A neural network modeling method for filter frequency response behavior prediction

Abstract

This invention discloses a neural network modeling method for predicting the frequency response behavior of filters, relating to the field of thin-film filter frequency response prediction technology, and is used to solve the problem of poor prediction of physically realizable frequency response of filters. This invention constructs a neural network modeling link that characterizes the frequency response from structural parameters, material parameters, and process deviations. First, it performs frequency grid unification and phase continuity processing on complex frequency response labels to form a training sample set. Then, the neural network model outputs a set of physically realizable frequency response characterization parameters, which are then used by a frequency response reconstruction operator to generate a complex frequency response sequence. During training, passivity, causality, and stability are determined for the reconstructed frequency response. If these conditions are not met, projection correction is performed on the parameter set and the result is written back to ensure that the prediction result conforms to the physically realizable constraints. The projection correction trace is output during the prediction stage, enabling reliable traceability and anomaly localization of frequency response prediction, thus improving the efficiency and consistency of thin-film filter design iteration and mass production debugging.

Description

Technical Field

[0001] This invention relates to the field of thin-film filter frequency response prediction technology, and more specifically, to a neural network modeling method for predicting filter frequency response behavior. Background Technology

[0002] In the development and mass production debugging of front-end devices for radio frequency communication, radar and satellite terminals, thin-film filters need to meet frequency response indicators such as insertion loss, out-of-band rejection and phase characteristics within the target frequency band. Existing solutions usually rely on electromagnetic simulation and equivalent circuit modeling combined with vector network analyzer frequency sweep testing to evaluate the frequency response, and iterate repeatedly when structural parameters, material parameters and process deviations change. Some solutions also attempt to use data-driven models to directly regress complex frequency response in order to accelerate design screening and process window evaluation.

[0003] However, existing technologies have inherent shortcomings in terms of data consistency and physical consistency in frequency response modeling. Specifically, the frequency point distribution generated by different test batches and simulation settings is not uniform, and the jump caused by phase wrapping is difficult to handle stably at the sample level. This results in poor comparability of training data and unstable model generalization. More importantly, direct regression of complex frequency response is prone to outputting results that violate passive, causal, or stability constraints. In engineering, this manifests as a prediction curve that seems to fit but is not achievable. Consequently, it can be misleading in design selection, process adjustment, and anomaly tracing, making it difficult to obtain reproducible, interpretable, and usable frequency response prediction data for closed-loop decision-making during mass production debugging. Summary of the Invention

[0004] To overcome the aforementioned deficiencies in the prior art, the following solution is proposed to address the problem of poor frequency response prediction in the physically achievable filter in the background art.

[0005] To achieve the above objectives, the present invention provides the following technical solution:

[0006] A neural network modeling method for predicting the frequency response behavior of filters includes the following steps:

[0007] Collect structural parameters, material parameters, and process deviations of thin-film filters to obtain corresponding complex frequency response labels. Perform frequency grid unification and phase continuity processing on the complex frequency response labels to form a training sample set.

[0008] Define a set of physically realizable frequency response characterization parameters and establish a frequency response reconstruction operator. The frequency response reconstruction operator is used to reconstruct the set of physically realizable frequency response characterization parameters into a complex frequency response sequence.

[0009] Construct a neural network model, input structural parameters, material parameters and process deviations into the neural network model, and output a set of physically realizable frequency response characterization parameters;

[0010] The neural network model is iteratively trained based on the training sample set. Each iteration includes: outputting a set of physically realizable frequency response characterization parameters from the neural network model, obtaining a complex frequency response sequence through a frequency response reconstruction operator, performing passivity determination, causality determination, and stability determination on the complex frequency response sequence, and performing projection correction on the set of physically realizable frequency response characterization parameters when the determination is not satisfied.

[0011] Input the structural parameters, material parameters and process deviation characterization of the thin-film filter to be predicted, output the set of physically realizable frequency response characterization parameters, generate the predicted complex frequency response sequence through projection correction and frequency response reconstruction operators, and output the projection correction trace.

[0012] Furthermore, the frequency grid unification for complex frequency response tags includes:

[0013] Determine the target frequency point set, and perform resampling mapping on the complex frequency response labels on the target frequency point set to generate a complex frequency response sequence aligned with the frequency points;

[0014] Structural parameters, material parameters, and process deviations are written into the sample entries, and the complex frequency response sequences of aligned frequency points are written into the same sample entry to form a training sample set.

[0015] Furthermore, performing phase continuity processing on the complex frequency response tags includes:

[0016] Extract the phase sequence of the complex frequency response sequence and calculate the phase difference between adjacent frequency points;

[0017] When the phase difference between adjacent frequency points exceeds the phase jump threshold, the phase sequence is compensated with an integer multiple of pi (2 times the circumference of a circle).

[0018] The phase sequence and amplitude sequence after correction are complexly recombined to obtain a complex frequency response tag with phase continuity.

[0019] Furthermore, the set of physically realizable frequency response characterization parameters includes stable dynamic parameter terms, static parasitic trend parameter terms, and time delay parameter terms;

[0020] The stable dynamic parameter term includes the state matrix, input matrix, output matrix, and pass-through matrix, and a stability domain constraint is imposed on the state matrix;

[0021] The delay parameter is limited to non-negative delay parameters;

[0022] The static parasitic trend parameter is used to describe the response change trend of the direct channel and the parasitic channel within the target frequency band.

[0023] Furthermore, the frequency response reconstruction operator is used to reconstruct a set of physically realizable frequency response characterization parameters into a complex frequency response sequence, including:

[0024] Calculate the dynamic response matrix corresponding to the stable dynamic parameter terms for each point in the target frequency set;

[0025] The through-response matrix is ​​calculated point by point based on the static parasitic trend parameter and combined with the dynamic response matrix to form a composite response matrix;

[0026] By generating frequency-dependent complex exponential phase factors point by point based on the time delay parameter and performing phase mapping on the composite response matrix, the complex frequency response sequences of the transmission response and reflection response are obtained.

[0027] Furthermore, constructing a neural network model includes:

[0028] A feature coding subnet is established to map the structural parameters, material parameters, and process deviations of the thin-film filter into frequency response-sensitive feature vectors;

[0029] Establish a parameter generation subnet, which includes a dynamic parameter output branch, a parasitic trend output branch, and a time delay output branch;

[0030] The dynamic parameter output branch outputs the state matrix, input matrix, output matrix, and pass-through matrix from the stable dynamic parameter items; the parasitic trend output branch outputs the static parasitic trend parameter items; and the time delay output branch outputs the time delay parameter items and performs non-negative constraint mapping on the time delay parameter items.

[0031] Furthermore, the passivity determination, causality determination, and stability determination of the complex frequency response sequence include:

[0032] Based on the transmission response and reflection response, a scattering response matrix is ​​constructed point by point at the target frequency point set, and a set of singular values ​​is calculated. Based on the relationship between the set of singular values ​​and the passivity boundary, a passivity determination result is generated.

[0033] The state matrix is ​​obtained based on the stable dynamic parameter terms, and the eigenvalues ​​of the state matrix are calculated. The stability determination result is generated based on the relationship between the eigenvalues ​​and the stable domain.

[0034] Extract the phase sequence of the complex frequency response sequence and calculate the phase difference between adjacent frequency points. Generate the phase prediction increment based on the time delay parameter and calculate the phase consistency residual. Generate the causality determination result based on the relationship between the phase consistency residual and the causality boundary.

[0035] Furthermore, when the condition is not met, the projection correction performed on the set of physically realizable frequency response characterization parameters includes:

[0036] Perform a stable-domain projection on the state matrix and write back the stable dynamic parameter terms;

[0037] For frequency points where passivity does not satisfy the label, singular value decomposition is performed and singular values ​​exceeding the passivity boundary are clipped to the boundary values. The corrected scattering response matrix is ​​reconstructed based on the clipped singular values ​​and the decomposition vector.

[0038] Based on the corrected scattering response matrix and frequency response reconstruction operator, the correction amount of the static parasitic trend parameter term and the through matrix is ​​determined and written back to the physical frequency response characterization parameter set;

[0039] Perform nonnegative projection on the time delay parameter term, and perform phase rectification on the phase sequence based on the time delay parameter term to update the phase mapping parameters used for frequency response reconstruction.

[0040] Furthermore, iterative training of the neural network model based on the training sample set includes:

[0041] For each training sample, the neural network model outputs a set of physically realizable frequency response characterization parameters and performs frequency response reconstruction. It also performs passivity determination, causality determination, and stability determination, and performs projection correction when the determination is not satisfied.

[0042] The frequency response is reconstructed again using the physically realizable frequency response characterization parameter set after projection correction to obtain the corrected complex frequency response sequence. The difference between the corrected complex frequency response sequence and the complex frequency response labels in the training sample set is calculated, and the neural network model parameters are updated by backpropagation based on the difference.

[0043] Furthermore, the output projection correction traces include:

[0044] Record the results of the passivity determination, causality determination, and stability determination;

[0045] Record the set of frequency points that trigger projection correction;

[0046] Record the differences in the state matrix before and after projection correction, the differences in the maximum singular value before and after singular value clipping, and the differences in the time delay parameter terms before and after correction.

[0047] Record the version identifiers of structural parameters, material parameters, and process deviations, as well as the version identifiers of the neural network model, and associate the projection correction traces with the predicted complex frequency response sequence as a traceability record.

[0048] The technical effects and advantages of the neural network modeling method for predicting filter frequency response behavior in this invention are as follows:

[0049] This invention constructs inputs representing structural parameters, material parameters, and process deviations, outputs a set of physically achievable frequency response characterization parameters, and then obtains an end-to-end modeling link for complex frequency response sequences through a frequency response reconstruction operator. This enables rapid prediction and consistent expression of the frequency response behavior of thin-film filters. In the sample construction stage, frequency grid unification and phase continuity processing are introduced to reduce the impact of different test grids and phase jumps on training convergence and inference stability, making the training sample set comparable and reusable.

[0050] On the model output side, a set of parameters representing physically realizable frequency responses is organized using stable dynamic parameters, static parasitic trend parameters, and time delay parameters. During training iterations, passivity, causality, and stability are determined for the reconstructed frequency response. If these conditions are not met, projection correction is performed and the parameter set is written back. This ensures that the neural network model maintains the embedded consistency of physical constraints while learning the frequency response mapping, reducing prediction distortion caused by unrealizable frequency responses. Simultaneously, projection correction traces are output, and the judgment results, trigger frequency point set, correction difference summary, and predicted complex frequency response sequence are associated and stored. This facilitates traceability analysis and process localization of abnormal predictions, thereby improving the prediction reliability, interpretability, and engineering implementation efficiency in thin-film filter design iteration and mass production debugging scenarios. Attached Figure Description

[0051] Figure 1 This is a flowchart illustrating a neural network modeling method for predicting the frequency response behavior of filters according to the present invention. Detailed Implementation

[0052] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0053] In order to achieve the above objectives, Figure 1 A schematic diagram of a neural network modeling method for predicting filter frequency response behavior according to the present invention is given, which specifically includes the following steps;

[0054] Collect structural parameters, material parameters, and process deviations of thin-film filters to obtain corresponding complex frequency response labels. Perform frequency grid unification and phase continuity processing on the complex frequency response labels to form a training sample set.

[0055] Define a set of physically realizable frequency response characterization parameters and establish a frequency response reconstruction operator. The frequency response reconstruction operator is used to reconstruct the set of physically realizable frequency response characterization parameters into a complex frequency response sequence.

[0056] Construct a neural network model, input structural parameters, material parameters and process deviations into the neural network model, and output a set of physically realizable frequency response characterization parameters;

[0057] The neural network model is iteratively trained based on the training sample set. Each iteration includes: outputting a set of physically realizable frequency response characterization parameters from the neural network model, obtaining a complex frequency response sequence through a frequency response reconstruction operator, performing passivity determination, causality determination, and stability determination on the complex frequency response sequence, and performing projection correction on the set of physically realizable frequency response characterization parameters when the determination is not satisfied.

[0058] Input the structural parameters, material parameters and process deviation characterization of the thin-film filter to be predicted, output the set of physically realizable frequency response characterization parameters, generate the predicted complex frequency response sequence through projection correction and frequency response reconstruction operators, and output the projection correction trace.

[0059] The structural parameters, material parameters, and process deviations of the thin-film filter are collected to characterize the corresponding complex frequency response labels. Frequency grid unification and phase continuity processing are then performed on these complex frequency response labels to form a training sample set, specifically including:

[0060] The training sample set is constructed using a neural network modeling device for predicting filter frequency response behavior. The modeling device includes a parameter access unit, a data processing unit, a model inference unit, a model training unit, and a storage unit.

[0061] The parameter access unit is used to collect the structural parameters, material parameters and process deviation characterization of the thin film filter, and generate a sample entry for each thin film filter instance. The sample entry includes at least three input fields: sample identifier, thin film filter structural parameters, material parameters, and process deviation characterization, as well as a complex frequency response label output field.

[0062] Complex frequency response tags are obtained through electromagnetic simulation or test measurement. Test measurement can be performed using a vector network analyzer to sweep the frequency points within the target frequency band to obtain the complex response that varies with frequency. The complex frequency response tag contains an amplitude sequence and a phase sequence in its data structure. The amplitude sequence and phase sequence correspond one-to-one with the frequency points to fully characterize the amplitude and phase characteristics of the device in the frequency domain. The complex frequency response tag is characterized by scattering parameters, including reflection scattering parameters and transmission scattering parameters, and is written into the sample entries according to the port definition.

[0063] The data processing unit performs frequency grid unification on the complex frequency response labels. Specifically, it first determines the target frequency point set, which is generated by the modeling device within the target frequency band according to the preset frequency resolution rules. After generation, it is used as a common frequency reference for the training sample set.

[0064] Subsequently, a resampling mapping is performed on the complex frequency response labels on the target frequency point set to generate a complex frequency response sequence aligned with the frequency points.

[0065] It should be noted that the preset frequency resolution rules, preset dynamic order, and the number and position of frequency support points are generated by the training configuration and written into the configuration record of the storage unit. The training configuration includes at least the target frequency band definition, target frequency point set generation rules, dynamic order setting rules, and frequency support point selection rules. During the prediction phase, the same configuration record associated with the neural network model version identifier is read to ensure that the training and prediction are consistent in the organization of the target frequency point set, dynamic order, and parasitic trend parameters.

[0066] The model inference unit is used to perform forward inference on the input vector to output a set of physically realizable frequency response representation parameters; the model training unit is used to perform backpropagation to update the neural network model parameters based on the difference; the storage unit is used to save the training sample set, the target frequency point set, the phase transition threshold, the causal boundary, the passive boundary, the stability domain constraint configuration, the neural network model version identifier, and the traceability record.

[0067] The resampling mapping calculation process is performed by taking values ​​per target frequency point, specifically as follows:

[0068] For each target frequency point in the target frequency point set, locate the original frequency point interval adjacent to the target frequency point in the original frequency point sequence of the complex frequency response tag, read the amplitude and phase values ​​corresponding to the original frequency points at both ends of the interval, and then perform interpolation calculation on the amplitude and phase values ​​according to the positional relationship of the target frequency point in the interval, so as to obtain the interpolated amplitude and interpolated phase values ​​corresponding to the target frequency point.

[0069] After performing the above interpolation transformation point by point on the target frequency point set, a complex frequency response sequence of aligned frequency points is formed. The structural parameters, material parameters and process deviations of the thin film filter are written into the input field of the sample entry. At the same time, the complex frequency response sequence of aligned frequency points is written into the output field of the same sample entry. Multiple sample entries are aggregated to form a training sample set.

[0070] Let's take a thin-film filter example as a sample entry for illustration:

[0071] The parameter access unit generates a sample identifier for the instance and writes the thin film filter structure parameters, material parameters and process deviation characterization into the input field of the sample entry respectively. The test station uses a vector network analyzer to sweep the target frequency band to obtain a complex frequency response label. The complex frequency response label is characterized by scattering parameters and includes reflection-type scattering parameters and transmission-type scattering parameters. The data processing unit writes its amplitude sequence and phase sequence into the complex frequency response label output field of the sample entry according to the port definition.

[0072] Subsequently, the data processing unit reads the target frequency point set fixed in the training configuration and performs resampling mapping on the complex frequency response labels to obtain the complex frequency response sequence with aligned frequency points;

[0073] Extract the phase sequence from the complex frequency response sequence of the aligned frequency points and calculate the phase difference between adjacent frequency points point by point. When the phase difference between adjacent frequency points exceeds the phase jump threshold, perform integer multiple of π compensation correction on the phase point that jumps and its subsequent phase points according to the minimum adjustment principle, so that the corrected phase difference between adjacent frequency points returns to within the phase jump threshold.

[0074] After the calibration is completed, the data processing unit performs complex recombination of the calibrated phase sequence and amplitude sequence, and updates the complex frequency response label output field of the sample entry with the phase-continuous complex frequency response label, so that the sample entry forms a unified data caliber on the target frequency point set that can be directly used for training and control.

[0075] Complex number recombination is performed point-by-point according to the target frequency point set, specifically: for the first point in the target frequency point set... Target frequency points The data processing unit reads the amplitude value at that frequency point from the amplitude sequence. And read the corrected phase value at that frequency point from the corrected phase sequence. Convert both to complex response values ​​at that frequency point. Satisfying equation (1): Or equivalently expressed as equation (2): ,in, , The total number of frequency points in the target frequency point set; A non-negative real number, representing the amplitude value at the aligned frequency point; This represents the phase value after compensation and correction by twice the value of pi, in radians. It is the imaginary unit and satisfies .

[0076] For complex frequency response tags characterized by scattering parameters, including both reflection and transmission scattering parameters, the data processing unit processes each scattering parameter component in the entire... Repeat the complex recombination of equation (1) or equation (2) and write the complex frequency response tag output field of the sample entry according to the port definition to ensure that the complex frequency response tag after phase continuity has a uniform and reproducible data caliber on the target frequency point set.

[0077] The model training unit uses the input field of the sample entry as input to drive the neural network model to output a set of physically realizable frequency response characterization parameters, and then reconstructs the complex frequency response sequence through the frequency response reconstruction operator. The data processing unit compares the reconstructed complex frequency response sequence with the phase-continuous complex frequency response label of the sample entry point by point on the same target frequency point set, forms a difference quantity, and uses it for backpropagation to update the neural network model parameters, so that the model learns the mapping relationship between structural parameters, material parameters, and process deviations and the complex frequency response behavior, while keeping the output consistent with the constraints of subsequent physical realizability determination and projection correction.

[0078] After unifying the frequency grid, the data processing unit performs phase continuity processing on the complex frequency response labels to avoid the impact of phase abrupt changes caused by phase wrapping on the modeling. Specifically:

[0079] Phase continuity processing includes extracting the phase sequence corresponding to the complex frequency response sequence of the aligned frequency points and calculating the phase difference between adjacent frequency points. The phase difference between adjacent frequency points is obtained by performing a difference operation on the phase values ​​corresponding to two adjacent target frequency points.

[0080] The modeling equipment predefines the phase jump threshold, which is determined by statistically summarizing the phase difference between adjacent frequency points of a set of representative thin-film filter samples, so that the phase jump threshold can distinguish between normal continuous phase changes and abrupt changes caused by phase wrapping.

[0081] When the phase difference between adjacent frequency points exceeds the phase jump threshold, the modeling device performs a double pi compensation correction on the phase sequence. The double pi compensation correction is performed by superimposing or subtracting a double pi multiple on the phase point where the jump occurs and its subsequent phase points, so that the phase difference between adjacent frequency points after correction returns to within the phase jump threshold and the phase sequence continues to extend along the frequency axis.

[0082] After completing the π-2 compensation correction, the corrected phase sequence and amplitude sequence are recombined in complex form. The complex recombination reads the amplitude value and the corrected phase value point by point according to the target frequency point set and converts them into complex form to obtain the phase-continuous complex frequency response label. Finally, the output field in the sample entry is updated with the phase-continuous complex frequency response label to obtain the training sample set that satisfies the frequency grid unification and phase continuity processing.

[0083] For example, in the mass production and debugging scenario of thin-film filters, engineers sort out the thin-film filter structural parameters, material parameters and process deviation characteristics of the device from process records and online test results, and write them into the input field of the sample entry. Then, at the offline testing station, a vector network analyzer is used to perform frequency sweep test on the device to obtain complex frequency response labels containing amplitude and phase sequences, and write them into the output field of the sample entry.

[0084] The data processing unit reads the target frequency point set in the training configuration, performs resampling mapping on the complex frequency response labels to form a complex frequency response sequence with aligned frequency points. When the phase sequence jumps at adjacent frequency points, it triggers double pi compensation correction and complex recombination according to the phase jump threshold to obtain the phase continuous complex frequency response labels, thereby forming a training sample set that can be used for training.

[0085] For the new batch of devices to be evaluated, the model inference unit uses its structural parameters, material parameters and process deviations as inputs and outputs a set of physically realizable frequency response characterization parameters. The predicted complex frequency response sequence is obtained through the frequency response reconstruction operator. If the passivity determination, causality determination or stability determination fails to meet the flag, the physically realizable frequency response characterization parameter set is projected and the projection correction trace is recorded. The determination result, the set of trigger frequencies and the summary of differences before and after correction are associated with the predicted complex frequency response sequence and stored, which is convenient for engineers to trace back and locate the source of the anomaly.

[0086] For example, during the same batch of thin-film filter mass production debugging, when a batch of devices underwent frequency sweep measurement with a vector network analyzer at the offline testing station, the complex frequency response labels exhibited amplitude fluctuations and discontinuous phase trends at the passband edges. To avoid performing full-frequency sweep measurements on each device in the batch, the engineers selected devices that had already undergone testing and measurement to establish a training sample set, and treated the remaining untested devices as examples of thin-film filters to be predicted.

[0087] The parameter access unit collects the thin film filter structure parameters, material parameters and process deviation characterization from the batch process records and online test results and writes them into the input field of the sample entry. The process deviation characterization includes thin film deposition thickness deviation mark, etching endpoint offset mark and annealing process temperature deviation mark.

[0088] During the prediction phase, the model inference unit outputs a set of physically realizable frequency response characterization parameters for each thin-film filter instance to be predicted, and generates a predicted complex frequency response sequence through the frequency response reconstruction operator.

[0089] After performing passivity, causality, and stability checks on the predicted complex frequency response sequence, the data processing unit writes a passivity non-satisfaction flag to a set of frequency points in the target frequency point set and triggers projection correction.

[0090] First, singular value decomposition is performed on the scattering response matrix, and singular values ​​exceeding the passive boundary are clipped to the boundary value to reconstruct the corrected scattering response matrix. Then, based on the corrected scattering response matrix, the static parasitic trend parameter term and the correction amount of the through matrix are written back, while keeping the time delay parameter term as a non-negative time delay parameter and completing phase rectification.

[0091] The storage unit writes the set of trigger frequency points corresponding to the passive non-satisfaction mark, the maximum difference in singular values ​​before and after singular value pruning, and the correction amount of the static parasitic trend parameter item after write-back into the trace record.

[0092] To verify the prediction results against the traceability records on-site, engineers selected devices with the same process deviation characteristics from the batch of thin-film filter examples to be predicted for testing and measurement. At the offline testing station, a vector network analyzer was used to perform frequency sweep measurements on the target frequency band, obtaining the complex frequency response tag for the device and writing it into the complex frequency response tag output field of the corresponding sample entry. The data processing unit performed frequency grid unification on the complex frequency response tag according to the target frequency point set fixed in the training configuration, and performed phase continuity processing according to the phase jump threshold, obtaining an aligned frequency point complex frequency response sequence that is on the same target frequency point set as the predicted complex frequency response sequence. Subsequently, the data processing unit read the aligned frequency point complex frequency response sequence and the predicted complex frequency response sequence point by point on the target frequency point set, forming a frequency point-by-frequency comparison record. This comparison record was then associated and stored with the device's traceability record, so as to establish a verifiable correspondence between the trigger frequency point set, projection correction traces, and actual measurement phenomena.

[0093] After engineers correlated and filtered the set of triggering frequency points with the process deviation characterization fields based on the traceability records, they found that the triggering sample entries all had a thin film deposition thickness deviation mark in the process deviation characterization. Based on this, they traced back the online monitoring and process control records of the thin film deposition equipment, and completed the location of the source of the abnormality in this batch and subsequent process correction.

[0094] In this mass production commissioning event, the modeling equipment associated and saved the predicted complex frequency response sequence with the projection correction trace, allowing engineers to complete batch screening without having to repeatedly perform full-frequency scans on all devices.

[0095] For devices whose passive properties do not meet the prediction criteria, the traceability record can provide the set of trigger frequencies and the difference in singularity clipping, and associate them with the field values ​​of the process deviation characterization, thereby establishing a verifiable correspondence between the frequency band positions where the predicted anomalies occur and the deviation marks in the process deviation characterization; for devices whose prediction results do not trigger the non-compliance mark, engineers can directly use the predicted complex frequency response sequence as input for subsequent screening and process window evaluation.

[0096] In this way, the modeling equipment unifies the data benchmark for training and prediction under the same target frequency point set and phase continuity caliber. It also avoids outputting unrealizable complex frequency response sequences through physical realizability judgment and projection correction, so that the prediction results can be used for batch handling decisions and anomaly tracing, reducing the repeated trial and error and positioning costs caused by inconsistent data caliber, phase jumps and physically unrealizable outputs.

[0097] In another thin-film filter trial production verification, the same model of device obtained complex frequency response tags at the electromagnetic simulation and offline testing stations, but the original frequency point sequences of the two types of complex frequency response tags were different, and the phase sequence obtained by the test measurement showed a phase wrap-up jump in the target frequency band, which made it difficult to directly align the sample entries from different sources when they were aggregated in the data processing unit.

[0098] The engineers incorporated the batch of simulation sample entries and test sample entries into the training sample set construction process: the data processing unit first generated a target frequency point set based on the training configuration and fixed it as a common frequency reference, and then performed resampling mapping on the complex frequency response labels in each sample entry to obtain the complex frequency response sequence of the aligned frequency points;

[0099] Subsequently, the phase sequence is extracted and the phase difference between adjacent frequency points is calculated point by point. When the phase difference between adjacent frequency points exceeds the phase jump threshold, a 2x pi compensation correction is triggered, and the compensation amount is determined according to the minimum adjustment principle to ensure that the corrected phase sequence remains continuous along the target frequency point set. Then, complex reconstruction is performed to update the output field of the sample entries. After this processing is completed, the model inference unit predicts the structural parameters, material parameters, and process deviations of the thin-film filter for untested devices in the same batch, outputs the set of physically realizable frequency response characterization parameters, and generates a predicted complex frequency response sequence through the frequency response reconstruction operator.

[0100] When the predicted complex frequency response sequence triggers the causality non-compliance mark at some frequency points, the data processing unit performs projection correction based on the phase consistency residual and causality boundary and updates the phase mapping parameters synchronously. The storage unit writes the set of triggering frequency points, the causality determination result and the difference in time delay parameters before and after correction into the traceability record.

[0101] According to the traceability records, the engineers traced the process deviation characteristics of the abnormal concentrated sample items back to the temperature deviation mark of the same annealing process. They further combined the results of a small number of sampled vector network analyzers to confirm that there was a repeatable phase trend anomaly in this batch. In this way, a verifiable correlation was established between the phase jump and the causal non-compliance and the process deviation characterization, which can be used for subsequent process window revision and prediction model version iteration.

[0102] It should be noted that the pi compensation correction is performed point-by-point in ascending order of the target frequency set. When a positive abrupt change in the phase difference between adjacent frequency points is detected, the data processing unit applies compensation in the same direction to the phase values ​​of the abrupt change point and its subsequent frequency points, so that the phase difference between the adjacent frequency points falls back to within the phase jump threshold. When a negative abrupt change in the phase difference between adjacent frequency points is detected, the data processing unit applies compensation in the opposite direction to the phase values ​​of the abrupt change point and its subsequent frequency points, so that the phase difference between the adjacent frequency points falls back to within the phase jump threshold. The integer multiples of the compensation follow the minimum adjustment principle, that is, the minimum compensation amount that can make the phase difference between the current adjacent frequency points enter the phase jump threshold range for the first time is selected, thereby ensuring that the phase sequence continuous processing has a unique executable rule.

[0103] Define a set of physically realizable frequency response characterization parameters and establish a frequency response reconstruction operator. The frequency response reconstruction operator is used to reconstruct the set of physically realizable frequency response characterization parameters into a complex frequency response sequence, specifically including:

[0104] After the training sample set is constructed, the data processing unit of the modeling device further defines the physically realizable frequency response characterization parameter set for each sample entry. The physically realizable frequency response characterization parameter set consists of stable dynamic parameter items, static parasitic trend parameter items, and time delay parameter items, specifically including:

[0105] The stable dynamic parameter term includes a state matrix, an input matrix, an output matrix, and a pass-through matrix. The state matrix is ​​used to describe the internal coupling relationship of the dynamic state as it evolves over time. The input matrix is ​​used to describe the driving relationship of the input port excitation on the internal state. The output matrix is ​​used to describe the mapping relationship of the internal state to the output port response. The pass-through matrix is ​​used to describe the direct path that does not pass through the internal state.

[0106] The method for applying stability domain constraints to the state matrix is ​​as follows: perform eigenvalue analysis on the state matrix to obtain the set of eigenvalues ​​of the state matrix. In this embodiment, the stability domain is the continuous-time stability domain, that is, the region where the real part of the eigenvalues ​​of the state matrix is ​​negative. When there is an eigenvalue that does not satisfy the stability domain constraint, the eigenvalue is moved into the stability domain according to a preset mapping rule and the state matrix is ​​written back accordingly, so that the updated state matrix satisfies the stability domain constraint.

[0107] The state matrix is ​​written back by the data processing unit through a similarity transformation:

[0108] First, perform an orthogonal similarity transformation on the state matrix to obtain a quasi-upper triangular structure representation, and then locate the diagonal block corresponding to the eigenvalue outside the stable domain in the quasi-upper triangular structure;

[0109] Then, the diagonal block is replaced according to the preset mapping rules, so that the eigenvalues ​​corresponding to the replaced diagonal block fall into the stable region, while keeping the other diagonal blocks unchanged;

[0110] Finally, the updated quasi-upper triangular structure is subjected to an inverse similarity transformation to obtain the updated state matrix and the stable dynamic parameter terms are written back. After the write-back is completed, the set of eigenvalues ​​of the state matrix is ​​recalculated to verify that the stability domain constraints are satisfied, so that the stability domain projection has a reproducible operation path.

[0111] The time delay parameter is limited to a non-negative time delay parameter. It is obtained by identifying the group delay or the linear term of phase with frequency in the complex frequency response label corresponding to the sample entry and estimating the initial time delay value. Then, the estimation result is corrected by non-negative constraint to obtain the non-negative time delay parameter.

[0112] The static parasitic trend parameter item is used to describe the response change trend of the through channel and the parasitic channel in the target frequency band. In this embodiment, the parameter item is organized with the through response control values ​​of several frequency support points in the target frequency band, and the frequency position of the support point and the corresponding control value are written into the static parasitic trend parameter item for point-by-point reconstruction.

[0113] After obtaining the set of physically realizable frequency response characterization parameters, the data processing unit establishes a frequency response reconstruction operator to reconstruct the set of physically realizable frequency response characterization parameters into a complex frequency response sequence.

[0114] The frequency response reconstruction operator uses the target frequency point set as a unified reconstruction grid and performs reconstruction calculations point-by-point on the target frequency point set. The specific steps include:

[0115] For any target frequency point, first calculate the dynamic response matrix based on the stable dynamic parameter terms:

[0116] After converting the target frequency point into the corresponding complex frequency operator, a linear operator is constructed with the identity matrix and the state matrix. The state transfer matrix at the frequency point is obtained by solving a system of linear equations. Then, the dynamic response matrix of the target frequency point is obtained by left multiplication of the output matrix, right multiplication of the input matrix, and superposition of the pass-through matrix.

[0117] Then, the through-response matrix is ​​calculated point by point based on the static parasitic trend parameter:

[0118] Read the two frequency support points adjacent to the target frequency point from the static parasitic trend parameter item, extract the direct response control values ​​corresponding to the two support points respectively, and perform interpolation conversion on the direct response control values ​​according to the position ratio of the target frequency point between the two support points to obtain the direct response matrix corresponding to the target frequency point.

[0119] After obtaining the dynamic response matrix and the through response matrix, the through response matrix and the dynamic response matrix are combined to form a composite response matrix, which serves as an intermediate reconstruction result before the application of time delay phase mapping.

[0120] After the composite response matrix is ​​constructed, the data processing unit generates frequency-dependent complex exponential phase factors point-by-point based on the time delay parameter and performs phase mapping on the composite response matrix, including:

[0121] Phase mapping is performed point-by-point based on the target frequency set, specifically as follows:

[0122] For the first Target frequency points The data processing unit first calculates the angular frequency. : Then, from the non-negative delay parameter in the delay parameter item Generate frequency-dependent complex exponential phase factor : ;in, , The amplitude is always 1 and the phase is .

[0123] Let the composite response matrix be... , In frequency point The intermediate reconstruction result consists of the dynamic response matrix and the through response matrix, and its matrix dimension is determined by the number of ports fixed in the training configuration;

[0124] The data processing unit will use the phase factor Applied to the composite response matrix The complex response matrix obtained after phase mapping is obtained above. ,satisfy: Or, in element form: ,in For port indexing.

[0125] The data processing unit handles all Repeated execution yields a sequence of complex response matrices after phase mapping on the target frequency point set. Based on this, port self-reflection elements are extracted to form a complex sequence of reflection response, and cross-port elements are extracted to form a complex sequence of transmission response, which constitutes the subsequent output complex frequency response sequence.

[0126] For each target frequency point in the target frequency point set, the target frequency point is converted into an angular frequency quantity. Then, the angular frequency quantity is multiplied by a non-negative time delay parameter to obtain the phase delay quantity corresponding to the frequency point. Subsequently, a complex exponential phase factor with an amplitude of one and a phase equal to the phase delay quantity is generated, and the complex exponential phase factor is applied to the composite response matrix to complete the phase mapping.

[0127] After phase mapping is completed, the complex response matrix corresponding to the target frequency point is obtained.

[0128] Repeat the above process for each target frequency point, and collect them in the order of the target frequency point set to form a complex frequency response sequence;

[0129] In this embodiment, the complex frequency response sequence includes a transmission response and a reflection response. The reflection response is extracted from the port self-reflection element of the complex response matrix, and the transmission response is extracted from the cross-port transmission element of the complex response matrix. Both the transmission response and the reflection response are arranged into a sequence according to the target frequency point set and written into the sample entries. This serves as a consistent input-output interface for the subsequent neural network model to output the physically realizable frequency response characterization parameter set and obtain the complex frequency response sequence through the frequency response reconstruction operator.

[0130] Construct a neural network model, inputting structural parameters, material parameters, and process deviations into the neural network model, and outputting a set of physically realizable frequency response characterization parameters, specifically including:

[0131] Based on the completion of frequency grid unification and phase continuity processing of the training sample set, the modeling equipment constructs a neural network model and realizes the input of structural parameters, material parameters and process deviations, and the physical mapping of the frequency response characterization parameter set output can be realized.

[0132] The modeling equipment includes a parameter access unit and a model inference unit. The data access unit reads the thin film filter structural parameters, material parameters and process deviation characterization from the sample entries and organizes them into an input vector with a fixed field order.

[0133] Normalization is performed on continuous parameters in the input vector, and dictionary encoding is performed on discrete parameters and mapped to dense representations before being concatenated into the input vector. The benchmark value used for normalization is determined by the statistics of the corresponding fields in the training sample set and is fixed and saved to ensure that the same normalization caliber is used in the training and inference stages.

[0134] The model inference unit includes a feature encoding subnet and a parameter generation subnet. The feature encoding subnet outputs frequency response sensitive feature vectors, and the parameter generation subnet outputs stable dynamic parameter terms, static parasitic trend parameter terms, and time delay parameter terms based on the frequency response sensitive feature vectors, forming a set of physically realizable frequency response representation parameters. The parameter generation subnet adopts a multi-branch structure with shared backbone and branch outputs to meet the generation requirements of different types of parameter terms.

[0135] The feature encoding subnet takes the input vector as input and performs linear mapping and nonlinear activation in layers to extract combined features that are sensitive to frequency response changes. The linear mapping is achieved by matrix multiplication and bias superposition, and the nonlinear activation uses a continuously differentiable activation function to maintain training stability.

[0136] Within the feature coding subnet, in order to suppress the influence of fields with different dimensions on the training process, a normalization layer is inserted after several coding layers to keep the numerical range of intermediate features consistent.

[0137] The output layer of the feature coding subnet compresses the final hidden representation into a fixed-length frequency response sensitive feature vector, which serves as the common input to the subsequent three output branches. This allows each output branch to learn a specific mapping related to its parameter terms while maintaining a shared representation.

[0138] The parameter generation subnet includes a dynamic parameter output branch, a parasitic trend output branch, and a time delay output branch, including:

[0139] After receiving the frequency response sensitive feature vector, the dynamic parameter output branch outputs the state matrix, input matrix, output matrix and pass-through matrix in the stable dynamic parameter terms. Specifically, it first outputs the flattened vector of the corresponding matrix, and then rearranges it into matrix form according to the preset dimension rule. The preset dimension rule is determined by the number of ports and the preset dynamic order and is fixed before training.

[0140] The parasitic trend output branch outputs static parasitic trend parameters. The static parasitic trend parameters are composed of control values ​​of several frequency support points within the target frequency band. When outputting, the same method of vector output followed by writing according to field structure is used to ensure consistency with the interpolation values ​​of the subsequent frequency response reconstruction operator.

[0141] The delay output branch outputs delay parameter terms and performs non-negative constraint mapping on the delay parameter terms. The non-negative constraint mapping is implemented by positive activation of the output layer, so that the output of any network internal is non-negative after the mapping, thereby ensuring that the delay parameter terms meet the constraint of non-negative delay parameters. Common positive activation methods include activation that truncates negative values ​​to zero or smooth positive activation. The modeling device can choose smooth positive activation to improve gradient stability during the training phase.

[0142] The neural network model is iteratively trained based on the training sample set. Each iteration includes:

[0143] The set of physically realizable frequency response characterization parameters output by the neural network model is used to obtain a complex frequency response sequence through a frequency response reconstruction operator. Passivity, causality, and stability are then determined on the complex frequency response sequence. If the determinations are not satisfied, projection correction is performed on the set of physically realizable frequency response characterization parameters, specifically including:

[0144] During the training phase, the modeling device reads sample entries from the training sample set in small batches. Each sample entry contains thin-film filter structural parameters, material parameters and process deviation characterization, as well as the corresponding complex frequency response label.

[0145] The model inference unit inputs the structural parameters, material parameters and process deviations of the thin film filter into the neural network model and outputs a set of physically realizable frequency response characterization parameters. The set of physically realizable frequency response characterization parameters includes stable dynamic parameters, static parasitic trend parameters and time delay parameters.

[0146] Then, the frequency response reconstruction operator is invoked to reconstruct the complex frequency response sequence point by point using the target frequency point set as the frequency reference. The complex frequency response sequence contains at least the complex sequences of the transmission response and the reflection response on the target frequency point set.

[0147] It should be noted that the number of ports is fixed in the training configuration of the neural network modeling device. The number of ports is used to determine the order and element indexing rules of the scattering response matrix. At any target frequency point, the data processing unit writes the reflection response into the port self-reflection element position of the scattering response matrix according to the port index, and writes the transmission response into the cross-port transmission element position of the scattering response matrix, thereby obtaining the scattering response matrix corresponding to the target frequency point. For example, when the number of ports is two ports, the reflection response of the first port and the reflection response of the second port are written into the two port self-reflection element positions respectively, and the transmission response from the first port to the second port and the transmission response from the second port to the first port are written into the two cross-port transmission element positions respectively.

[0148] During the training loop, passivity, causality and stability are determined for each forward output complex frequency response sequence, generating corresponding determination results and a set of non-satisfied marked frequency points;

[0149] If any judgment is not satisfied, the output is not directly used to participate in parameter update. Instead, projection correction is first performed on the set of physically realizable frequency response representation parameters to bring it back into the set of physically realizable constraints. Then, based on the corrected set of physically realizable frequency response representation parameters, the frequency response reconstruction operator is used to obtain the corrected complex frequency response sequence. The difference between the corrected complex frequency response sequence and the complex frequency response label is used to drive backpropagation to update the neural network model parameters.

[0150] The passivity determination involves constructing a scattering response matrix at each target frequency point and calculating a set of singular values, including:

[0151] The scattering response matrix is ​​obtained by filling the reflection response and transmission response at the target frequency point according to the port position. Singular value decomposition is performed on the scattering response matrix to obtain the set of singular values.

[0152] In this embodiment, the passive boundary is the boundary that does not generate power gain. That is, the passive property is determined to be satisfied when the maximum singular value in the singular value set does not exceed the passive boundary value; otherwise, a passive property not satisfied mark is written at the corresponding target frequency point.

[0153] Stability determination is performed directly based on eigenvalue analysis of the state matrix in the stable dynamic parameter terms, calculating the set of eigenvalues ​​of the state matrix, and using stability domain constraints as the basis for determination. Under the continuous-time modeling approach, stability is determined when the real part of the eigenvalues ​​of the state matrix is ​​negative; otherwise, a stability non-satisfaction flag is written.

[0154] Causality determination is based on expanding the phase sequence of the complex frequency response sequence into a phase sequence and calculating the phase difference between adjacent frequency points. Simultaneously, it generates a phase prediction increment based on the time delay parameter, including:

[0155] For two adjacent frequency points in the target frequency point set, the phase prediction increment corresponding to the frequency interval is calculated, and the phase difference between the adjacent frequency points and the phase prediction increment is subtracted to obtain the phase consistency residual. In this embodiment, the causality boundary is determined and fixed by the statistical upper bound of the phase consistency residual in the training sample set. When the phase consistency residual exceeds the causality boundary, a causality non-satisfaction flag is written, thereby realizing the causality constraint check of phase change and time delay consistency.

[0156] The statistical object of the causal boundary is the phase consistency residual sequence of each sample item in the training sample set on the target frequency point set. The data processing unit performs full-band convergence statistics on the phase consistency residual sequence and extracts the upper bound features to form the causal boundary. Once the causal boundary is determined, it is written into the model version configuration of the storage unit and associated with the target frequency point set, phase jump threshold and passive boundary, so that when the causal determination is called in the prediction stage, the same boundary caliber and frequency benchmark can be maintained as in the training stage.

[0157] When any judgment result fails to meet the flag, projection correction is performed in the order of stability, passivity, and causality, and the physically realizable frequency response characterization parameter set is written back. The stable domain projection is implemented for the state matrix as follows:

[0158] The eigenvalues ​​that fall outside the stable region in the set of eigenvalues ​​of the state matrix are shifted into the stable region according to a preset mapping rule, and the state matrix that satisfies the stable region constraint is written back based on the shifted eigenvalues ​​and the original eigenvector structure, thereby updating the stable dynamic parameter terms.

[0159] Passive projection is applied to frequency points where the passivity does not satisfy the label: singular value decomposition is performed on the scattering response matrix of the frequency point, singular values ​​exceeding the passivity boundary value are clipped to the passivity boundary value, and the corrected scattering response matrix is ​​reconstructed based on the clipped singular values ​​and the decomposition vector.

[0160] Subsequently, the correction amounts of the static parasitic trend parameter and the direct pass matrix are determined and written back using a linear equation system solution method that converges at frequency points, constrained by the response contributions of the corrected scattering response matrix and the frequency response reconstruction operator to the static parasitic trend parameter and the direct pass matrix. This ensures that the corrected scattering response matrix can be approximated when reconstructed by the frequency response reconstruction operator.

[0161] It should be noted that the passive boundary, as the threshold parameter used for passive determination, is fixed by the training configuration and remains consistent during the training and prediction phases. It represents the boundary condition that the scattering response matrix does not generate power gain. At the target frequency point that triggers projection correction, the data processing unit performs singular value decomposition on the scattering response matrix to obtain a set of singular values ​​and a corresponding decomposition vector. Singular values ​​exceeding the passive boundary are replaced and pruned, while singular values ​​not exceeding the passive boundary remain unchanged. Subsequently, the corrected scattering response matrix is ​​reconstructed using the pruned set of singular values ​​and the original decomposition vector. This corrected scattering response matrix is ​​used as the constraint benchmark for subsequently determining the static parasitic trend parameter and the correction amount of the through matrix, thereby ensuring that passive projection has a clear threshold meaning, pruning rules, and reconstruction path.

[0162] Causality- and time-delay-related projection correction involves two steps:

[0163] First, perform non-negative projection on the time delay parameter item to adjust the negative time delay parameter to zero or the minimum non-negative value to meet the non-negative time delay parameter constraint. Then, perform phase rectification on the phase sequence based on the updated time delay parameter item. Specifically, correct the phase sequence point by point along the target frequency point set so that the phase consistency residual between the phase difference of adjacent frequency points and the phase prediction increment falls back to within the causality boundary, and update the phase mapping parameters used for frequency response reconstruction simultaneously.

[0164] After completing the projection correction, the frequency response reconstruction operator is re-executed with the corrected set of physically realizable frequency response characterization parameters to obtain the corrected complex frequency response sequence. The difference between the sequence and the complex frequency response label is then calculated and used for backpropagation update of the neural network model parameters, so that each iteration can achieve training convergence under the physical realizable constraint.

[0165] The input consists of the structural parameters, material parameters, and process deviation characterization of the thin-film filter to be predicted. The output is a set of physically realizable frequency response characterization parameters. After projection correction and frequency response reconstruction operators, a predicted complex frequency response sequence is generated, and the projection correction trace is output, specifically including:

[0166] After the modeling equipment completes training and solidifies the neural network model version identifier, it enters the prediction phase. The data access unit receives the structural parameters, material parameters, and process deviation characterization of the thin-film filter to be predicted, and forms an input vector according to the field order and normalization caliber consistent with the training phase.

[0167] The model inference unit inputs the input vector into the neural network model and outputs a set of physically realizable frequency response characterization parameters. The set of physically realizable frequency response characterization parameters includes stable dynamic parameters, static parasitic trend parameters, and time delay parameters. The time delay parameters are mapped to non-negative time delay parameters through non-negative constraint mapping.

[0168] Subsequently, the data processing unit first invokes the passivity determination, causality determination, and stability determination processes according to the same target frequency point set during the training phase to screen for potentially physically unrealizable outputs, including:

[0169] The passivity determination involves constructing a scattering response matrix at each target frequency point and calculating a set of singular values. The passivity determination result is generated based on whether the maximum singular value crosses the passivity boundary.

[0170] The stability determination process calculates the eigenvalues ​​of the state matrix and generates a stability determination result based on the stability domain relationship.

[0171] The causality determination process extracts the phase sequence of the complex frequency response sequence, calculates the phase difference between adjacent frequency points, and generates a phase prediction increment by combining the time delay parameter to obtain the phase consistency residual. Then, the causality determination result is generated based on the relationship between the phase consistency residual and the causality boundary.

[0172] The above-mentioned judgment approach is consistent with the engineering approach of scattering parameter measurement, passivity characterized by singular value limits, and state-space stability characterized by eigenvalues ​​falling into the stability domain.

[0173] When any judgment result fails to meet the flag, the data processing unit performs projection correction on the physically realizable frequency response characterization parameter set and writes it back. The specific content includes:

[0174] If the stability is not satisfied, first perform a stable domain projection on the state matrix, that is, move the eigenvalues ​​of the state matrix that fall outside the stable domain into the stable domain according to the preset mapping rules and update the state matrix accordingly, and write it back to the stable dynamic parameter item;

[0175] For cases where passivity is not satisfied, singular value decomposition is performed on the scattering response matrix corresponding to the set of trigger frequencies. Singular values ​​exceeding the passivity boundary are clipped to the boundary values. The corrected scattering response matrix is ​​reconstructed based on the clipped singular values ​​and the decomposition vector. Then, the contribution of the static parasitic trend parameter and the through matrix to the scattering response matrix is ​​back-calculated using the frequency response reconstruction operator. The correction amount of the static parasitic trend parameter and the through matrix is ​​determined and written back.

[0176] For cases where causality is not satisfied, non-negative projection is first performed on the time delay parameter to eliminate negative time delay parameters. Then, phase rectification is performed on the phase sequence based on the updated time delay parameter to bring the phase consistency residual back within the causality boundary, and the phase mapping parameters used for frequency response reconstruction are updated synchronously.

[0177] After projection correction is completed, the data processing unit calls the frequency response reconstruction operator to reconstruct the set of physically realizable frequency response characterization parameters after projection correction into a predicted complex frequency response sequence. The predicted complex frequency response sequence outputs the complex sequences of transmission response and reflection response according to the target frequency point set. Singular value pruning is used to restore passivity and to check the causality and physical consistency of sampled scattering parameters, which are common engineering implementation paths.

[0178] In this embodiment, iterative training during the training phase is performed cyclically according to sample entries, specifically including:

[0179] For each training sample, the neural network model outputs a set of physically realizable frequency response characterization parameters and performs frequency response reconstruction. After obtaining the complex frequency response sequence, it performs passivity determination, causality determination, and stability determination.

[0180] When the condition is not met, projection correction is performed on the set of physically realizable frequency response characterization parameters, and then frequency response reconstruction is performed using the projected and corrected set of physically realizable frequency response characterization parameters to obtain the corrected complex frequency response sequence.

[0181] The calculation process for the difference is as follows:

[0182] On the same target frequency point set, read the complex values ​​of the corrected complex frequency response sequence and the complex frequency response labels in the training sample set point by point. Calculate the magnitude of the complex difference for each frequency point and accumulate them in order of frequency points to obtain the difference of the sample. Then, average the difference of each sample in a small batch to obtain the batch difference.

[0183] The model training unit uses batch difference as loss input to perform backpropagation and update the neural network model parameters.

[0184] When outputting projection correction traces during the prediction phase, the storage unit generates a retrospective record for each prediction and writes it to the projection correction trace field, including:

[0185] Record the results of the passivity determination, causality determination, and stability determination;

[0186] Record the set of frequency points that trigger projection correction;

[0187] Record the state matrix difference before and after projection correction, the maximum singular value difference before and after singular value clipping, and the time delay parameter difference before and after correction. The state matrix difference is obtained by calculating the difference between the elements before and after correction element by element-by-element and summing them over all elements. The maximum singular value difference is obtained by reading the maximum singular value before and after clipping and calculating the difference between them. The time delay parameter difference is obtained by reading the non-negative time delay parameters before and after correction and calculating the difference.

[0188] Simultaneously, the version identifiers of structural parameters, material parameters, and process deviation characterizations, as well as the neural network model version identifier, are recorded. The projection correction traces and the predicted complex frequency response sequence are stored together in the same traceability record so that the traceability record can be directly reused as a consistent audit and playback input.

[0189] The above embodiments can be implemented, in whole or in part, by software, hardware, firmware, or any other combination thereof. When implemented using software, the above embodiments can be implemented, in whole or in part, in the form of a computer program product.

[0190] Those skilled in the art will recognize that the modules and algorithm steps of the various examples described in conjunction with the embodiments disclosed herein can be implemented in electronic hardware, or a combination of computer software and electronic hardware. Whether these functions are implemented in hardware or software depends on the specific application and design constraints of the technical solution. Those skilled in the art can use different methods to implement the described functions for each specific application, but such implementation should not be considered beyond the scope of this application.

[0191] In addition, the functional modules in the various embodiments of this application can be integrated into one processing module, or each module can exist physically separately, or two or more modules can be integrated into one module.

[0192] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

[0193] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A neural network modeling method for predicting the frequency response behavior of filters, characterized in that: The specific steps include: Collect structural parameters, material parameters, and process deviations of thin-film filters to obtain corresponding complex frequency response labels. Perform frequency grid unification and phase continuity processing on the complex frequency response labels to form a training sample set. Define a set of physically realizable frequency response characterization parameters and establish a frequency response reconstruction operator. The frequency response reconstruction operator is used to reconstruct the set of physically realizable frequency response characterization parameters into a complex frequency response sequence. Construct a neural network model, input structural parameters, material parameters and process deviations into the neural network model, and output a set of physically realizable frequency response characterization parameters; The neural network model is iteratively trained based on the training sample set. Each iteration includes: outputting a set of physically realizable frequency response characterization parameters from the neural network model, obtaining a complex frequency response sequence through a frequency response reconstruction operator, performing passivity determination, causality determination, and stability determination on the complex frequency response sequence, and performing projection correction on the set of physically realizable frequency response characterization parameters when the determination is not satisfied. Input the structural parameters, material parameters and process deviation characterization of the thin-film filter to be predicted, output the set of physically realizable frequency response characterization parameters, generate the predicted complex frequency response sequence through projection correction and frequency response reconstruction operators, and output the projection correction trace.

2. The neural network modeling method for predicting filter frequency response behavior according to claim 1, characterized in that: The frequency grid unification for complex frequency response tags includes: Determine the target frequency point set, and perform resampling mapping on the complex frequency response labels on the target frequency point set to generate a complex frequency response sequence aligned with the frequency points; Structural parameters, material parameters, and process deviations are written into the sample entries, and the complex frequency response sequences of aligned frequency points are written into the same sample entry to form a training sample set.

3. The neural network modeling method for predicting filter frequency response behavior according to claim 2, characterized in that: Performing phase continuity processing on complex frequency response tags includes: Extract the phase sequence of the complex frequency response sequence and calculate the phase difference between adjacent frequency points; When the phase difference between adjacent frequency points exceeds the phase jump threshold, the phase sequence is compensated with an integer multiple of pi (2 times the circumference of a circle). The phase sequence and amplitude sequence after correction are recombined in a complex manner to obtain a complex frequency response tag with phase continuity.

4. The neural network modeling method for predicting filter frequency response behavior according to claim 1, characterized in that: The set of physically realizable frequency response characterization parameters includes stable dynamic parameters, static parasitic trend parameters, and time delay parameters. The stable dynamic parameter term includes the state matrix, input matrix, output matrix, and pass-through matrix, and a stability domain constraint is imposed on the state matrix; The delay parameter is limited to non-negative delay parameters; The static parasitic trend parameter is used to describe the response change trend of the direct channel and the parasitic channel within the target frequency band.

5. The neural network modeling method for predicting filter frequency response behavior according to claim 4, characterized in that: Frequency response reconstruction operators are used to reconstruct a set of physically realizable frequency response characterization parameters into a complex frequency response sequence, including: Calculate the dynamic response matrix corresponding to the stable dynamic parameter terms for each point in the target frequency set; The through-response matrix is ​​calculated point by point based on the static parasitic trend parameter and combined with the dynamic response matrix to form a composite response matrix; By generating frequency-dependent complex exponential phase factors point by point based on the time delay parameter and performing phase mapping on the composite response matrix, the complex frequency response sequences of the transmission response and reflection response are obtained.

6. The neural network modeling method for predicting filter frequency response behavior according to claim 4, characterized in that: Building a neural network model includes: A feature coding subnet is established to map the structural parameters, material parameters, and process deviations of the thin-film filter into frequency response-sensitive feature vectors; Establish a parameter generation subnet, which includes a dynamic parameter output branch, a parasitic trend output branch, and a time delay output branch; The dynamic parameter output branch outputs the state matrix, input matrix, output matrix, and pass-through matrix from the stable dynamic parameter items; the parasitic trend output branch outputs the static parasitic trend parameter items; and the time delay output branch outputs the time delay parameter items and performs non-negative constraint mapping on the time delay parameter items.

7. The neural network modeling method for predicting filter frequency response behavior according to claim 6, characterized in that: Performing passivity, causality, and stability determination on complex frequency response sequences includes: Based on the transmission response and reflection response, a scattering response matrix is ​​constructed point by point at the target frequency point set, and a set of singular values ​​is calculated. Based on the relationship between the set of singular values ​​and the passivity boundary, a passivity determination result is generated. The state matrix is ​​obtained based on the stable dynamic parameter terms, and the eigenvalues ​​of the state matrix are calculated. The stability determination result is generated based on the relationship between the eigenvalues ​​and the stable domain. Extract the phase sequence of the complex frequency response sequence and calculate the phase difference between adjacent frequency points. Generate the phase prediction increment based on the time delay parameter and calculate the phase consistency residual. Generate the causality determination result based on the relationship between the phase consistency residual and the causality boundary.

8. The neural network modeling method for predicting filter frequency response behavior according to claim 7, characterized in that: When the criteria are not met, projection correction is performed on the set of physically realizable frequency response characterization parameters, including: Perform a stable-domain projection on the state matrix and write back the stable dynamic parameter terms; For frequency points where passivity does not satisfy the label, singular value decomposition is performed and singular values ​​exceeding the passivity boundary are clipped to the boundary values. The corrected scattering response matrix is ​​reconstructed based on the clipped singular values ​​and the decomposition vector. Based on the corrected scattering response matrix and frequency response reconstruction operator, the correction amount of the static parasitic trend parameter term and the through matrix is ​​determined and written back to the physical frequency response characterization parameter set; Perform nonnegative projection on the time delay parameter term, and perform phase rectification on the phase sequence based on the time delay parameter term to update the phase mapping parameters used for frequency response reconstruction.

9. A neural network modeling method for predicting filter frequency response behavior according to claim 8, characterized in that: Iterative training of neural network models based on training sample sets includes: For each training sample, the neural network model outputs a set of physically realizable frequency response characterization parameters and performs frequency response reconstruction. It also performs passivity determination, causality determination, and stability determination, and performs projection correction when the determination is not satisfied. The frequency response is reconstructed again using the physically realizable frequency response characterization parameter set after projection correction to obtain the corrected complex frequency response sequence. The difference between the corrected complex frequency response sequence and the complex frequency response labels in the training sample set is calculated, and the neural network model parameters are updated by backpropagation based on the difference.

10. A neural network modeling method for predicting filter frequency response behavior according to claim 9, characterized in that: Output projection correction artifacts include: Record the results of the passivity determination, causality determination, and stability determination; Record the set of frequency points that trigger projection correction; Record the differences in the state matrix before and after projection correction, the differences in the maximum singular value before and after singular value clipping, and the differences in the time delay parameter terms before and after correction. Record the version identifiers of structural parameters, material parameters, and process deviations, as well as the version identifiers of the neural network model, and associate the projection correction traces with the predicted complex frequency response sequence as a traceability record.

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