal division and overlapping expansion, and then extracts key boundary points to divide the entire domain into mutually exclusive "minimum units", distinguishing between overlapping units and non-overlapping units. Subsequently, DOE-AMG hybrid sampling is implemented for non-overlapping units: first, the Design of Experiment (DOE) method is used to generate initial samples, and then combined with Automatic Model Generation (AMG) technology, key regions (such as high nonlinear regions and sub-region boundaries) are dynamically identified based on model errors, and sampling points in these regions are adaptively increased to achieve "non-uniform high information density" sampling; for overlapping units, sampling is differentiated based on their volume to ensure sufficient data in the boundary regions. This mechanism significantly reduces the dependence on a large number of uniform samples and improves the sampling targeting and efficiency. (2) To overcome the boundary discontinuity problem that easily occurs when multiple sub-models are directly spliced, this invention proposes a boundary smoothing splicing method based on the Sigmoid function. By sharing overlapping unit samples between adjacent sub-regions, rich data support is provided for the boundary regions. On this basis, an adaptive correction function is constructed using the Sigmoid function: according to the position of the sub-model in each dimension, a single-sided Sigmoid correction is used in the boundary partition, and a double-sided correction is used in the middle partition. This correction is only weighted and fused in the boundary overlapping region, so that the output of adjacent sub-regions is smoothly transitioned without affecting the internal accuracy of each sub-model. Finally, all the corrected sub-models are superimposed to form a globally continuous and seamlessly stitched ANN model, effectively solving the problem of boundary discontinuity in multi-dimensional and wide-range modeling.

[0017] The method proposed in this invention specifically includes the following steps:

[0018] Step 1: Initialize modeling parameters.

[0019] For the modeling problem of N-dimensional microwave devices, the input design parameter vector x and its large-range modeling interval are defined, and the target model error threshold E is set. d (Recommendation E) d ≤ 2%), number of divisions in each dimension L i (Recommendation L)i ≥ 3) with spatial overlap coefficient δ.

[0020] Step 2: Spatial grid division and overlapping region construction.

[0021] Divide the parameter range equally into L in each dimension i First, mutually exclusive grid sub-regions are constructed. Then, the boundaries of each sub-region are expanded outward according to the overlap coefficient δ to construct training sub-regions with overlapping areas, providing a structural basis for subsequent boundary smoothing.

[0022] Step 3: Key point extraction and minimum unit division.

[0023] Extract the boundary points of all training sub-regions in each dimension, sort them to form a keypoint sequence; use this sequence to subdivide the global N-dimensional parameter space into multiple mutually exclusive minimum units, and count the number P of training sub-regions covering each minimum unit. c According to P c The value divides the smallest unit into two categories: overlapping units (P) c >1) and non-overlapping units (P) c =1).

[0024] Step 4: Dynamic adaptive sampling execution.

[0025] For each non-overlapping unit, initial samples are generated using the DOE method. Combined with AMG technology, the sampling density is dynamically adjusted based on the current error of the sub-model, and sampling points are adaptively increased in key regions until the local model converges. For each overlapping unit, discriminative sampling is performed based on its geometric volume to ensure that all overlapping units have effective training data to support boundary fusion. The sampling process is model accuracy-oriented and implements efficient, non-uniform sampling across the entire domain.

[0026] Step 5: Sample allocation and parallel training of sub-models.

[0027] If a minimum unit is K c K training sub-regions cover (K c > 1), whose samples are shared by these sub-regions; if only one training sub-region is covered (K c = 1), then the sample is dedicated to that sub-region. Collect all the smallest unit samples covered by each training sub-region to form its training dataset, and train each local sub-model in parallel using a lightweight ANN structure (such as a single hidden layer network) until each sub-model reaches the target accuracy.

[0028] Step 6: Sigmoid boundary smoothing and integration with the global model.

[0029] To eliminate discontinuities at sub-model boundaries, a sigmoid correction function is adaptively applied based on the sub-model's position in the dimension: a one-sided correction is used when it is located at the dimension boundary, and a two-sided correction is used when it is located in the middle. The correction weights are naturally determined by the data distribution in the overlapping regions, ensuring a smooth transition. All corrected sub-models are then stacked and integrated into a globally continuous model.

[0030] Step 7: Global verification and iterative adjustment.

[0031] Evaluate the global model test error E on the independent test set. If E ≤ E d If the modeling is successful, then the modeling is successful; otherwise, return to step 1 and adjust the number of partitions L. i Alternatively, the overlap coefficient δ can be remodeled.

[0032] Compared to traditional methods, this invention significantly reduces the reliance on high-cost samples for wide-range microwave device modeling through a dynamic adaptive sampling mechanism. By sharing strong boundary information density through overlapping unit data and achieving seamless fusion of sub-models through Sigmoid boundary smoothing, it rapidly constructs high-precision, globally continuous ANN models of microwave devices within a wide-range, high-dimensional parameter space, significantly improving modeling efficiency and model usability.

[0033] The invention differs from existing technologies in two closely related core innovations, which together constitute a complete, efficient, and high-precision wide-range ANN modeling solution for microwave devices.

[0034] 1. Parallel modeling framework based on spatial grid partitioning and overlapping region sample reuse

[0035] Traditional parallel modeling methods achieve parallel training through region decomposition, but typically require each sub-region to generate training samples independently. This leads to inconsistencies in samples within overlapping areas of adjacent sub-regions, increasing the overall sampling cost and causing differences in response fitting in overlapping regions, which can easily lead to model boundary discontinuities. Steps 1 to 5 of this invention propose a systematic spatial grid partitioning and sample reuse mechanism, the core process of which is as follows:

[0036] For a wide-range modeling problem of a microwave device, the design parameter vector is first defined. and its corresponding electromagnetic response vector Where N represents the number of design parameters and M represents the number of corresponding electromagnetic responses. Each (x, y) constitutes a training data point.

[0037] Let the range matrix of the modeling space be...

[0038] (1)

[0039] Where X imin and X i max Let x represent the minimum and maximum values ​​of the i-th geometric parameter, respectively. i Range D i for

[0040] (2)

[0041] Each dimension x i Divided into L i Segments, each segment is [length missing]

[0042] (3)

[0043] Let the partition vector be L = [L1, L2, …, L N ] T Then the total number of mutually exclusive initial grid subregions is

[0044] (4)

[0045] To establish a foundation for a smooth transition, an overlap coefficient δ (typically δ ≤ 10%) is introduced, and the overlap length d in each dimension is calculated. 0i ,Right now

[0046] (5)

[0047] Based on this, the boundaries of each initial sub-region are expanded to generate N. R The k-th training sub-region with clearly overlapping areas. i -1) The interval of the i-th dimension of the subregion is [X i min +(k-1)d i X i min +(k-1)d i +d 0i When k = L i When the interval is [X i min +(L i -1)d i X i min +L i d i ].

[0048] Key Innovation 1: Constructing a mapping between key point grids and minimum units to achieve sample reuse.

[0049] Extract the boundary points of all training sub-regions in each dimension, and sort them to obtain the keypoint sequence P.i These key points are used to subdivide the global space into a series of mutually exclusive "minimum units." Each minimum unit is a multidimensional geometry between adjacent key points, totaling [number missing].

[0050] (6)

[0051] Where M i It is the number of key points in the i-th dimension.

[0052] Record the number P that each smallest unit is covered by the training sub-region. c When P c When P = 1, it is defined as a non-overlapping unit; when P = 1, it is defined as a non-overlapping unit. c When the value is greater than 1, it is defined as an overlapping unit. The core reuse mechanism established by this invention is: if a minimum unit is P c If a training sub-region is covered, then all sample points within it will be covered by this P. c Each sub-region shares the same data; otherwise, sample points are used only to cover a single sub-region. This fundamentally eliminates boundary sample inconsistencies and reduces the sampling requirements for overlapping regions by approximately (P0). c -1) / P c .

[0053] Key Innovation 2: Dynamic Adaptive Sampling Strategy

[0054] Based on the above classification, differentiated sampling is implemented to further improve efficiency:

[0055] (1) For non-overlapping units, DOE-AMG dynamic adaptive sampling is adopted. This process is carried out in stages. In the k-th stage, the horizontal vector l is defined. k The term is used to specify the number of partitions for each input dimension of the sample space. The concept of "level" is central to orthogonal sampling; it determines how the parameter space for each design variable is partitioned. For an N-dimensional problem, the "level" for each dimension can be viewed as an (N-1)-dimensional hyperplane.

[0056] First, use g-level ( Orthogonal DOE initialization of training sample set P 1 The corresponding initial horizontal vector l 1 Subsequently, for each subregion R ij Establish a local interpolation model F(x) ij Its output can be expressed as F(x) ij )=Jh, where J is the coefficient matrix to be determined, and h is a matrix containing... The vector of the product of all combinations, y ij This is the output value of the test sample. The model error e of each sub-region is evaluated using the test sample. ij k ,Right now

[0057] (7)

[0058] If the maximum error e max k =max(e ij k Less than the preset threshold E t (Recommendation E) t If the error rate is ≤ 2%, then the training samples are sufficient to represent the input-output relationship of the microwave device, and adaptive orthogonal sampling stops; otherwise, a new level l is added at the center of the sub-region with the largest error. new And generate a new sample x new The horizontal vector is then updated to proceed to the next stage (k=k+1). This mechanism enables "on-demand" dense sampling of highly nonlinear regions.

[0059] (2) For overlapping units, a fixed number of samples are taken based on their geometric volume to ensure that there is sufficient and consistent data support at the boundaries of the sub-regions, laying the foundation for smooth model splicing in the future. The core of the sampling strategy is to quantify the volume of each overlapping unit according to its combination characteristics in multidimensional space and allocate the number of sample points accordingly.

[0060] For the i-th dimension (i=1, 2, … , N), its parameter range can be systematically divided into three types of sub-intervals:

[0061] Type A (Long Non-overlapping Interval): Appears only at the beginning of this dimension, with a length of d. i The quantity is 1.

[0062] Type B (overlapping interval): appears at the boundary of every two adjacent equally divided segments, with a length of d. 0i The quantity is (L) i -1) items.

[0063] Type C (short non-overlapping interval): appears at the end of each equally divided segment except the initial segment, with a length of (d i -d 0i ), quantity is (L i -1) items.

[0064] Therefore, the total number of subintervals in each dimension is (2L) i -1), including L i One non-overlapping interval (1 Class A+(L) i -1) of C classes) and (L i -1) overlapping intervals (Class B).

[0065] An N-dimensional minimum overlapping unit is formed by independently selecting a type of sub-interval (A, B, or C) for each dimension, and at least one dimension must fall on the overlapping interval (type B). To achieve this, a set of binary selection variables α is defined for the i-th dimension. i , β i , γ i ∈{0, 1}, and satisfy α i + β i + γ i =1. These represent whether the dimension is selected from intervals A, B, and C, respectively. Let k A , k B , k C These represent the number of times type A, B, and C are selected from the number of design parameters N, respectively. , satisfying k A +k B +k C =N, and k B ≥ 1.

[0066] The geometric volume V of this minimum overlapping unit can be given by the product of the lengths of the selected intervals in each dimension:

[0067] (8)

[0068] Substituting into formula (5), the above volume formula can be simplified to:

[0069] (9)

[0070] Given that the overlap coefficient δ is typically small (δ ≤ 0.1), then δ < 1-2δ < 1-δ < 1. Therefore, the value of the volume V is mainly determined by... Dominant, i.e., the number of overlapping dimensions k B It is the key factor in determining the volume size.

[0071] Among all overlapping elements, the element with the smallest volume appears at k. B When N (i.e., all dimensions fall within the B-class interval) is equal to the volume of N, its volume is... .

[0072] We set a base sampling number m (which can be preset by the user according to accuracy requirements), which corresponds to the smallest unit of volume (V). min The number of sampling points is calculated. For any other overlapping unit, its volume and minimum volume V are calculated first. min The ratio R,

[0073] (10)

[0074] Then, combining the volume formula analysis, the ratio R is mainly determined by the number of overlapping dimensions k of the unit. B The decision was made. The number of sampling points was determined to be... .

[0075] After sampling, each training sub-region collects samples from all the smallest units it covers, forming an independent training dataset. Since boundary sample consistency has been resolved, each sub-region can be trained independently and in parallel using a simple ANN (a simple MLP structure with 1 or 2 hidden layers). The training of the t-th sub-model is achieved by minimizing its error function:

[0076] (11)

[0077] in This represents the output of the t-th sub-model. For the corresponding real electromagnetic simulation response, N t N represents the number of training samples required to train the t-th sub-model. f Indicates the number of frequency points, x k Let w represent the k-th training sample. t f represents the internal weights of the ANN in the t-th sub-model. q This represents the q-th frequency point. The training processes of different sub-models are independent of each other, making them naturally suitable for parallel training, thus significantly accelerating modeling.

[0078] 2. Sub-model boundary smoothing and global continuity ensemble method based on the Sigmoid function

[0079] The sub-models obtained from domain decomposition and parallel training are intermediate results. Directly concatenating them can lead to response jumps at the boundaries of sub-regions, resulting in complex multidimensional discontinuities that fail to meet design requirements such as gradient optimization. To address this issue, this invention proposes a boundary smoothing method based on the Sigmoid function. First, an index vector is defined for each sub-model. This is used to precisely locate its position in the global grid, i.e.

[0080] (12)

[0081] Where mod represents the modulo operation, and the sign pair This indicates rounding down to the nearest integer.

[0082] The necessary and sufficient condition for two sub-models to be adjacent is

[0083] (13)

[0084] Here, t1 and t2 represent the numbers of different sub-models.

[0085] For the t-th sub-model, based on its index λ i t Total number of divisions L i Adaptively along each dimension x i Constructing the correction function :

[0086] (1) If L i =1 (this dimension is not divided), then =1, no correction needed.

[0087] (2) If λ i t =1 (starting partition), then only apply along x i The corrected sigmoid function S on the boundary of the dimension i t,u (x i ),Right now

[0088] (14)

[0089] (3) If λ i t =L i (Termination partition), then only apply along x i The corrected sigmoid function S on the boundary of the dimension i t,l (x i ),Right now

[0090] (15)

[0091] (4) If 1 < λ i t < L i (For the middle partition), a bilateral correction is applied simultaneously at both the upper and lower boundaries, i.e.

[0092] (16)

[0093] The key parameters a (controlling the transition slope) and c (transition center) of the correction function are precisely calculated from the overlapping range of adjacent sub-regions. For example, for the upper boundary correction, its transition center c i t,u The center point of the boundary between adjacent sub-regions, with slope a i t,u =12 / d 0i Ensure that the correction is strictly limited to a width of d. 0i Within the overlapping area.

[0094] The total correction function of the t-th sub-model is the product of the correction functions of all its dimensions, i.e.

[0095] (17)

[0096] The corrected sub-model output is

[0097] (18)

[0098] Finally, by linearly superimposing all the corrected sub-models, a globally continuous model covering the entire modeling space is obtained, i.e.

[0099] (19)

[0100] The model's input consists of the microwave device's design parameters, and its output is the device's response. Due to the characteristics of the Sigmoid function, the sub-model functions in the internal regions remain unchanged, while only the sub-models at the boundaries are modified, thus ensuring the continuity, smoothness, and uniqueness of the global output.

[0101] In summary, the wide-range modeling method for microwave devices based on multi-dimensional spatial partitioning and dynamic adaptive sampling proposed in this invention has the following significant advantages over existing technologies: First, it significantly improves modeling efficiency. By introducing a systematic spatial grid partitioning, overlapping unit sample reuse mechanism, and DOE-AMG dynamic adaptive sampling strategy, this invention achieves efficient sharing and intelligent allocation of training data among multi-dimensional sub-regions. This mechanism not only avoids the problem of repeated generation and inconsistency of boundary samples in traditional parallel modeling, but also significantly reduces the total demand for high-cost electromagnetic simulation data by focusing on adaptive encrypted sampling in highly nonlinear regions. Thus, while ensuring the accuracy of more local sub-models, the overall modeling cycle is effectively shortened, providing key technical support for the rapid design and iteration of microwave devices. Second, it ensures the high accuracy and continuity of the global model. Addressing the core challenge of boundary response jumps caused by direct splicing of multiple sub-models, this invention proposes a dimension-adaptive boundary smoothing technique based on the Sigmoid function. This method utilizes the shared sample information provided by overlapping regions to accurately construct correction functions, achieving a natural and smooth transition of sub-models at the boundaries, and successfully constructing a globally continuous and high-precision unified ANN model. This characteristic enables the model to not only fit accurately over a wide range of parameter spaces, but also to produce smooth and differentiable outputs. It can be directly and reliably applied to gradient-based automated optimization design processes for microwave devices, greatly expanding the model's value. Attached Figure Description

[0102] Figure 1 This is a flowchart of the wide-range modeling method for microwave devices based on multi-dimensional spatial partitioning and dynamic adaptive sampling proposed in this invention;

[0103] Figure 2This is the device structure of an embodiment of the present invention (microstrip bandstop filter);

[0104] Figure 3 This is a comparison between the modeling results of the embodiment of the present invention (microstrip bandstop filter) and the global modeling method;

[0105] Figure 4 This is a comparison of the output characteristic curves of two models of the embodiment of the present invention (microstrip bandstop filter).

[0106] Figure 5 This is a comparison of the output characteristic curves of the test data of two models in this embodiment of the invention. Detailed Implementation

[0107] To make the objectives, technical solutions, and advantages of the present invention clearer, the implementation process of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments (microwave bandstop filter).

[0108] This embodiment uses, as follows: Figure 1 The illustrated artificial neural network modeling process based on multidimensional space partitioning and dynamic adaptive sampling is used for... Figure 2 The microstrip bandstop filter shown is modeled parametrically. Among all the dimensional and electrical parameters of the filter, three key dimensional parameters are selected as input variables for the model: x = [L0, L1, L2]. T Where L0 is the transmission line length between the two open branches, and L1 and L2 are the lengths of the open stubs on both sides and in the middle, respectively. Other dimensional parameters are set to fixed values: open stub widths W1 = 0.10523 mm, W2 = 0.2097 mm, microstrip line width W0 = 0.635 mm (characteristic impedance 50 Ω), alumina substrate thickness of 0.635 mm, and dielectric constant of 9.4. The model's output variable is the reflection coefficient S. 11 The real and imaginary parts, i.e., y = [RS] 11 IS 11 ] T The frequency range covers 5 GHz to 20 GHz, with 201 frequency points sampled uniformly. The parameter ranges for this modeling problem are: L0 from 1.7 to 4.8 mm, L1 from 1.8 to 4.8 mm, and L2 from 1.8 to 4.7 mm. All training and test data were generated using electromagnetic simulation software. The model accuracy target is set as the test error E. d ≤ 2%.

[0109] For this modeling problem, the parameters are first initialized. The input dimension N = 3, the output dimension M = 2, and the partition vector for each dimension L = [4, 4, 4]. TThe overlap coefficient δ = 1 / 11 ≈ 9.09%. Second, spatial partitioning and minimum unit generation are performed. Based on L, each dimension is equally divided to form 64 mutually exclusive grid sub-regions; the boundaries of each sub-region are expanded based on the overlap coefficient δ to generate 64 training sub-regions with overlapping areas; then, the boundary points of all training sub-regions are extracted, sorted, and deduplicated to obtain keypoint sequences, thus dividing the global space into 343 mutually exclusive minimum units, of which 64 are non-overlapping units and 279 are overlapping units. Third, dynamic adaptive sampling is performed. For each non-overlapping unit, the DOE method is used to generate initial samples, combined with AMG technology, to dynamically identify key regions (such as highly nonlinear regions) based on local interpolation model errors, and adaptively increase sampling points until the local model converges; for each overlapping unit, a fixed number of samples are sampled differentially based on its geometric volume to ensure consistent and sufficient data in the boundary regions; after all samples are generated, data are allocated to each training sub-region. Fourth, parallel training of sub-models is performed. Each training sub-region collects samples from all the smallest units it covers, forming an independent training dataset. A simple, lightweight ANN structure is used to train each sub-region in parallel to minimize local output errors. Fifth, a sigmoid correction function is adaptively applied based on the sub-model's position in the dimensionality, and all corrected sub-models are superimposed to form a globally continuous unified model. Finally, the test error of the global model is evaluated on an independent test set. This embodiment automatically obtains an accurate ANN replacement model with a test error of 1.97%, meeting the user's target accuracy requirements. The entire modeling process involved 2412 sample data points, with an adaptive sampling time of 29.31 hours and a total modeling time of 31.06 hours.

[0110] For comparison, a single global ANN modeling method is also used. [9] Modeling the microwave filter under the same precision target and comparing the results are as follows: Figure 3 and 4 As shown, traditional global modeling methods require significantly more samples and drastically increase modeling time. The algorithm proposed in this invention, through multi-dimensional space decomposition, sample reuse, dynamic adaptive sampling, and boundary smoothing techniques, reduces the sample size by approximately 24.6% and shortens the total modeling time by approximately 19% while maintaining accuracy, effectively improving modeling efficiency. This method effectively reduces reliance on high-cost simulation data, significantly improves modeling efficiency, and generates a globally continuous, high-precision ANN alternative model, suitable for subsequent rapid optimization design, and has good engineering practical value.

Claims

1. A wide-range modeling method for microwave devices based on multi-dimensional spatial partitioning and dynamic adaptive sampling using artificial neural networks. Step 1: Initialize modeling parameters; For the modeling problem of N-dimensional microwave devices, the input design parameter vector x and its large-range modeling interval are defined, and the target model error threshold E is set. d Number of divisions in each dimension L i Spatial overlap coefficient δ; Step 2: Spatial grid generation and overlapping region construction; Divide the parameter range equally into L in each dimension i First, mutually exclusive grid sub-regions are constructed. Then, the boundaries of each sub-region are expanded outward according to the overlap coefficient δ to construct training sub-regions with overlapping regions, providing a structural basis for subsequent boundary smoothing. Step 3: Key point extraction and minimum unit division; Extract the boundary points of all training sub-regions in each dimension, sort them to form a keypoint sequence; use this sequence to subdivide the global N-dimensional parameter space into multiple mutually exclusive minimum units, and count the number P of training sub-regions covering each minimum unit. c According to P c The value divides the smallest unit into two categories: overlapping units, i.e., P. c >1 and non-overlapping unit P c =1; Step 4: Dynamic adaptive sampling execution; For each non-overlapping unit, the DOE method is used to generate initial samples. Combined with AMG technology, the sampling density is dynamically adjusted according to the current error of the sub-model. The sampling points are adaptively increased in key regions until the local model converges. For each overlapping unit, differentiated sampling is performed based on its geometric volume. Step 5: Sample allocation and parallel training of sub-models; If a minimum unit is K c The training sub-region coverage is K c > 1, its samples are shared by these sub-regions; if it is only covered by one training sub-region, then K c = 1, then the sample is dedicated to this sub-region; collect all the smallest unit samples covered by each training sub-region to form its training dataset, and use a lightweight ANN structure to train each local sub-model in parallel until each sub-model reaches the target accuracy. Step 6: Integrating Sigmoid boundary smoothing with the global model; To eliminate the discontinuity of sub-model boundaries, a sigmoid correction function is adaptively applied based on the sub-model's position in the dimension: a one-sided correction is used when it is located at the dimension boundary, and a two-sided correction is used when it is located in the middle; all corrected sub-models are superimposed and integrated into a global continuous model. Step 7: Global verification and iterative adjustment; Evaluate the global model test error E on the independent test set; if E ≤ E d If so, the modeling is successful; Otherwise, return to step 1 and adjust the number of partitions L. i Alternatively, the overlap coefficient δ can be remodeled.

2. The method according to claim 1, characterized in that: For a wide-range modeling problem of a microwave device, the design parameter vector is first defined. and its corresponding electromagnetic response vector Where N represents the number of design parameters and M represents the number of corresponding electromagnetic responses; each (x, y) constitutes a training data point. Let the range matrix of the modeling space be... (1) Where X i min and X i max Let x represent the minimum and maximum values ​​of the i-th geometric parameter, respectively; parameter x i Range D i for (2) Each dimension x i Divided into L i Segments, each segment is [length missing] (3) Let the partition vector be L = [L1, L2, …, L N ] T Then the total number of mutually exclusive initial grid subregions is (4) To establish a foundation for a smooth transition, an overlap coefficient δ is introduced, and the overlap length d in each dimension is calculated. 0i ,Right now (5) Based on this, the boundaries of each initial sub-region are expanded to generate N. R The k-th training sub-region with clearly overlapping areas; the k-th (k = 1, 2, …, L) i -1) The interval of the i-th dimension of the subregion is [X i min +(k-1)d i X i min +(k-1)d i +d 0i When k = L i When the interval is [X i min +(L i -1)d i X i min +L i d i ]; Extract the boundary points of all training sub-regions in each dimension, and sort them to obtain the keypoint sequence P. i And using these key points, the global space is subdivided into a series of mutually exclusive "minimum units"; each minimum unit is a multidimensional geometry between adjacent key points, totaling 1. (6) Where M i It is the number of key points in the i-th dimension; Record the number P that each smallest unit is covered by the training sub-region. c When P c When P = 1, it is defined as a non-overlapping unit; when P = 1, it is defined as a non-overlapping unit. c When the value is greater than 1, it is defined as an overlapping unit; The reuse mechanism is: if a minimum unit is P c If a training sub-region is covered, then all sample points within it will be covered by this P. c Each sub-region shares the same data; otherwise, sample points are used only to cover a single sub-region. This fundamentally eliminates boundary sample inconsistencies and reduces the sampling requirements for overlapping areas by approximately (P0). c -1) / P c ; Based on the above classification, differentiated sampling is implemented to further improve efficiency: (1) For non-overlapping units, DOE-AMG dynamic adaptive sampling is adopted; this process is carried out in stages. In the k-th stage, the horizontal vector l is defined. k , is used to specify the number of partitions for each input dimension of the sample space; for an N-dimensional problem, the "level" of each dimension can be viewed as an (N-1)-dimensional hyperplane; First, use g-level ( Orthogonal DOE initialization of training sample set P 1 The corresponding initial horizontal vector l 1 ; Subsequently, for each subregion R ij Establish a local interpolation model F(x) ij Its output can be expressed as F(x) ij )=Jh, where J is the coefficient matrix to be determined, and h is a matrix containing... The vector of the product of all combinations, y ij This is the output value of the test sample; the model error e of each sub-region is evaluated using the test sample. ij k ,Right now (7) If the maximum error e max k =max(e ij k Less than the preset threshold E t E t If the error is ≤ 2%, then the training samples are sufficient to represent the input-output relationship of the microwave device, and adaptive orthogonal sampling stops; otherwise, a new level l is added at the center of the sub-region with the largest error. new And generate a new sample x new Update the horizontal vector to enter the next stage, i.e., update k to k+1; (2) For overlapping units, a different fixed number of samples are taken based on their geometric volume; For the i-th dimension, i=1, 2, … , N, it is divided into three types of subintervals: Type A, i.e., long non-overlapping intervals: appear only at the beginning of this dimension, with a length of d. i The quantity is 1; Type B, or overlapping interval, occurs at the boundary between any two adjacent equally divided segments, with a length of d. 0i The quantity is (L) i -1) items; Type C, i.e., short non-overlapping intervals: appear at the end of each equally divided segment except the initial segment, with a length of (d i -d 0i ), quantity is (L i -1) items; Therefore, the total number of subintervals in each dimension is (2L) i -1), including L i One non-overlapping interval, i.e., one Class A+(L) i -1) C classes; and (L) i -1) overlapping intervals constitute class B; An N-dimensional minimum overlapping unit is formed by independently selecting a sub-interval (A, B, or C) for each dimension, and at least one dimension must fall on the overlapping interval (type B). To achieve this, a set of binary selection variables α is defined for the i-th dimension. i ,β i , γ i ∈{0, 1}, and satisfy α i + β i + γ i =1; these represent whether the dimension is selected from intervals A, B, and C, respectively; let k A , k B , k C These represent the number of times type A, B, and C are selected from the number of design parameters N, respectively. , satisfying k A +k B +k C =N, and k B ≥ 1; The geometric volume V of this minimum overlapping unit can be given by the product of the lengths of the selected intervals in each dimension: (8) Substituting into formula (5), the above volume formula can be simplified to: (9) Given that the overlap coefficient δ is usually small (δ ≤ 0.1), then δ < 1-2δ < 1-δ < 1; Among all overlapping elements, the element with the smallest volume appears at k. B =N, meaning that when all dimensions fall within the B-class interval, its volume is ; Let a base number of samples m be defined, which corresponds to the smallest unit of volume V. min The number of sampling points; for any other overlapping unit, first calculate its volume and minimum volume V. min The ratio R, (10) Then, combining the volume formula analysis, the ratio R is mainly determined by the number of overlapping dimensions k of the unit. B Decide; The number of sampling points was determined to be ; After sampling, each training sub-region collects samples from all the smallest units it covers, forming an independent training dataset. Since the boundary sample consistency has been resolved, each sub-region can be trained independently and in parallel using a simple ANN structure, i.e., a simple MLP structure with 1 or 2 hidden layers. The training of the t-th sub-model is achieved by minimizing its error function. (11) in This represents the output of the t-th sub-model. For the corresponding real electromagnetic simulation response, N t N represents the number of training samples required to train the t-th sub-model. f Indicates the number of frequency points, x k Let w represent the k-th training sample. t f represents the internal weights of the ANN in the t-th sub-model. q Indicates the q-th frequency point; A boundary smoothing method based on the Sigmoid function is proposed; firstly, an index vector is defined for each sub-model. This is used to precisely locate its position in the global grid, i.e. (12) Where mod represents the modulo operation, and the sign pair Indicates rounding down; The necessary and sufficient condition for two sub-models to be adjacent is (13) Where t1 and t2 represent the numbers of different sub-models; For the t-th sub-model, based on its index λ i t Total number of divisions L i Adaptively along each dimension x i Constructing the correction function : (1) If L i =1, this dimension is not divided. =1, no correction needed; (2) If λ i t =1, starting partition, then only apply along x i The corrected sigmoid function S on the boundary of the dimension i t,u (x i ),Right now (14) (3) If λ i t =L i That is, if the partition is terminated, then only the x-axis is applied. i The corrected sigmoid function S on the boundary of the dimension i t,l (x i ),Right now (15) (4) If 1 < λ i t < L i If the partition is in the middle, then bilateral corrections are applied simultaneously at both the upper and lower boundaries. (16) The key parameters of the correction function, controlling the transition slope 'a' and the transition center 'c', are precisely calculated from the overlapping range of adjacent sub-regions; for the upper boundary correction, its transition center 'c'... i t,u The center point of the boundary between adjacent sub-regions, with slope a i t,u =12 / d 0i Ensure that the correction is strictly limited to a width of d. 0i Within the overlapping area; The total correction function of the t-th sub-model is the product of the correction functions of all its dimensions, i.e. (17) The corrected sub-model output is (18) Finally, by linearly superimposing all the corrected sub-models, a globally continuous model covering the entire modeling space is obtained, i.e. (19) The input to the model is the design parameters of the microwave device, and the output is the response of the microwave device.

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