A physical information fusion-based surface acoustic wave resonator reverse design method

Abstract

The application discloses a kind of based on physical information fusion's surface acoustic wave resonator reverse design method, belong to surface acoustic wave device design technical field.The method includes model training stage and reverse design stage: model training stage is trained forward agent model by constructing the feature vector containing coupled mode theory physical prior, construct the reverse model with the bounded mapping mechanism of output layer, complete training by parameter supervision and closed loop consistency joint loss fine tuning;Reverse design stage inputs the target performance specification into reverse model, generates multiple starting point discrete candidate center after processing, then utilizes forward agent model to carry out multidimensional score and two-stage local repair from coarse to fine, finally, the optimal structure parameter is output by multi-objective joint constraint determination.The application integrates physical prior into agent model, improves the success rate of multi-objective reverse design and the prediction accuracy of forward by bounded reverse output, manufacturing constraint filtering and closed loop local repair link, and considers efficiency and practicability.

Description

Technical Field

[0001] This invention relates to the field of surface acoustic wave (SAW) device design technology, and in particular to a reverse design method for SAW resonators based on physical information fusion. Background Technology

[0002] Surface acoustic wave (SAW) resonators are micro-acoustic devices that utilize the propagation of acoustic waves on the surface of a piezoelectric substrate to achieve frequency selection. With their advantages of small size, high integration, and excellent frequency selectivity, they are widely used in RF front-end modules in mobile communications, IoT terminals, and satellite navigation, and are key fundamental components of modern wireless communication systems. A typical two-port resonant SAW device consists of a piezoelectric substrate, an interdigital transducer (IDT), and a reflector grating. Its core design requirement is to achieve precise matching of key performance indicators such as quality factor Q, insertion loss IL, and bandwidth bw by optimizing key structural parameters such as the number of electrode pairs in the interdigital transducer, the number of electrode pairs in the reflector grating, and the spacing between them.

[0003] Based on coupled-mode (COM) theory, the reflectivity of the periodic electrode structure of a surface acoustic wave (SAW) resonator approximately satisfies a tanh-type nonlinear saturation relationship with the number of electrode pairs. Furthermore, the effective coupling coefficients of the interdigital transducers and reflective gratings differ due to variations in structural function, value range, and coupling strength. These physical characteristics result in a highly nonlinear, multi-peak, and multimodal response surface from structural parameters to performance indicators. Simultaneously, numerous failure regions exist within the parameter boundaries, preventing the formation of effective resonance. This presents a significant technical challenge to the reverse engineering of the SAW resonator's structural parameters.

[0004] Currently, there are three main approaches to reverse engineering the structural parameters of SAW resonators, each with its own significant drawbacks. The first approach is heuristic search methods, including genetic algorithms, particle swarm optimization, and Bayesian optimization. These methods search a continuous parameter space, but key structural parameters of SAW devices, such as the number of electrode pairs, are inherently discrete integers and are constrained by process limitations such as lithography resolution and grid layout. The results of continuous optimization require additional discretization before use, which can easily introduce accuracy loss in intermediate steps.

[0005] The second approach is the direct inverse mapping method using neural networks. In recent years, publicly available schemes have directly used the complete admittance response spectrum of SAW devices as input to the inverse network to predict structural parameters and material properties. Other schemes employ a multi-subnetwork parallel output structure to alleviate the one-to-many mapping problem. However, these methods generally suffer from three limitations: first, the inverse model output is an unbounded continuous value, not correlated with the device's physical boundaries and manufacturing constraints; second, it does not embed prior physical knowledge such as COM theory into the model input, limiting prediction accuracy; and third, existing inverse outputs are often directly used as the final design result, or only perform simple local searches, lacking scoring and local repair stages after candidate generation, making it difficult to stably obtain feasible solutions in scenarios where multiple performance indicators must be satisfied simultaneously.

[0006] The third method is the full-space exhaustive method, which enumerates all discrete parameter combinations and evaluates them one by one. This method is still manageable in two-dimensional parameter spaces, but when extended to three dimensions or above, the number of combinations rapidly expands to tens of thousands or even higher, making the computational cost unacceptable in practical engineering. Summary of the Invention

[0007] The purpose of this invention is to provide a reverse design method for surface acoustic wave resonators (SAW) based on physical information fusion. This method overcomes the inherent defects of existing SAW resonator reverse design methods. By using a surrogate model based on physical information fusion and a closed-loop optimization link, it collaboratively integrates COM physical priors, manufacturing discrete constraints, prediction uncertainty evaluation, and local repair mechanisms. This gives the forward surrogate model better physical perception capabilities, makes the reverse output more consistent with actual manufacturing constraints, and improves the stable positioning capability of feasible structural parameters under the condition that multiple objective performance indicators are simultaneously limited. It achieves multi-objective structural parameter reverse design that balances prediction accuracy, solution efficiency, manufacturability, and physical consistency, while also being compatible with high-dimensional parameter space expansion.

[0008] To achieve the above objectives, this invention provides a reverse design method for surface acoustic wave resonators based on physical information fusion, which targets the performance specifications of quality factor Q, insertion loss IL, and bandwidth bw of 3 dB, and forms a continuous model training stage and reverse design stage. The model training phase includes the following steps: S1. Sample data acquisition: Acquire a sample dataset of surface acoustic wave resonators. Each sample contains a set of structural parameters and performance indicators corresponding to the structural parameters. S2. Physically Inspired Feature Construction: Based on the Coupled Mode COM theory, feature transformation is performed on the structural parameters of the samples to construct physically inspired feature vectors; S3. Training of the forward proxy model F: Using the physical heuristic feature vector as input and the performance index corresponding to the sample as output, train the forward proxy model F of the multi-task learning architecture using the sample dataset; S4. Construction and pre-training of inverse model G: Construct an inverse model G with a fully connected network architecture. The output layer of the inverse model G is equipped with a bounded mapping mechanism to strictly constrain the output structural parameters within a preset physical boundary range. The inverse model G is pre-trained using the performance index of the sample as input and the corresponding structural parameters of the sample as output. S5. Closed-loop consistency training: The structural parameters output by the inverse model G are constructed using the same physically inspired features as in S2 and then input into the forward proxy model F with frozen parameters to obtain the reconstructed performance prediction value. The structural parameter supervised loss L is then used to obtain the predicted value. param A joint loss function L is constructed using the closed-loop consistency loss of the reconstructed performance prediction value relative to the input performance metric. cycle The inverse model G is fine-tuned using the joint loss function to complete model training; The reverse engineering phase includes the following steps: S6. Inverse Initial Prediction: Input the target performance specification vector to be achieved into the trained inverse model G, and output continuous structural parameter candidates within the preset physical boundary interval; S7. Post-processing: The continuous structural parameter candidates output by the inverse model G are sequentially subjected to boundary trimming, rounding to the nearest positive integer, and discrete adsorption processing to obtain discrete candidate centers that fall within the set of manufacturable discrete parameters. S8. Multi-starting point candidate generation: Apply at least two sets of random perturbations to the target performance specification vector to generate a corresponding number of input vectors, which are then input into the inverse model G. After the post-processing in step S7, a local neighborhood candidate set is obtained. S9. Candidate Scoring and Local Repair: The forward proxy model F is used to predict the performance of each candidate in the local neighborhood candidate set. Based on the prediction results, a multi-dimensional scoring function is constructed, which includes the target mismatch score M, the prediction uncertainty score U, and the cost proxy score C, to score all candidates. A two-stage local search from coarse to fine is used to optimize and repair the candidates. S10. Output Results: Perform multi-objective joint constraint judgment on all candidates and output the structural parameters with the best score that satisfy all constraints; if there are no candidates that satisfy the constraints, output the approximate feasible solution with the lowest score.

[0009] Preferably, in S1, the structural parameters include at least the number of interdigital transducer electrode pairs N1 and the number of reflector grating electrode pairs N2; the performance indicators include at least the quality factor Q, insertion loss IL, and 3 dB bandwidth bw; the sample dataset is derived from finite element simulation data aligned with actual measurements, measured data, and a combination of both.

[0010] Preferably, in S2, the physically inspired feature vector includes at least the tanh(κIDT·N1) type interdigital transducer reflection feature constructed for the number of interdigital transducer electrode pairs N1, the tanh(κg·N2) type reflective grating reflection feature constructed for the number of reflective grating electrode pairs N2, and the interaction feature between N1 and N2, wherein κg is less than κIDT, so that the physically inspired feature vector characterizes the nonlinear saturation law of the periodic electrode reflectivity of the surface acoustic wave resonator as a function of the number of electrode pairs; The physical heuristic feature vector further includes basic engineering features, nonlinear surrogate features, and normalized features; the basic engineering features include at least one of linear combination, product, square, ratio, and reciprocal of structural parameters; the nonlinear surrogate features include at least one of logarithmic transformation and square transformation of structural parameters; the normalized features include N1 / N1max and N2 / N2max, where N1max and N2max are the physical boundary upper limits of N1 and N2, respectively.

[0011] Preferably, in S2, for the number of interdigital transducer electrode pairs N1, at least two coupling coefficients κIDT are selected; for the number of reflector grating electrode pairs N2, at least two coupling coefficients κg are selected, and κg is less than κIDT; the COM physical prior features also include the interactive features after the transformation of N1 and N2.

[0012] Preferably, in S3, the forward proxy model F uses several independent models to form an integrated prediction structure, and outputs the predicted mean and prediction uncertainty of the performance index corresponding to the candidate structure parameters. The forward proxy model F includes a shared feature extraction backbone and multiple target-specific prediction heads. The shared feature extraction backbone consists of an input mapping layer and K residual modules connected in series, where K is an integer from 1 to 6, used to extract intermediate representations shared by multiple performance metrics. The input mapping layer is used to linearly project physically inspired feature vectors onto a hidden space of a preset dimension. The residual modules include a linear transformation layer, a nonlinear activation layer, a regularization layer, and an identity jump connection. Each target-specific prediction head corresponds to a performance metric and independently outputs the predicted value of the corresponding performance metric, including an independent normalization layer and a hidden layer. During training, a weighted robust loss function is used, and weights are configured differently for different performance indicators according to their dimensional range and learning difficulty. E independent forward agent models F are initialized and trained with E different random seeds, where E is an integer from 2 to 10. During inference, the mean of the predictions of the E models is output as the performance prediction value, and the standard deviation is output as the prediction uncertainty.

[0013] Preferably, in S4, the bounded mapping mechanism specifically refers to: ; Among them, Z iThis is the original output of the i-th structural parameter corresponding to the last layer of the inverse model G; N is the output value of the i-th structural parameter; imin and N imax These are the lower and upper limits of the physical boundary of the parameter, respectively; f(·) is a smooth activation function with a value range in the interval [0,1]; the smooth activation function includes the sigmoid function and the scaled tanh function.

[0014] Preferably, in S5, the joint loss function is: L=λ1×L param +λ2×L cycle ; Where λ1 and λ2 are positive real number weighting coefficients; L param Used to measure the deviation between the structural parameters output by the inverse model G and the true structural parameters of the sample; L cycle This is used to measure the deviation between the reconstructed performance prediction value of the forward proxy model F for the output structural parameters of the inverse model G and the input performance index; the reconstructed performance prediction value is obtained by first constructing the structural parameters output by the inverse model G into a physically inspired feature vector Φ(G(y)), and then inputting it into the forward proxy model F with frozen parameters, where y is the performance index vector of the input inverse model G.

[0015] Preferably, in S7, the boundary trimming is to trim the continuous structural parameter candidates to a preset physical boundary interval; the rounding is to round the trimmed continuous values ​​to positive integers; the discrete adsorption is to match the rounded integer parameters to the element with the smallest Euclidean distance in the set of manufacturable discrete parameters; the set of manufacturable discrete parameters consists of at least one of historical simulation samples, measured samples, and process permission parameter library, used to ensure that the discrete candidate centers satisfy the structural discreteness and manufacturing constraints of the surface acoustic wave resonator.

[0016] Preferably, in S9, the multi-dimensional scoring function is: ; Where M is the target mismatch score, measuring the deviation between the predicted performance and the target performance specification; U is the uncertainty score, derived from the standard deviation of the integrated predictions of the forward surrogate model F; C is the cost surrogate score, representing the manufacturing cost based on the combination of structural parameters; W m W u W c The weight coefficients are positive real numbers and satisfy W. m >W u >W c ; The two-stage local search includes: a coarse search stage: starting from the discrete candidate center, a first local neighborhood candidate set in Cartesian product form is generated in each structural parameter direction according to a preset first search radius and a first step length. The forward surrogate model F is used for scoring to select the optimal candidate for coarse repair; a fine search stage: starting from the optimal candidate for coarse repair, a second local neighborhood candidate set is generated according to a second search radius smaller than the first search radius and a second step length not greater than the first step length. The candidates are scored again; after deduplication of all candidates in the two stages, they are jointly sorted to obtain the optimal candidate after local repair.

[0017] Preferably, in S10, when determining the joint constraints of multiple objectives, a differentiated error measurement method is used for different performance indicators: a relative error is used for the quality factor. Absolute error is used for insertion loss. Absolute error is used for the 3 dB bandwidth. ;in, , and For the target performance specifications, Q IL and bw is the predicted mean output of the forward surrogate model F; when εQ≤τQ, εIL≤τIL and εbw≤τbw, the candidate structural parameters are determined to satisfy the multi-objective joint constraints, where τQ is the relative error threshold, and τIL and τbw are the absolute error thresholds.

[0018] Therefore, this invention employs the aforementioned reverse design method for surface acoustic wave resonators based on physical information fusion, incorporating the physical priors of COM theory as features into the surrogate model, effectively improving the accuracy of forward performance prediction. Simultaneously, a closed-loop design chain integrating bounded reverse output, discrete manufacturing constraints, multi-starting point generation, and coarse-to-fine local repair is constructed, reducing the probability of reverse prediction falling into the physical mismatch region, improving the stable location capability of feasible solutions under multi-objective joint constraints, and ensuring the manufacturability and engineering practicality of the design results.

[0019] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Attached Figure Description

[0020] Figure 1 This is an overall flowchart of the reverse design method for surface acoustic wave resonators based on physical information fusion, as described in this invention. Figure 2 This is a flowchart of the feature construction process of the present invention; Figure 3 This is a diagram of the forward proxy model architecture of the present invention; Figure 4 This is a flowchart of the reverse output post-processing of the present invention; Figure 5 This is a flowchart of the multi-starting point generation and coarse-to-fine local repair process of the present invention; Figure 6 This is the prediction fitting result of the forward proxy model F of the present invention on the sample data of surface acoustic wave resonators; Figure 7 This is a diagram illustrating the reverse closed-loop repair link effect of the present invention; Figure 8 This is a statistical graph of the forward integration prediction uncertainty of the present invention. Detailed Implementation

[0021] The technical solution of the present invention will be further described below with reference to the accompanying drawings and embodiments.

[0022] Unless otherwise defined, the technical or scientific terms used in this invention shall have the ordinary meaning understood by one of ordinary skill in the art to which this invention pertains. The terms "first," "second," and similar terms used in this invention do not indicate any order, quantity, or importance, but are merely used to distinguish different components. Terms such as "comprising" or "including" mean that the element or object preceding the word encompasses the elements or objects listed following the word and their equivalents, without excluding other elements or objects. Terms such as "connected" or "linked" are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. Terms such as "upper," "lower," "left," and "right" are used only to indicate relative positional relationships; when the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0023] Example 1 This embodiment provides a reverse design method for surface acoustic wave resonators based on physical information fusion. This method constructs a design chain that integrates physical priors, manufacturing constraints, and closed-loop optimization. The goal is to efficiently and accurately solve for manufacturable structural parameters based on desired performance indicators. For example... Figure 1 As shown, this method is divided into two consecutive stages: the model training stage and the reverse design stage.

[0024] I. Model Training Phase.

[0025] This phase aims to build and train the core models for subsequent reverse engineering, including a high-precision forward proxy model and a reverse model with physical boundary awareness. Specifically, it includes the following steps: S1. Sample Data Acquisition. Acquire a sample dataset of surface acoustic wave (SAW) resonators. Each sample contains a set of structural parameters and corresponding performance indicators. In this embodiment, the structural parameters include at least the number of interdigital transducer (IDT) electrode pairs N1 and the number of reflector grating electrode pairs N2. The performance indicators include at least the quality factor Q, insertion loss IL, and 3 dB bandwidth bw.

[0026] The sample data in this embodiment comes from finite element simulation. The finite element model is a high-fidelity COMSOL model verified by measured data, ensuring the reliability of the simulation data as a training source. The total number of samples is 2080, divided into 1664 training sets and 416 validation sets in an 8:2 ratio. The physical boundary interval of N1 is [20, 170], and the physical boundary interval of N2 is [60, 400]. The corresponding Q, IL, and bw of each sample are obtained through simulation calculation.

[0027] S2. Physically Inspired Feature Construction. Based on Coupled Mode COM theory, feature transformation is performed on the structural parameters of the samples to construct a set of physically inspired feature vectors. The total dimension is between 10 and 30; in this embodiment, it is set to 21 dimensions. The feature construction process is as follows: Figure 2 As shown, the features are specifically divided into four categories: 1) Basic engineering characteristics: used to characterize the coupling trend of the interdigital transducer and the reflector grid on a geometric scale, specifically including: linear combinations of structural parameters (e.g., N1, N2, N1+N2), products (e.g., N1×N2), squares (e.g., N1... 2 ), ratios (such as N2 / N1) and reciprocals (such as 1 / N1, 1 / N2), etc.

[0028] 2) COM physical prior features: 8 dimensions in total, which are the core features of this embodiment. Based on the physical law of the COM theory that the reflectivity of the periodic electrode structure exhibits a tanh-type saturation relationship with the number of electrode pairs, multiple sets of hyperbolic tangent tanh nonlinear transformations are performed on N1 and N2 respectively. Its core innovation lies in the use of "two-sided differentiated coupling coefficients".

[0029] For the number of IDT electrode pairs N1, at least two different coupling coefficients κIDT are selected, covering from weak to strong coupling. In this embodiment, κIDT values ​​of 0.03, 0.05, and 0.10 are chosen, and the feature tanh(κIDT·N1) is calculated. For the number of reflector electrode pairs N2, since the range of N2 is usually much larger than that of N1, to avoid premature saturation of this feature and loss of discriminability, the selected coupling coefficient κg should be smaller than κIDT to ensure that the tanh transform maintains a sufficient nonlinear gradient within the effective value range of N2. In this embodiment, κg values ​​of 0.005, 0.01, and 0.02 are chosen, and the feature tanh(κg·N2) is calculated. Further, intermediate coupling coefficients (κIDT=0.05, κg=0.01) are selected to construct interactive features tanh(κg·N2)×N1 and tanh(κIDT·N1)×N2, supplementing the 2-dimensional interactive features, for a total of 8-dimensional COM physical prior features.

[0030] 3) Nonlinear surrogate characteristics: Used to compensate for residual nonlinear effects in the resonant cavity characteristics, including logarithmic and square transformations of structural parameters. In this embodiment, these are specifically set as ln(N1), ln(N2), and N1. 2 N2 2 , .

[0031] 4) Normalization features: including N1 / N1max and N2 / N2max, where N1max and N2max are the upper limits of the physical boundaries of N1 and N2, respectively.

[0032] S3. Training the Forward Agent Model F. A multi-task learning architecture neural network is constructed as the forward agent model F. The forward agent model F uses several independent models to form an ensemble prediction structure, outputting the predicted mean and prediction uncertainty of the performance indicators corresponding to the candidate structure parameters. Training is performed using the physically inspired feature vectors constructed in S2 as input and the corresponding Q, IL, and bw performance indicators as outputs. Its specific architecture is as follows... Figure 3 As shown.

[0033] The forward proxy model F comprises a shared feature extraction backbone and three target-specific prediction heads. The shared feature extraction backbone consists of an input mapping layer and K residual modules cascaded together, used to extract intermediate representations shared by multiple performance metrics. K is an integer from 1 to 6, and in this embodiment, K is 3. The input mapping layer linearly projects the 21-dimensional input features into a 256-dimensional hidden space, followed by a GELU nonlinear activation function. Each residual module contains two linear transformation layers, a GELU activation layer, and a Dropout regularization layer. An identity jump connection is set at the end of the module, which adds the transformed path output to the input and then normalizes it using LayerNorm, used to extract intermediate representations shared by multiple performance metrics. The three target-specific prediction heads correspond to the three performance metrics Q, IL, and bw, respectively. Each prediction head contains one LayerNorm layer, one hidden layer (GELU activation), and a linear output layer, independently outputting the predicted value of the corresponding performance metric.

[0034] During training, a weighted Huber robust loss function is used, with weights allocated according to the dimensional range and learning difficulty of each metric. Since IL (Internal Loss) fluctuates significantly and is sensitive to structural changes, it has a higher learning difficulty and is assigned a higher task weight; Q (Quantitative Loss) and bw (Browser Loss) are relatively stable and assigned lower weights. To assess prediction uncertainty in subsequent steps, E forward proxy models F are initialized and trained independently using E different random seeds, forming a deep ensemble. In this embodiment, E is set to 5. During subsequent inference, the mean of the predictions from the five models is used as the final performance prediction value, and their prediction standard deviations are used as the prediction uncertainty.

[0035] S4, Construction and pre-training of the inverse model G.

[0036] Construct an inverse model G with a fully connected network architecture. The model's output layer has a bounded mapping mechanism. Pre-training is completed using the performance metrics of the samples as input and the structural parameters of the corresponding samples as output. The specific implementation details are as follows: The inverse model G is a fully connected network with an input layer → 3 hidden layers → output layer. Each hidden layer has a dimension of 128 and contains linear transformation, GELU nonlinear activation function and LayerNorm normalization layer. The model input is a standardized 3-dimensional target performance specification vector (Q, IL, bw), and the output is a 2-dimensional structural parameter candidate (N1, N2).

[0037] The output layer of the inverse model G is equipped with a bounded mapping mechanism to strictly constrain the output structural parameters within a preset physical boundary range; the bounded mapping mechanism is as follows: ; Among them, Z i This is the original output of the i-th structural parameter corresponding to the last layer of the inverse model G; N is the output value of the i-th structural parameter; imin and N imax These represent the lower and upper bounds of the physical boundary of the parameter, respectively; f(·) is a smooth activation function with a value range in the interval [0,1], including the sigmoid function and the scaled tanh function. In this embodiment, the boundary of N1 is [20,170], and the boundary of N2 is [60,400]; f(·) is the sigmoid activation function, with its value range strictly limited to the interval (0,1). During pre-training, the mean squared error loss function is used to initially train the inverse model G.

[0038] S5. Closed-Loop Consistency Training. To ensure that the output of the inverse model G not only closely approximates the true parameters numerically, but also that its performance, after validation by the forward model F, is consistent with the target specifications, this step fine-tunes the pre-trained inverse model G. Specifically, the structural parameters output by the inverse model G are constructed using the same physically inspired features as in S2 and then input into the frozen-parameter forward proxy model F to obtain the reconstructed performance prediction value. The predicted value is then determined based on the structural parameter supervised loss L. param A joint loss function L is constructed using the closed-loop consistency loss of the reconstructed performance predictions relative to the input performance metrics. cycle The inverse model G is fine-tuned using a joint loss function to complete model training. During this stage, a joint loss function is constructed that includes parameter supervision loss and loop closure consistency loss. The five ensemble model parameters of the forward proxy model F are frozen and do not participate in gradient updates.

[0039] The joint loss function consists of two parts: the parameter supervision loss L param Used to measure the deviation between the structural parameters output by the inverse model G and the true structural parameters of the sample; L cycle This is used to measure the deviation between the reconstructed performance prediction of the forward surrogate model F and the input performance index of the output structural parameters of the inverse model G. The reconstructed performance prediction is obtained by first constructing a physically inspired feature vector Φ(G(y)) from the output structural parameters of the inverse model G, and then inputting it into the forward surrogate model F with frozen parameters, where y is the performance index vector input to the inverse model G. The joint loss function is: L = λ1 × L param +λ2×L cycle Wherein, λ1 and λ2 are positive real-valued weight coefficients. In this embodiment, the weight coefficients λ1 and λ2 are set to 0.4 and λ2 to 0.6. Using this joint loss function as the optimization objective, the inverse model G is fine-tuned and trained, thereby establishing a consistency constraint between the inverse output and the forward physical response, completing the training chain of the entire model.

[0040] II. Reverse Engineering Stage.

[0041] This stage, based on the trained model, performs inverse structural parameter solving, process constraint filtering, local optimization, and result output for the target performance specifications, specifically including S6 to S10. The target performance specifications to be achieved in this embodiment are: target quality factor Q*=1300, target insertion loss IL*=15dB, and target bandwidth bw*=0.2MHz.

[0042] S6. Initial Inverse Prediction. After processing the target performance specification vector with standardized parameters consistent with the training phase, it is input into the trained inverse model G, and the output is a continuous candidate structure parameter located within the preset physical boundary interval. In this embodiment, the continuous candidates obtained by the initial prediction are N1=87.6 and N2=122.4, both of which fall within the preset physical boundary interval.

[0043] S7. Post-processing for industrial applications. The candidate continuous structural parameters output from the inverse model G are sequentially subjected to boundary trimming, rounding, and discretization. The post-processing flow is as follows: Figure 4 As shown, the specific steps are as follows: 1) Boundary clipping: The continuous candidates are clipped to the preset physical boundary interval [20,170], [60,400]. In this embodiment, the initial prediction result is already within the boundary, and the value remains unchanged after clipping. 2) Integer rounding: Round the clipped consecutive values ​​to the nearest positive integer to obtain integer candidates N1=88 and N2=122; 3) Discrete Adsorption: In this embodiment, the set of manufacturable discrete parameters consists of 2080 sets of historical simulation samples and 50 sets of actually verified process-permitted parameters. These parameters are used to ensure that the discrete candidate centers meet the structural discreteness and manufacturing constraints of the surface acoustic wave resonator. The rounded integer parameters are matched to the element with the smallest Euclidean distance in this set, ultimately resulting in discrete candidate centers N1=88 and N2=120, ensuring that the output parameters fall within the process-verified manufacturable range. This step yields the final "discrete candidate centers".

[0044] S8. Multiple Starting Point Candidate Generation. To address the "one-to-many" mapping relationship between the target performance and structural parameters of SAW devices and avoid getting trapped in local solutions in a single prediction, this step generates multiple candidate starting points around the target specifications. At least two sets of random perturbations (e.g., adding Gaussian noise numerically) are applied to the original target performance specification vector, generating at least two slightly different input vectors. These vectors are sequentially input into the inverse model G and processed through the post-processing steps in S7 to obtain P (P≥2) discrete candidate centers, i.e., local neighborhood candidate sets. These center points are expected to be distributed in different potential solution regions, providing multiple high-quality starting points for subsequent comprehensive searches. In this embodiment, the number of perturbations is 10, and the standard deviation of the perturbations is 0.05.

[0045] S9. Candidate Scoring and Local Repair. The performance of each candidate in the local neighborhood candidate set is predicted using a forward surrogate model F. A multi-dimensional scoring function is constructed, and a two-stage local search, from coarse to fine, is used to optimize and repair the candidates. The process is as follows: Figure 5 As shown, the specific implementation details are as follows: S91. Constructing a multi-dimensional scoring function: ; Where M is the target mismatch score, which measures the deviation between the predicted performance and the target performance specification, and its weight remains consistent with that of the forward model training phase; U is the uncertainty score, which is derived from the standard deviation of the integrated prediction of the forward surrogate model F. The larger the standard deviation, the higher the score, indicating that the model's prediction of the candidate point is more uncertain; C is the cost surrogate score, which characterizes the manufacturing cost based on the combination of structural parameters. In this embodiment, it is specifically the sum of the number of electrode pairs (N1+N2); W m W u W c The weight coefficients are positive real numbers and satisfy W. m >W u >W c， Specifically, the values ​​are set to 0.7, 0.2, and 0.1 respectively.

[0046] S92. Coarse Search Stage: Starting from each discrete candidate center, the first search radius in the N1 direction is set to ±8 pairs, and the first step length is 2 pairs. The first search radius in the N2 direction is set to ±80 pairs, and the first step length is 10 pairs. A first local neighborhood candidate set in Cartesian product form is generated. After constructing physical heuristic features for all candidates in the set, the features are input into the forward proxy model integration for performance prediction and scoring, and the optimal candidate for coarse repair is selected.

[0047] S93. Fine search stage: Taking the optimal candidate of coarse repair as the new starting point, set the second search radius of ±4 pairs and the second step size of 1 pair in the N1 direction, and set the second search radius of ±40 pairs and the second step size of 5 pairs in the N2 direction to generate the second local neighborhood candidate set, and perform prediction and scoring again; after deduplication of all candidates in the two stages, sort them together to obtain the optimal candidate after local repair.

[0048] S10. Result Output. For all optimal candidates generated from multiple starting points and after local refinement, a final multi-objective joint constraint determination is performed to select the final design scheme. During the determination, differentiated error measurement methods are used for different performance indicators: relative error is used for the quality factor. Absolute error is used for insertion loss. Absolute error is used for the 3 dB bandwidth. ;in, , and For the target performance specifications, Q IL and bw is the predicted mean output of the forward surrogate model F; when εQ≤τQ, εIL≤τIL, and εbw≤τbw, the candidate structural parameters are determined to satisfy the multi-objective joint constraints, where τQ is the relative error threshold, and τIL and τbw are the absolute error thresholds. Only when the errors of all performance indicators of a candidate do not exceed their corresponding thresholds is the candidate considered to satisfy the joint constraints.

[0049] The relevant results in this embodiment are as follows: This embodiment further validates the forward proxy model, reverse candidate generation, and closed-loop repair mechanism. First, the predicted values ​​and actual performance metrics of the forward proxy model are fitted using sample data, and the results are as follows: Figure 6 As shown. The quality factor Q, insertion loss IL, and bandwidth bw are related to R. 2 The values ​​are 0.8914, 0.9766, and 0.8218, respectively. These results demonstrate that the physically inspired features are physically consistent with the model training results, providing an effective performance prediction basis for subsequent candidate scores and local repairs.

[0050] Secondly, ablation verification was performed on the closed-loop repair link in the reverse design phase. For example... Figure 7 As shown, in the validation of 30 target specifications, the joint constraint satisfaction rate of the old behavior compatible configuration was 13.33%; this increased to 63.33% after using only bounded output; and further increased to 86.67% after adding multi-starting point candidate generation; the average total error was further reduced after superimposed coarse-to-fine local repair. Subsequently, end-to-end validation was performed on 100 target specifications. When only reverse output post-processing was performed, the multi-objective joint constraint satisfaction rate was 50.00%; after further performing local search based on forward surrogate model scoring, the joint constraint satisfaction rate reached 97.00%, with single-index satisfaction rates of Q, IL, and bw at 99.00%, 98.00%, and 99.00%, respectively. These results indicate that bounded output and fabrication post-processing can reduce unmanufacturable candidates, the multi-starting point mechanism can cover multiple potential solution regions, and coarse-to-fine local repair can further reduce performance mismatch and improve the stability of feasible solution localization under multi-objective joint constraints. Furthermore, the forward surrogate model uses an ensemble structure trained with 5 different random seeds. For the same candidate structural parameters, the ensemble model outputs the mean and standard deviation of the performance predictions, where the standard deviation serves as the uncertainty score U in the candidate scoring function. For example... Figure 8As shown, the prediction standard deviations P95 for Q, IL, and bw are approximately 53.32, 3.573 dB, and 0.01664 MHz, respectively (P95 is the 95th percentile, which means that after sorting all samples by their prediction standard deviations from smallest to largest, approximately 95% of the samples have prediction standard deviations not exceeding this threshold, with the remaining approximately 5% of samples located in the high uncertainty tail). Therefore, when target mismatches are similar, candidates with lower prediction uncertainties can be prioritized, thereby reducing the probability of high-risk candidates entering the final output.

[0051] Therefore, this invention employs the aforementioned reverse design method for surface acoustic wave resonators based on physical information fusion, incorporating the physical priors of COM theory as features into the surrogate model, effectively improving the accuracy of forward performance prediction. Simultaneously, a closed-loop design chain integrating bounded reverse output, discrete manufacturing constraints, multi-starting point generation, and coarse-to-fine local repair is constructed, reducing the probability of reverse prediction falling into the physical mismatch region, improving the stable location capability of feasible solutions under multi-objective joint constraints, and ensuring the manufacturability and engineering practicality of the design results.

[0052] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and not to limit them. Although the present invention has been described in detail with reference to preferred embodiments, those skilled in the art should understand that modifications or equivalent substitutions can still be made to the technical solutions of the present invention, and these modifications or equivalent substitutions cannot cause the modified technical solutions to deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A reverse design method for surface acoustic wave resonators based on physical information fusion, characterized in that, This includes a continuous model training phase and a reverse engineering phase; The model training phase includes the following steps: S1. Sample data acquisition: Acquire a sample dataset of surface acoustic wave resonators. Each sample contains a set of structural parameters and performance indicators corresponding to the structural parameters. S2. Physically Inspired Feature Construction: Based on the Coupled Mode COM theory, feature transformation is performed on the structural parameters of the samples to construct physically inspired feature vectors; S3. Training of the forward proxy model F: Using the physical heuristic feature vector as input and the performance index corresponding to the sample as output, train the forward proxy model F of the multi-task learning architecture using the sample dataset; S4. Construction and pre-training of inverse model G: Construct an inverse model G with a fully connected network architecture. The output layer of the inverse model G is equipped with a bounded mapping mechanism to strictly constrain the output structural parameters within a preset physical boundary range. The inverse model G is pre-trained using the performance index of the sample as input and the corresponding structural parameters of the sample as output. S5. Closed-loop consistency training: The structural parameters output by the inverse model G are constructed using the same physically inspired features as in S2 and then input into the forward proxy model F with frozen parameters to obtain the reconstructed performance prediction value. The structural parameter supervised loss L is then used to obtain the predicted value. param A joint loss function L is constructed using the closed-loop consistency loss of the reconstructed performance prediction value relative to the input performance metric. cycle The inverse model G is fine-tuned using the joint loss function to complete model training; The reverse engineering phase includes the following steps: S6. Inverse Initial Prediction: Input the target performance specification vector to be achieved into the trained inverse model G, and output continuous structural parameter candidates within the preset physical boundary interval; S7. Post-processing: The continuous structural parameter candidates output by the inverse model G are sequentially subjected to boundary trimming, rounding to the nearest positive integer, and discrete adsorption processing to obtain discrete candidate centers that fall within the set of manufacturable discrete parameters. S8. Multi-starting point candidate generation: Apply at least two sets of random perturbations to the target performance specification vector to generate a corresponding number of input vectors, which are then input into the inverse model G. After the post-processing in step S7, a local neighborhood candidate set is obtained. S9. Candidate Scoring and Local Repair: The forward proxy model F is used to predict the performance of each candidate in the local neighborhood candidate set. Based on the prediction results, a multi-dimensional scoring function is constructed, which includes the target mismatch score M, the prediction uncertainty score U, and the cost proxy score C, to score all candidates. A two-stage local search from coarse to fine is used to optimize and repair the candidates. S10. Output Results: Perform multi-objective joint constraint judgment on all candidates and output the structural parameters with the best score that satisfy all constraints; if there are no candidates that satisfy the constraints, output the approximate feasible solution with the lowest score.

2. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S1, the structural parameters include at least the number of interdigital transducer electrode pairs N1 and the number of reflective grating electrode pairs N2; the performance indicators include at least the quality factor Q, the insertion loss IL, and the bandwidth bw of 3 dB; the sample dataset is derived from finite element simulation data aligned with actual measurements, measured data, and a combination of both.

3. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S2, the physically inspired feature vector includes at least the tanh(κIDT·N1) type interdigital transducer reflection feature constructed for the number of interdigital transducer electrode pairs N1, the tanh(κg·N2) type reflection grating reflection feature constructed for the number of reflection grating electrode pairs N2, and the interaction feature between N1 and N2, wherein κg is less than κIDT, so that the physically inspired feature vector characterizes the nonlinear saturation law of the periodic electrode reflectivity of the surface acoustic wave resonator as a function of the number of electrode pairs; The physical heuristic feature vector further includes basic engineering features, nonlinear surrogate features, and normalized features; the basic engineering features include at least one of linear combination, product, square, ratio, and reciprocal of structural parameters; the nonlinear surrogate features include at least one of logarithmic transformation and square transformation of structural parameters; the normalized features include N1 / N1max and N2 / N2max, where N1max and N2max are the physical boundary upper limits of N1 and N2, respectively.

4. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S2, for the number of interdigital transducer electrode pairs N1, at least two coupling coefficients κIDT are selected; for the number of reflector grating electrode pairs N2, at least two coupling coefficients κg are selected, and κg is less than κIDT; the COM physical prior features also include the interactive features after the transformation of N1 and N2.

5. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S3, the forward proxy model F uses several independent models to form an integrated prediction structure, and outputs the predicted mean and prediction uncertainty of the performance index corresponding to the candidate structure parameters. The forward proxy model F includes a shared feature extraction backbone and multiple target-specific prediction heads. The shared feature extraction backbone consists of an input mapping layer and K residual modules connected in series, where K is an integer from 1 to 6, used to extract intermediate representations shared by multiple performance metrics. The input mapping layer is used to linearly project physically inspired feature vectors onto a hidden space of a preset dimension. The residual modules include a linear transformation layer, a nonlinear activation layer, a regularization layer, and an identity jump connection. Each target-specific prediction head corresponds to a performance metric and independently outputs the predicted value of the corresponding performance metric, including an independent normalization layer and a hidden layer. During training, a weighted robust loss function is used, and weights are configured differently for different performance indicators according to their dimensional range and learning difficulty. E independent forward agent models F are initialized and trained with E different random seeds, where E is an integer from 2 to 10. During inference, the mean of the predictions of the E models is output as the performance prediction value, and the standard deviation is output as the prediction uncertainty.

6. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S4, the bounded mapping mechanism is specifically as follows: ； Among them, Z i This is the original output of the i-th structural parameter corresponding to the last layer of the inverse model G; N is the output value of the i-th structural parameter; imin and N imax These are the lower and upper limits of the physical boundary of the parameter, respectively; f(·) is a smooth activation function with a value range in the interval [0,1]; the smooth activation function includes the sigmoid function and the scaled tanh function.

7. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S5, the joint loss function is: L=λ1×L param +λ2×L cycle ; Where λ1 and λ2 are positive real number weighting coefficients; L param Used to measure the deviation between the structural parameters output by the inverse model G and the true structural parameters of the sample; L cycle This is used to measure the deviation between the reconstructed performance prediction value of the forward proxy model F for the output structural parameters of the inverse model G and the input performance index; the reconstructed performance prediction value is obtained by first constructing the structural parameters output by the inverse model G into a physically inspired feature vector Φ(G(y)), and then inputting it into the forward proxy model F with frozen parameters, where y is the performance index vector of the input inverse model G.

8. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S7, the boundary trimming is to trim the continuous structural parameter candidates to a preset physical boundary interval; the rounding is to round the trimmed continuous values ​​to positive integers; and the discrete adsorption is to match the rounded integer parameters to the element with the smallest Euclidean distance in the set of manufactureable discrete parameters. The set of manufacturable discrete parameters consists of at least one of historical simulation samples, measured samples, and a process permission parameter library, and is used to ensure that the discrete candidate centers satisfy the structural discreteness and manufacturing constraints of the surface acoustic wave resonator.

9. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S9, the multi-dimensional scoring function is: Where M is the target mismatch score, measuring the deviation between the predicted performance and the target performance specification; U is the uncertainty score, derived from the standard deviation of the integrated predictions of the forward surrogate model F; C is the cost surrogate score, representing the manufacturing cost based on the combination of structural parameters; W m W u W c The weight coefficients are positive real numbers and satisfy W. m >W u >W c ; The two-stage local search includes: a coarse search stage: starting from the discrete candidate center, a first local neighborhood candidate set in Cartesian product form is generated in each structural parameter direction according to a preset first search radius and a first step length. The forward surrogate model F is used for scoring to select the optimal candidate for coarse repair; a fine search stage: starting from the optimal candidate for coarse repair, a second local neighborhood candidate set is generated according to a second search radius smaller than the first search radius and a second step length not greater than the first step length. The candidates are scored again; after deduplication of all candidates in the two stages, they are jointly sorted to obtain the optimal candidate after local repair.

10. The reverse design method for surface acoustic wave resonators based on physical information fusion according to claim 1, characterized in that, In S10, when determining multi-objective joint constraints, differentiated error measurement methods are used for different performance indicators: relative error is used for the quality factor. Absolute error is used for insertion loss. Absolute error is used for the 3 dB bandwidth. ;in, , and For the target performance specifications, Q, IL and bw is the predicted mean output of the forward surrogate model F; when εQ≤τQ, εIL≤τIL and εbw≤τbw, the candidate structural parameters are determined to satisfy the multi-objective joint constraints, where τQ is the relative error threshold, and τIL and τbw are the absolute error thresholds.

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