A neural network-based s-parameter fitting method

Abstract

The application discloses a kind of S parameter fitting methods based on neural network, belong to microwave network modeling and electronic design automation technical field.This method is executed by processor, obtains the discrete S parameter data of to-be-fitted radio frequency network in target frequency range and carries out pre-processing, executes inverse Fourier transform to obtain time domain impulse response to standardized S parameter data set, after time gating, continuous wavelet transform is executed to obtain time-frequency joint feature, according to adjacent frequency point variation, second variation and model uncertainty Frequency point encryption index is calculated and enhanced data set is generated, the variational autoencoder including encoder and decoder is constructed, latent variable is generated and the S parameter fitting value of continuous frequency point is output by reparameterization skill, during training process, causality constraint term, passive constraint term and reciprocity constraint term are added to loss function.The local precision of S parameter fitting under wide frequency band multi-resonance scene can be improved by the application, to ensure that the fitting result meets the physical characteristics of radio frequency network.

Description

Technical Field

[0001] This invention relates to the field of microwave network modeling and electronic design automation technology, specifically to a neural network-based S-parameter fitting method. Background Technology

[0002] S-parameters, or scattering parameters, are core parameters describing the high-frequency reflection and transmission characteristics of multiport RF networks. In RF integrated circuit design, high-speed interconnect analysis, and electromagnetic compatibility simulation, S-parameters are typically obtained as discrete frequency points through full-wave electromagnetic simulation or vector network analyzer measurements. As the operating frequency of RF systems extends into the millimeter-wave band, parasitic effects, multipath reflections, and resonance phenomena in the circuit structure become increasingly significant. S-parameters exhibit characteristics of multiple resonances, rapid phase rotation, and local non-stationarity over a wide frequency band.

[0003] Traditional S-parameter fitting methods mainly include rational function fitting, spline interpolation, and polynomial fitting. While rational function fitting can characterize the zero-pole properties of a system, it is highly sensitive to the model order and initial values ​​in regions with uneven frequency distribution and dense resonance peaks. It is prone to local distortion near resonance spikes and struggles to simultaneously and strictly satisfy physical constraints such as causality, passivity, and reciprocity. Spline interpolation performs well in smooth regions, but loses local details at steep resonance peaks, resulting in the Gibbs phenomenon. Polynomial fitting is prone to Runge's phenomenon as the order increases, leading to oscillatory distortion in edge regions.

[0004] Existing neural network-based S-parameter fitting methods mostly employ a purely data-driven feedforward network structure, directly mapping frequency values ​​to the real and imaginary parts of the S-parameters. These methods suffer from three inherent drawbacks. First, the original frequency-domain S-parameters are high-dimensional complex sequences; directly inputting them into the network results in information redundancy, unstable gradient propagation, and insufficient generalization ability under sparse sampling conditions. Second, S-parameters are non-stationary signals over a wide frequency band; relying solely on single-frequency-domain features cannot capture the local time-varying characteristics of the resonant peak neighborhood, limiting their ability to express phase jumps and abrupt changes in group delay. Third, purely data-driven neural networks lack physical priors; the output results may violate the energy conservation law of passive networks, exhibiting non-causal responses or passive destruction, leading to divergence in subsequent circuit simulations.

[0005] Therefore, there is an urgent need for an S-parameter fitting method that can simultaneously guarantee local fitting accuracy and physical consistency under sparse sampling conditions. Summary of the Invention

[0006] The purpose of this invention is to overcome the shortcomings of existing technologies and propose an S-parameter fitting method based on neural networks, in which a processor executes the following steps:

[0007] S1: Obtain the discrete S-parameter data of the radio frequency network to be fitted within the target frequency range;

[0008] S2: Preprocess the discrete S-parameter data to obtain a standardized S-parameter dataset;

[0009] S3: Perform inverse Fourier transform on the standardized S-parameter dataset to obtain the time-domain impulse response, perform time gating on the time-domain impulse response to obtain a gated time-domain signal, and perform continuous wavelet transform on the gated time-domain signal to obtain time-frequency joint features;

[0010] S4: Calculate the frequency densification index based on the changes in adjacent frequency points, the second-order changes, and the model uncertainty. Determine the frequency points to be supplemented within the target frequency range based on the frequency densification index. Generate S-parameter supplementary data at the frequency points to be supplemented through the forward inference of the variational autoencoder. Add the S-parameter supplementary data to the standardized S-parameter dataset to obtain the enhanced dataset.

[0011] S5: Construct a variational autoencoder including an encoder and a decoder. Input the time-frequency joint features into the encoder to obtain a mean vector and a variance vector. Perform a reparameterization operation on the mean vector and the variance vector to obtain latent variables. Input the latent variables into the decoder to obtain S-parameter fitting values ​​for continuous frequency points.

[0012] S6: During the training process of the variational autoencoder, causal constraints, passive constraints, and reciprocity constraints are added to the loss function, and the weights of the variational autoencoder are iteratively updated based on the augmented dataset;

[0013] S7: Output the continuous S-parameter fitting results within the target frequency range.

[0014] Preferably, the preprocessing of the discrete S-parameter data includes:

[0015] The discrete S-parameter data are uniformly converted to a 50-ohm reference impedance.

[0016] Perform deduplication, sorting, and normalization on the frequency axis;

[0017] The complex S-parameters are decomposed into real and imaginary components; phase expansion is performed on the phase components; abnormal data points are identified based on changes in adjacent frequency points, local curvature, and repeated measurement deviations, and the abnormal data points are then removed, corrected, or downweighted.

[0018] Perform a consistency check on the S12 and S21 parameters of the reciprocal network.

[0019] Further preferably, performing an inverse Fourier transform on the standardized S-parameter dataset to obtain the time-domain impulse response includes:

[0020] The standardized S-parameter dataset is resampled to an equally spaced frequency grid.

[0021] Perform an inverse fast Fourier transform on each S-parameter channel to obtain the time-domain pulse. The inverse fast Fourier transform satisfies:

[0022] ;

[0023] In the formula This represents the number of frequency sampling points. For the first Frequency values ​​at each frequency point For the first Complex values ​​of S-parameters at each frequency point; a time-gated interval is set according to the main lobe energy distribution of the time-domain impulse response, the starting position of the time-gated interval is the equivalent delay position 5% before the main lobe peak, and the ending position of the time-gated interval is the equivalent delay position 5% after the main lobe peak.

[0024] Further preferably, performing a continuous wavelet transform on the gated time-domain signal to obtain joint time-frequency features includes: performing a continuous wavelet transform on the gated time-domain signal using a Morlet mother wavelet, wherein the continuous wavelet transform satisfies: In the formula For scale parameters, For translation parameters, The complex conjugate of the mother wavelet function; the scale parameter has 32 possible values; the original frequency domain features, the gated time domain signal, and the continuous wavelet transform output features are concatenated along the feature dimension to obtain the time-frequency joint features.

[0025] Further preferably, the frequency densification index is calculated based on the changes in adjacent frequency points, the second-order changes, and the model uncertainty, including: the frequency densification index satisfies:

[0026] ;

[0027] In the formula For the first The S-parameter at the i-th frequency point is relative to the i-th frequency point. First-order difference at each frequency point For the first The second-order difference of the S-parameters at each frequency point For the first Model prediction uncertainty at each frequency point , as well as The weighting coefficients; , as well as satisfy Based on the frequency point encryption index, the frequency intervals within the target frequency range are sorted from largest to smallest, and the frequency points to be supplemented are inserted in the first 30% of the frequency intervals.

[0028] A further preferred embodiment of constructing a variational autoencoder, including an encoder and a decoder, includes:

[0029] The encoder includes multiple levels of one-dimensional convolutional layers, batch normalization layers, and SiLU activation functions; the operations of the one-dimensional convolutional layers satisfy:

[0030] ;

[0031] In the formula These are the convolution kernel weight parameters. For bias parameters, Let be the SiLU activation function, and the SiLU activation function satisfies ;

[0032] The decoder includes multiple fully connected layers, the output dimension of which is equal to twice the total number of frequency points within the target frequency range, corresponding to the real and imaginary parts of the S-parameters, respectively.

[0033] Further preferably, performing a reparameterization operation on the mean vector and the variance vector to obtain the latent variables includes: the approximate posterior distribution of the latent variables is represented as follows: In the formula Let the mean vector be... Let Variance be the variance vector; the reparameterization operation satisfies:

[0034]

[0035] In the formula To obtain from the standard normal distribution Random variables obtained from sampling For the latent variables.

[0036] Further preferably, adding causality constraints, passivity constraints, and reciprocity constraints to the loss function includes: the loss function being a joint loss function, which satisfies:

[0037] ;

[0038] In the formula To reconstruct the loss term, For KL divergence regularization, For causal loss items, For passive loss terms, For reciprocity loss items, For smoothness loss term, , , as well as The weighting coefficients for each loss are: the reconstructed loss term calculates the mean square error between the predicted real part and the true value of the S-parameter and the mean square error between the predicted imaginary part and the true value of the S-parameter; the passive loss term constrains the maximum singular value of the S-parameter matrix at each frequency point to be no greater than 1; the reciprocity loss term constrains the L2 norm of the difference between the predicted values ​​of the S12 and S21 parameters.

[0039] Further preferably, iteratively updating the weights of the variational autoencoder based on the augmented dataset includes:

[0040] The variational autoencoder was trained end-to-end using the Adam optimizer.

[0041] A gradient clipping operation is performed during backpropagation, which restricts the gradient norm to below 1.0;

[0042] Training is stopped when the loss value on the validation set does not decrease after 20 consecutive training iterations.

[0043] When the amplitude error of the S-parameters on the validation set exceeds 0.5dB or the maximum singular value of the S-parameter matrix at a frequency point is greater than 1, return to the frequency point encryption index calculation step, redetermine the frequency points to be supplemented, and retrain the variational autoencoder.

[0044] Further preferably, obtaining the discrete S-parameter data of the radio frequency network to be fitted within the target frequency range includes:

[0045] The measured S-parameter data can be obtained by sweeping the frequency of the RF network to be fitted using a vector network analyzer; or, the simulated S-parameter data can be obtained by calling a full-wave electromagnetic solver in an electronic design automation environment to perform electromagnetic simulation on the parameterized layout structure.

[0046] Alternatively, the measured S-parameter data and the simulated S-parameter data can be merged in the frequency dimension to obtain combined S-parameter data;

[0047] The radio frequency network to be fitted includes on-chip inductors, radio frequency filters, connectors, packaged interconnect structures, and high-speed transmission channels.

[0048] Technical Effects: This invention maps frequency-domain S-parameters to the time domain using inverse Fourier transform, suppresses non-physical reflection components through time gating, and extracts multi-resolution time-frequency features through continuous wavelet transform, thus solving the problem of insufficient expression of non-stationary resonance characteristics by single frequency-domain features. An adaptive encryption mechanism based on frequency point changes and model uncertainty dynamically supplements sampling points in the resonance region and the region of rapid phase change, reducing local distortion under sparse sampling conditions. The variational autoencoder architecture combined with reparameterization techniques enhances the model's generalization ability. Joint training with multiple physical constraints of causality, passivity, and reciprocity ensures that the fitting results strictly conform to the physical laws of RF networks, and the output results can be directly used for subsequent circuit simulations. Attached Figure Description

[0049] Figure 1 This is a flowchart of the overall process of an S-parameter fitting method based on a neural network according to the present invention.

[0050] Figure 2 This is a structural block diagram of an S-parameter fitting system based on a neural network according to the present invention;

[0051] Figure 3 This is a schematic diagram of the feature enhancement process from frequency domain S-parameters to time domain gating and continuous wavelet transform in this invention;

[0052] Figure 4 This is a schematic diagram of the variational autoencoder fitting structure and physical constraint training process in this invention;

[0053] Figure 5 This is a schematic diagram of the original frequency domain amplitude spectrum in this invention;

[0054] Figure 6 This is a schematic diagram of the frequency domain amplitude spectrum after time-gated operation in this invention;

[0055] Figure 7 This is a schematic diagram of the temporal amplitude spectrum and gating threshold after IFFT in this invention. Detailed Implementation

[0056] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0057] Traditional S-parameter fitting produces non-physical oscillations in the multi-resonance region.

[0058] Based on this, please refer to Figures 1-7This invention provides a neural network-based S-parameter fitting method. The method comprises the following steps executed by a processor: acquiring discrete S-parameter data of the radio frequency network to be fitted within a target frequency range; preprocessing the discrete S-parameter data to obtain a standardized S-parameter dataset; performing an inverse Fourier transform on the standardized S-parameter dataset to obtain a time-domain impulse response; performing time gating on the time-domain impulse response to obtain a gated time-domain signal; performing a continuous wavelet transform on the gated time-domain signal to obtain joint time-frequency features; calculating a frequency point encryption index based on the changes in adjacent frequency points, second-order changes, and model uncertainty; determining the frequency points to be supplemented within the target frequency range based on the frequency point encryption index; and performing forward inference through the variational autoencoder within the target frequency range. S-parameter supplementary data is generated at the frequency points to be supplemented. This supplementary data is then added to the standardized S-parameter dataset to obtain an augmented dataset. A variational autoencoder (VAE) comprising an encoder and a decoder is constructed. The time-frequency joint features are input into the encoder to obtain a mean vector and a variance vector. A reparameterization operation is performed on the mean vector and the variance vector to obtain latent variables. These latent variables are then input into the decoder to obtain S-parameter fitting values ​​for continuous frequency points. During the training of the VAE, causality constraints, passivity constraints, and reciprocity constraints are added to the loss function. The weights of the VAE are iteratively updated based on the augmented dataset. Finally, continuous S-parameter fitting results within the target frequency range are output.

[0059] The discrete S-parameter data is a scattering parameter matrix of a multi-port RF network at discrete frequency points. Each matrix element is a complex number containing amplitude and phase information. The processor reads the S-parameter file from the storage medium, parses the frequency unit, reference impedance value, number of ports, and data format markers in the file header, and extracts the S-parameter matrix for each frequency point in ascending frequency order. The target frequency range is specified by the user and covers a continuous frequency band from the start frequency to the end frequency. The preprocessing operation performs a standardization transformation on S-parameter data from different sources and in different formats to eliminate the impact of data heterogeneity on subsequent training. The standardized S-parameter dataset is an S-parameter sequence that has undergone format unification, anomaly handling, and numerical normalization, with all samples having the same frequency axis length and numerical range.

[0060] The inverse Fourier transform converts frequency-domain scattering parameters into a time-domain impulse response. Physically, it decomposes the frequency response into a superposition of pulse echoes with different time delays. The RF network generates a time-domain response under unit pulse excitation. Electromagnetic signals from different propagation paths arrive at the port at different times. The intrinsic response of the device corresponds to the earliest arriving main pulse, while connector reflection, transmission line resonance, and fixture reflection correspond to later arriving pulses on the time axis. The inverse Fourier transform utilizes the orthogonality of sinusoidal basis functions to project frequency-domain measurements onto time-domain basis functions, achieving separation of signals with different time delays. The time-gating operation is a time-domain windowing operation, retaining the interval containing the main lobe on the time axis and setting time-domain sampled values ​​outside the interval to zero. The gated time-domain signal is a time-domain pulse sequence truncated by the time window function, containing only the early components corresponding to the intrinsic response of the device. The continuous wavelet transform performs multi-scale decomposition on the gated time-domain signal to obtain time-frequency coefficients at different scales. The time-frequency joint feature is a combination of the original frequency domain feature, gated time domain feature, and wavelet coefficients in the feature dimension, forming a multi-domain representation of the S-parameter electromagnetic response.

[0061] The frequency point encryption index is a scalar value measuring the information density at each frequency point. A larger value indicates more drastic changes in the S-parameters in that region or a lower confidence level in the model prediction. The change in adjacent frequency points is the F-norm of the difference between the S-parameter matrices at two adjacent frequency points, reflecting the slope of the S-parameter change with frequency. The second-order change is the difference in the changes of adjacent frequency points, reflecting the curvature of the S-parameter curve, with an extreme value of curvature at the resonance peak. The model uncertainty is calculated from the prediction variance of multiple random forward propagations during variational autoencoder inference. A larger variance indicates that the model's prediction for that frequency point is less stable. The frequency points to be supplemented are newly inserted frequency coordinates within the frequency intervals ranked higher by the encryption index. The forward inference of the variational autoencoder refers to inputting the coordinates of the frequency points to be supplemented into the decoder during training and outputting the predicted S-parameter values ​​at that frequency as supplementary data. The augmented dataset is a higher-density dataset formed by merging the original standardized S-parameter data and the supplementary S-parameter data on the frequency axis.

[0062] The variational autoencoder is a generative neural network structure comprising an encoder and a decoder. The encoder is a neural network that maps high-dimensional time-frequency features to low-dimensional latent space parameters, consisting of stacked one-dimensional convolutional layers, batch normalization layers, and activation function layers. The mean vector is the mathematical expectation of the Gaussian distribution in the latent space, and the variance vector is the variance parameter of the Gaussian distribution in the latent space. The reparameterization operation is a mathematical technique that transforms the random sampling process into a deterministic transformation, enabling gradients to propagate back through the sampling operation. The latent variables are low-dimensional vectors sampled from the latent Gaussian distribution, carrying the essential feature encoding of the input S-parameters. The decoder is a neural network that maps the low-dimensional latent variables back to the high-dimensional S-parameter space, consisting of fully connected layers. The S-parameter fitting values ​​at continuous frequency points are the sequence of real and imaginary parts of the full-band S-parameters output by the decoder, corresponding to a densely sampled continuous curve on the frequency axis.

[0063] The loss function is the objective function optimized during training, composed of a weighted average of data fitting terms and physical constraint terms. The causality constraint term penalizes predicted values ​​that violate the response characteristics of a causal system, ensuring that the output response does not precede the excitation time. The passivity constraint term penalizes singular values ​​in the S-parameter matrix greater than 1, ensuring that the RF network does not generate energy externally. The reciprocity constraint term penalizes... and The unequal predicted values ​​ensure that the network, which does not contain non-reciprocal media, satisfies the reciprocity theorem. The weights are the learnable parameter matrix in the neural network, iteratively updated using the backpropagation algorithm. This iterative update refers to the cyclical process of calculating the loss via forward propagation, calculating the gradient via backpropagation, and updating the parameters using the optimizer. The S-parameter fitting result is the full-band continuous S-parameters output by the variational autoencoder after training, written to a file in standard Touchstone format.

[0064] The multi-source S-parameters exhibit reference impedance differences. Therefore, preprocessing of the discrete S-parameter data includes: converting the discrete S-parameter data to a 50-ohm reference impedance; performing deduplication, sorting, and normalization on the frequency axis; decomposing the complex S-parameters into real and imaginary components; performing phase expansion on the phase components; identifying outlier data points based on changes in adjacent frequencies, local curvature, and repeated measurement deviations, and performing removal, correction, or weight reduction on these outlier data points; and preprocessing the reciprocal network... Parameters and Perform a consistency check on the parameters.

[0065] The reference impedance is the port characteristic impedance defined in the S-parameter definition. Different measurement devices or simulation settings may use 75 ohms or other impedance values. Impedance conversion is achieved through the conversion formula between S-parameters and Z-parameters. First, the S-parameters under the original impedance are converted into an impedance matrix, and then the impedance matrix is ​​converted into S-parameters under 50 ohms. 50 ohms is the standard reference impedance in the RF field, and unifying to this value ensures the comparability of data from different sources. Frequency axis deduplication refers to removing duplicate sampling points with identical frequency values ​​and retaining the first sample that appears. Frequency axis sorting refers to rearranging the S-parameter samples in ascending order of frequency value to ensure monotonically increasing frequency. Frequency axis normalization refers to dividing the frequency value by the maximum frequency value and mapping it to the zero-to-one interval to eliminate the influence of frequency dimensions on neural network training. The real part of the complex S-parameters is the real part of the complex scattering parameter, and the imaginary part is the imaginary part of the complex scattering parameter. Both the real and imaginary parts are real numbers and serve as two channels for the neural network output. Phase unwrapping refers to unwinding the principal phase values. When the difference between adjacent phases exceeds... Addition and subtraction Integer multiples of the phase, eliminating phase differences between positive and negative values. The transition at the boundary results in a continuous phase curve. Outlier data points refer to outliers that do not conform to the smoothness characteristics of S-parameters, including measurement glitches, simulation non-convergence points, and data recording errors. When the change in adjacent frequency points exceeds a set threshold, it is determined as a sudden change point; when the local curvature exceeds a set threshold, it is determined as a curvature anomaly point; and when the repeated measurement deviation exceeds a set threshold, it is determined as a random noise point. The removal refers to removing outliers from the dataset; the correction refers to replacing outliers with interpolated adjacent points; and the weighting refers to reducing the weight coefficient of outlier samples in the loss function. The reciprocal network refers to a passive radio frequency network that does not contain non-reciprocal media such as ferrite or plasma. The parameter is the transmission coefficient from port 2 to port 1. The parameter represents the transmission coefficients from port 1 to port 2, and the reciprocity theorem requires that they be equal. The consistency check refers to the calculation... and The norm of the difference is used to issue a warning when it exceeds a threshold, and the average of the two values ​​is taken as the correction value.

[0066] Non-uniform sampling leads to inverse transform artifacts. Therefore, performing an inverse Fourier transform on the standardized S-parameter dataset to obtain the time-domain impulse response includes: resampling the standardized S-parameter dataset to an equally spaced frequency grid; and performing an inverse fast Fourier transform on each S-parameter channel to obtain the time-domain impulse response. The inverse fast Fourier transform satisfies In the formula This represents the number of frequency sampling points. For the first Frequency values ​​at each frequency point For the first Complex values ​​of S-parameters at each frequency point; a time-gated interval is set according to the main lobe energy distribution of the time-domain impulse response, the starting position of the time-gated interval is the equivalent delay position 5% before the main lobe peak, and the ending position of the time-gated interval is the equivalent delay position 5% after the main lobe peak.

[0067] The resampling refers to obtaining S-parameter values ​​on an equally spaced frequency grid through linear interpolation between the original non-uniform frequency points. Equal-spaced sampling is an input requirement for the Fast Fourier Transform algorithm. The S-parameter channel refers to each element of the S-parameter matrix of a multi-port network; a two-port network contains... , , , Four channels, each performing an inverse transform independently. This formula is the standard definition of the discrete inverse Fourier transform, and its physical meaning is to transform the frequency domain... Each sampling point is represented as A linear combination of complex exponential basis functions, the combination coefficients of which are the time-domain sampled values. In the formula... This is a dimensionless integer representing the total number of sampling points on the frequency axis. The value range is determined by the number of frequency points specified by the user, with typical values ​​being 256, 512, or 1024. For the first The frequency values ​​at each frequency point are in Hertz, and the values ​​are distributed at equal intervals from the starting frequency to the ending frequency. For the first The S-parameters at each frequency point are complex, dimensionless, and represent the complex ratios defined in the scattering parameter definition. This represents the time value corresponding to the time domain sampling point, measured in seconds, and determined by the sampling frequency. The imaginary unit satisfies Exponential term For discrete Fourier basis functions, the corresponding frequency is A complex sinusoidal signal. Coefficients This is a normalization factor to ensure the energy of the inverse transform is normalized. The theoretical derivation of this formula is based on Fourier series expansion, where a periodic signal can be decomposed into a superposition of complex exponential signals of different frequencies. The summation under discrete sampling replaces continuous integration. The Fast Fourier Transform utilizes the symmetry and periodicity of the basis functions to reduce computational complexity from... Reduce to The main lobe is the lobe with the largest amplitude in the time-domain impulse response, concentrating most of the signal energy and corresponding to the direct transmission and reflection paths of the radio frequency network. The equivalent time delay is the time resolution corresponding to the reciprocal of the frequency range, equal to... The first and last 5% of the main lobe peak value were verified through time-domain windowing experiments. The main lobe energy accounted for over 99%, while the energy outside this range was due to multiple reflections and stray responses introduced by the test fixture. Time gating was implemented using a rectangular window function. The time-domain sampled values ​​inside the window remained unchanged, while the sampled values ​​outside the window were set to zero. After gating, the time-domain signal was Fourier transformed back to the frequency domain to obtain the filtered S-parameters.

[0068] Fixed-window time-frequency resolution is limited. Therefore, performing a continuous wavelet transform on the gated time-domain signal to obtain joint time-frequency features includes: performing a continuous wavelet transform on the gated time-domain signal using a Morlet mother wavelet, wherein the continuous wavelet transform satisfies… In the formula For scale parameters, For translation parameters, The complex conjugate of the mother wavelet function; the scale parameter has 32 possible values; the original frequency domain features, the gated time domain signal, and the continuous wavelet transform output features are concatenated along the feature dimension to obtain the time-frequency joint features.

[0069] This formula is the definition of continuous wavelet transform. Mathematically, it is the inner product of a signal and a wavelet basis function that has undergone scaling and translation. It measures the similarity between the signal and the wavelet basis at a specific time position and scale. In the formula... The input is a gated time-domain signal with dimensionless dimensions, representing time. The complex value of the impulse response at the location. is a scale parameter, a dimensionless positive real number, that controls the scaling of the wavelet basis functions. A larger value indicates a wider wavelet, corresponding to low-frequency components. The smaller the value, the narrower the wavelet, corresponding to high-frequency components. The translation parameter, measured in seconds, controls the position of the wavelet basis function on the time axis. The value corresponds to the time point where the wavelet center is located. For the mother wavelet function, To determine its complex conjugate, taking the conjugate for complex-valued wavelets ensures correct inner product operations. The Morlet mother wavelet is defined as... It is composed of a complex sinusoidal signal modulated by a Gaussian envelope, exhibiting locality in both the time and frequency domains. The theoretical basis of this formula is wavelet frame theory; a family of functions formed by scaling and translating the mother wavelet that satisfies the admissibility condition can completely represent... Arbitrary signals in space. The integration operation traverses the entire time axis, calculating the integral of the product of the signal and the wavelet basis at each time point. Unlike the short-time Fourier transform with a fixed window length, the wavelet transform uses a scaling parameter. A variable window length analysis is implemented, with wide time windows and narrow frequency windows corresponding to large scales for low-frequency analysis, and narrow time windows and wide frequency windows corresponding to small scales for high-frequency transient analysis. The 32 scale parameters are distributed proportionally from the smallest to the largest scale in a logarithmic manner, covering a continuous range from the highest frequency resolution to the highest time resolution. The logarithmic distribution ensures uniform analytical granularity across different frequency bands. The original frequency domain features are sequences of the real and imaginary parts of the standardized S-parameter dataset, preserving amplitude and phase information across the entire frequency band. The gated time domain signal is a time-gated impulse response sequence, preserving echo information at different time delays. The continuous wavelet transform output features are the wavelet coefficient magnitudes and phases at 32 scales, preserving multi-scale time-frequency local information. Feature concatenation refers to merging the three types of features into a one-dimensional feature vector along the channel dimension, which serves as the encoder input. The three types of features characterize S-parameter properties from different physical perspectives: frequency domain features represent the global frequency response, time domain features represent the echo delay distribution, and wavelet features represent local time-frequency transients. These three complement each other to form a complete feature set.

[0070] The density of the key area in uniform sampling is insufficient. Therefore, the frequency densification index is calculated based on the changes in adjacent frequency points, second-order changes, and model uncertainty. The frequency densification index satisfies the following conditions: In the formula For the first The S-parameter at the i-th frequency point is relative to the i-th frequency point. First-order difference at each frequency point For the first The second-order difference of the S-parameters at each frequency point For the first Model prediction uncertainty at each frequency point , as well as The weighting coefficients; , as well as satisfy Based on the frequency point encryption index, the frequency intervals within the target frequency range are sorted from largest to smallest, and the frequency points to be supplemented are inserted in the first 30% of the frequency intervals.

[0071] This formula is a quantization index for adaptive frequency point encryption. It weights and fuses three physical quantities reflecting the local characteristics of S-parameters into a single scalar to guide sampling density allocation. In the formula... For the first The encryption index at each frequency point is dimensionless; the larger the value, the more encrypted sampling is needed in that area. It is a first-order difference, dimensionless, representing the rate of change of S-parameters with frequency. Its physical meaning is the slope of the response curve at that frequency. A large slope indicates a fast amplitude or phase change, requiring a higher sampling rate. It is a second-order difference, dimensionless, representing the curvature of the S-parameter curve. Its physical meaning is the rate of change of the slope. The curvature reaches a maximum at the resonance peak, corresponding to a sharp inflection point in the S-parameter curve. The model uncertainty is dimensionless and is calculated from the prediction variance obtained by multiple random samplings of the same input during the inference of the variational autoencoder. A large variance indicates that the mapping of that region in the latent space is unstable and the model prediction confidence is low. It is a first-order difference weighting coefficient, dimensionless, with a value range of 0 to 1, which controls the proportion of the slope term in the encryption index. It is a second-order difference weighting coefficient, dimensionless, with a value range of 0 to 1, which controls the proportion of the curvature term in the encryption index. This is the uncertainty weighting coefficient, dimensionless, ranging from 0 to 1, controlling the proportion of the model confidence term in the encryption index. The sum of the three factors (uncertainty, confidence, and uncertainty) equals 1 to ensure the index is normalized to the 0-1 interval; a typical value is [value missing]. , , The curvature term has a slightly higher weight because the resonant peak position is mainly manifested as a curvature extremum. The formula is designed based on the sampling theorem in numerical analysis: the more drastic the function change, the greater the curvature, and the more uncertain the model, the higher the sampling density is required to ensure interpolation accuracy. First-order difference detection detects amplitude abrupt changes, second-order difference locates the resonant peak, and uncertainty detection detects model blind spots; these three dimensions cover three typical scenarios of insufficient sampling. After calculating the encryption index for all frequency points, the frequency axis is divided into equal-width intervals. The average value of the encryption index within each interval is calculated, and the intervals are sorted in descending order of average value. The top 30% of intervals are selected, and a new frequency point is inserted at the midpoint of each selected interval. The S-parameter value for this point is generated by the variational autoencoder through forward inference. The 30% encryption ratio increases the total number of frequency points by 30%, achieving a balance between computational load and accuracy improvement.

[0072] Ordinary networks have insufficient feature extraction capabilities. Therefore, a variational autoencoder comprising an encoder and a decoder is constructed, wherein the encoder includes multiple levels of one-dimensional convolutional layers, batch normalization layers, and a SiLU activation function; the operations of the one-dimensional convolutional layers satisfy... In the formula These are the convolution kernel weight parameters. For bias parameters, Let be the SiLU activation function, and the SiLU activation function satisfies The decoder includes multiple fully connected layers, the output dimension of which is equal to twice the total number of frequency points within the target frequency range, corresponding to the real and imaginary parts of the S-parameters, respectively.

[0073] This formula defines a one-dimensional convolution operation, which is the basic operational unit of a convolutional neural network. It extracts local features from the input sequence by sliding the convolution kernel. In the formula... For the input sequence, the first... Feature values ​​at each position, For the output sequence of the first... The convolution result at each position, For the convolution kernel Weight parameters for each position, For bias parameters, The summation range covers the entire width of the convolution kernel, serving as the position index within the kernel. The physical meaning of convolution is to slide a window across the input sequence, calculating the degree of matching between the features within the window and the kernel template. A larger output value indicates a greater similarity between the position and the pattern encoded by the kernel. Multiple layers of convolution are stacked to form hierarchical feature extraction. The first layer detects simple patterns such as edges and peaks; the second layer combines simple patterns to form complex patterns such as resonant lobes; and higher layers combine to form complete resonant structure features. The batch normalization layer calculates the mean and variance of the feature map output from each convolutional layer in the batch dimension, normalizing the features to zero mean and unit variance. Then, learnable scaling and translation parameters are used to restore expressive power, alleviate internal covariate shift problems, and allow for a larger learning rate to accelerate convergence. The SiLU activation function is defined as... Multiply , The function is in For positive time approximation linearity, in When the gradient is negative, it smoothly approaches zero. Compared to ReLU, the negative half-axis retains a non-zero gradient, avoiding neuron death issues. The gradient curve is smooth and without abrupt changes, making it suitable for deep network training. The encoder contains three levels of one-dimensional convolutional layers, each followed by batch normalization and SiLU activation. The convolutional kernel sizes are 7, 5, and 5, with 32, 64, and 128 channels respectively. The sequence length is progressively compressed to increase the number of channels, compressing high-dimensional input features into a compact feature map. Then, global average pooling and fully connected layers output the mean and variance vectors of the latent space. The fully connected layer is a linear transformation layer connecting each neuron to all neurons in the previous layer. The decoder uses three fully connected layers with dimensions of 256, 512, and... , The total number of target frequency points, correspond The real and imaginary parts of each frequency point are represented. The global connectivity of the fully connected layer enables it to model long-range coupling relationships between different frequency points. The full-band S-parameter response exhibits global correlation; a single resonant peak affects the response of the entire band. The fully connected structure is suitable for modeling this global characteristic. The decoder starts from low-dimensional latent variables and, through layer-by-layer linear transformation and nonlinear activation, ultimately maps them to a sequence of real and imaginary parts of the full-band S-parameters.

[0074] Deterministic autoencoders cannot interpolate. Therefore, performing a reparameterization operation on the mean vector and the variance vector to obtain latent variables includes: the approximate posterior distribution of the latent variables is represented as... In the formula Let the mean vector be... Let Variance be the variance vector; the reparameterization operation satisfies In the formula To obtain from the standard normal distribution Random variables obtained from sampling For the latent variables.

[0075] This formula represents the core reparameterization technique of variational autoencoders, solving the problem that non-differentiability of random sampling operations prevents end-to-end training. In the formula... The latent variable is a vector in a high-dimensional space, typically 32-dimensional, with each dimension independently following a Gaussian distribution. Given input Latent variables The approximate posterior distribution is assumed to be an isotropic Gaussian distribution, and the mean of the encoder output is... and variance Parameterization. It is the mean vector, with the same dimension as the latent variables, representing the central location of the latent distribution. It is a variance vector with the same dimension as the latent variables, representing the broadening of the latent distribution in each dimension. Let the multidimensional Gaussian distribution be represented by the probability density function. , As a potential spatial dimension, Let be a diagonal covariance matrix, with diagonal elements as follows: . To obtain from the standard normal distribution The random noise sampled in the middle is independent of the network parameters and does not participate in gradient calculation. The mathematical derivation of the reparameterization technique is as follows: direct sampling Operations related to and It is not differentiable because the randomness of the sampling results makes it impossible to calculate the gradient. Utilizing the additivity of the Gaussian distribution, if... ,but obey Distribution, transferring randomness to external noise , and As a parameter of deterministic transformation, the gradient can be obtained through... and Backpropagation along the path. This transformation does not change... The marginal distribution of the latent space makes the sampling process differentiable and supports end-to-end backpropagation training. Reparameterization gives the latent space a good structure; similar inputs correspond to similar positions in the latent space, and any point in the latent space corresponds to reasonable S-parameters after decoding, supporting smooth interpolation between two S-parameter samples. The loss function of the variational autoencoder includes a KL divergence term, penalizing... With standard normal prior The differences in parameters force the latent space to be normalized, preventing posterior collapse. After training, moving along a certain direction in the latent space corresponds to a continuous change in a physical property of the S-parameters, such as a shift in resonant frequency or a change in Q value, supporting parameterized S-parameter generation. Model uncertainty. By performing the same input during inference The next random forward propagation is calculated. The prediction result is in the first... The variance of each frequency point is obtained. The typical value is 20. The larger the variance, the more unstable the prediction at that frequency point.

[0076] Purely data-driven output violates physics. Therefore, adding causality constraints, passivity constraints, and reciprocity constraints to the loss function includes: the loss function being a joint loss function, which satisfies... In the formula To reconstruct the loss term, For KL divergence regularization, For causal loss items, For passive loss terms, For reciprocity loss items, For smoothness loss term, , , as well as The weighting coefficients for each loss term; the reconstruction loss term calculates the mean square error between the predicted and actual values ​​of the real part of the S-parameters and the mean square error between the predicted and actual values ​​of the imaginary part of the S-parameters; the passive loss term constrains that the maximum singular value of the S-parameter matrix at each frequency point is no greater than 1; the reciprocity loss term constrains... Parameter prediction values ​​and The L2 norm of the difference between the predicted parameter values.

[0077] This formula is a multi-task joint loss function, which weights and combines the data fitting objective with multiple physical constraint objectives, guiding the neural network to satisfy radio frequency physical laws while fitting the data. In the formula... To reconstruct the loss term, the mean square error between the predicted S-parameters and the true S-parameters is calculated. The real and imaginary parts are calculated separately and then added together. The dimension is dimensionless, ensuring that the predicted value is numerically close to the measured or simulated value. For the KL divergence regularization term, calculate the approximate posterior. With standard normal prior The Kullback-Leibler divergence between them is dimensionless and is expressed by the formula: Forced latent space regularization ensures generation capability. As a causal loss term, based on the Kramers-Kronig relation, the real and imaginary parts of the frequency response of the causal system are Hilbert transforms of each other. The predicted S-parameters are subjected to a Hilbert transform, and the norm of the difference between the transformed imaginary part and the predicted imaginary part is calculated as a causal penalty. The dimensionless value ensures that the response does not precede the excitation time. For the passive loss term, singular value decomposition is performed on the S-parameter matrix at each frequency point, and the maximum singular value is taken. ,like The penalty value is Otherwise, the penalty value is 0, the dimension is dimensionless, and the physical basis is that passive networks cannot output energy to the outside world, and the operator norm of the scattering matrix does not exceed 1. For the reciprocity loss term, calculate Predicted values ​​and The L2 norm of the predicted value difference is dimensionless and is based on the Lorentz reciprocity theorem, which states that the transmission coefficients of networks without non-reciprocal media are equal in both directions. As a smoothness loss term, the L2 norm of the second difference of the predicted S-parameters is calculated. It is dimensionless and suppresses non-physical high-frequency oscillations on the frequency domain curve. For causal loss weight, For passive loss weights, For reciprocity loss weight, The weights for smoothness loss are all dimensionless hyperparameters, with typical values ​​of [value missing]. , , , The weight of the physical constraint term is less than that of the reconstruction loss, allowing the network to prioritize fitting the data and then gradually satisfy the physical constraints. During training, the weighted sum of the various losses yields the total loss. Backpropagation calculates the gradient of the total loss with respect to the network parameters, and the optimizer updates the parameters based on the gradient. Physical constraints are added to the loss as a soft penalty, without hard-limiting the output range. Constraint violations are allowed in the early stages of training. As training progresses, the physical constraint term guides the network parameters to move towards the feasible solution region, ultimately ensuring that the output simultaneously satisfies data fitting accuracy and physical consistency.

[0078] Deep network training is prone to gradient explosion. Therefore, the iterative update of the variational autoencoder's weights based on the augmented dataset includes: end-to-end training of the variational autoencoder using the Adam optimizer; performing gradient pruning during backpropagation, whereby the gradient norm is restricted to below 1.0; stopping training when the loss value on the validation set fails to decrease after 20 consecutive training iterations; and returning to the frequency point encryption index calculation step when the S-parameter magnitude error on the validation set exceeds 0.5 dB or the maximum singular value of the S-parameter matrix at a frequency point is greater than 1, re-determining the frequency points to be supplemented, and retraining the variational autoencoder.

[0079] The Adam optimizer is an adaptive moment estimation optimization algorithm that maintains first-order and second-order moment estimates for each parameter, dynamically adjusts the learning rate for each parameter, and updates the parameters after performing bias correction on the first and second-order moments of the gradient. It is suitable for non-stationary objectives and sparse gradient scenarios. Training adopts an end-to-end approach, ensuring the entire computational graph from encoder input to decoder output is differentiable, and the gradient of the loss function is directly backpropagated to all learnable parameters. The gradient pruning operation calculates the global L2 norm of the gradient vector after backpropagation to obtain the gradients of all parameters. If the norm is greater than 1.0, the gradient vector is scaled proportionally to a norm of 1.0 before parameter updates. 1.0 is the gradient norm threshold, dimensionless. Large prediction errors at the resonant peak positions can lead to excessively large gradients; gradient pruning prevents excessively large parameter update steps from causing training oscillations or even divergence. A training epoch refers to traversing the entire training set once. After each epoch, the loss value is calculated on the validation set. If the validation loss does not fall below the historical best value for 20 consecutive epochs, early stopping is triggered, terminating training. Twenty rounds represent the early stopping patience value, dimensionless, balancing training sufficiency and overfitting risk. After training, the amplitude error is calculated frequency-by-frequency on the validation set, and the amplitude error is... The unit is decibels (dB). If a frequency point error exceeds 0.5 dB, it indicates that the region is underfitted. Singular value decomposition is performed on the predicted S-parameter matrix for each frequency point in the validation set. If the maximum singular value is greater than 1, it indicates that passivity has been violated. If either of these two situations occurs, instead of adjusting the network structure or hyperparameters, the process returns to the frequency encryption step. The encryption index for all frequencies is calculated using the current model. New frequency points are inserted in the region with the highest index. The S-parameters of the new points are generated through forward inference to supplement the data. This supplementary data is added to the augmented dataset, and the model is retrained from scratch using the expanded dataset. Iterative retraining forms a closed loop, with data encryption and model training alternating. Each iteration increases the sample density in key regions, gradually improving model accuracy until all regions in the validation set meet the amplitude error and passivity requirements. This mechanism transforms the model accuracy problem into a data distribution problem, eliminating the need for manually designed complex network structures. By adaptively increasing sample density, the model is guided to autonomously correct local errors, aligning with the principles of active learning.

[0080] Single-source data exhibits model bias. Therefore, obtaining discrete S-parameter data of the RF network to be fitted within the target frequency range includes: obtaining measured S-parameter data by performing frequency sweep measurements on the RF network to be fitted using a vector network analyzer; or, obtaining simulated S-parameter data by calling a full-wave electromagnetic solver in an electronic design automation environment to perform electromagnetic simulation on the parameterized layout structure; or, merging the measured S-parameter data and the simulated S-parameter data in the frequency dimension to obtain combined S-parameter data. The RF network to be fitted includes on-chip inductors, RF filters, connectors, packaged interconnect structures, and high-speed transmission channels.

[0081] The vector network analyzer is an RF measurement instrument that generates a swept excitation signal to input to the device under test (DUT), measures the amplitude and phase of the reflected and transmitted waves, and obtains the S-parameters after calibration. The measurement data includes actual manufacturing process deviations, material property tolerances, and assembly effects, reflecting the true electromagnetic response of the device. However, the number of measurement samples is limited, and the coverage of structural parameters is narrow. The electronic design automation environment is an integrated circuit design software platform that supports layout parameter extraction and electromagnetic simulation calls. The full-wave electromagnetic solver is based on the numerical solution of Maxwell's equations, using the finite element method, finite integral method, or method of moments to discretize the solution space and calculate the S-parameter response of a given layout structure over a wide frequency band. Parameterized layout structure refers to setting the device geometry as variable parameters, automatically traversing parameter combinations for batch simulation via scripts, generating a large number of S-parameter samples covering different numbers of turns, linewidths, spacing, and outer diameters. The simulation data sample size is large, and the parameter coverage is wide, but there are modeling errors compared to actual devices, such as metal roughness and dielectric loss tangent deviation. Merging measurement and simulation data in the frequency dimension means placing both types of samples into the same training set. Simulation data provides breadth, allowing the model to encounter a sufficient number of structural variations, while measurement data provides accuracy to calibrate the systematic biases of the simulation model. The model learns common physical laws from both types of data while correcting systematic errors. On-chip inductors are passive devices in integrated circuits that achieve impedance matching and resonance. A typical structure is a planar spiral metal coil, and its S-parameters exhibit obvious inductive resonance characteristics. RF filters are frequency-selective devices containing multiple resonant cavities. Their S-parameters transition rapidly between the passband and stopband, and multiple transmission zeros exist. Connectors are coaxial or waveguide connection structures. Their S-parameters are mainly characterized by the slow variation of insertion loss and return loss with frequency, generating local resonances at discontinuities. Package interconnect structures are vias, pads, and traces within the chip package. Their S-parameters are affected by parasitic parameters, resulting in multiple resonance peaks at high frequencies. High-speed transmission channels are differential traces on printed circuit boards. Their S-parameters include dielectric loss, conductor loss, and reflections caused by impedance discontinuities. Long channels generate significant inter-symbol interference, corresponding to periodic ripples in the frequency domain. This method covers the S-parameter modeling scenarios of the five typical RF passive networks mentioned above and is applicable in millimeter-wave bands and high-speed digital designs.

[0082] The above are merely preferred embodiments of the present invention and are not intended to limit the present invention in any other way. Any person skilled in the art may make changes or modifications to the above-disclosed technical content to create equivalent embodiments that can be applied to other fields. However, any simple modifications, equivalent changes, and modifications made to the above embodiments based on the technical essence of the present invention without departing from the scope of the present invention shall still fall within the protection scope of the present invention.

Claims

1. A method for S-parameter fitting based on neural networks, characterized in that, The processor performs the following steps: S1: Obtain the discrete S-parameter data of the radio frequency network to be fitted within the target frequency range; S2: Preprocess the discrete S-parameter data to obtain a standardized S-parameter dataset; S3: Perform inverse Fourier transform on the standardized S-parameter dataset to obtain the time-domain impulse response, perform time gating on the time-domain impulse response to obtain a gated time-domain signal, and perform continuous wavelet transform on the gated time-domain signal to obtain time-frequency joint features; S4: Calculate the frequency densification index based on the changes in adjacent frequency points, the second-order changes, and the model uncertainty. Determine the frequency points to be supplemented within the target frequency range based on the frequency densification index. Generate S-parameter supplementary data at the frequency points to be supplemented through the forward inference of the variational autoencoder. Add the S-parameter supplementary data to the standardized S-parameter dataset to obtain the enhanced dataset. S5: Construct a variational autoencoder including an encoder and a decoder. Input the time-frequency joint features into the encoder to obtain a mean vector and a variance vector. Perform a reparameterization operation on the mean vector and the variance vector to obtain latent variables. Input the latent variables into the decoder to obtain S-parameter fitting values ​​for continuous frequency points. S6: During the training process of the variational autoencoder, causal constraints, passive constraints, and reciprocity constraints are added to the loss function, and the weights of the variational autoencoder are iteratively updated based on the augmented dataset; S7: Output the continuous S-parameter fitting results within the target frequency range.

2. The S-parameter fitting method based on a neural network according to claim 1, characterized in that, Preprocessing the discrete S-parameter data includes: The discrete S-parameter data are uniformly converted to a 50-ohm reference impedance. Perform deduplication, sorting, and normalization on the frequency axis; The complex S-parameters are decomposed into real and imaginary components; phase expansion is performed on the phase components; abnormal data points are identified based on changes in adjacent frequency points, local curvature, and repeated measurement deviations, and the abnormal data points are then removed, corrected, or downweighted. Perform a consistency check on the S12 and S21 parameters of the reciprocal network.

3. The S-parameter fitting method based on neural networks according to claim 1, characterized in that, Performing an inverse Fourier transform on the standardized S-parameter dataset to obtain the time-domain impulse response includes: The standardized S-parameter dataset is resampled to an equally spaced frequency grid. Perform an inverse fast Fourier transform on each S-parameter channel to obtain the time-domain pulse. The inverse fast Fourier transform satisfies: ; In the formula This represents the number of frequency sampling points. For the first Frequency values ​​at each frequency point For the first Complex values ​​of S-parameters at each frequency point; a time-gated interval is set according to the main lobe energy distribution of the time-domain impulse response, the starting position of the time-gated interval is the equivalent delay position 5% before the main lobe peak, and the ending position of the time-gated interval is the equivalent delay position 5% after the main lobe peak.

4. The S-parameter fitting method based on a neural network according to claim 3, characterized in that, Obtaining time-frequency joint features by performing continuous wavelet transform on the gated time-domain signal includes: performing continuous wavelet transform on the gated time-domain signal using the Morlet mother wavelet, wherein the continuous wavelet transform satisfies: ; In the formula For scale parameters, For translation parameters, The scale parameter is the complex conjugate of the mother wavelet function; the scale parameter has 32 possible values; the original frequency domain features, the gated time domain signal, and the continuous wavelet transform output features are concatenated along the feature dimension to obtain the time-frequency joint features.

5. The S-parameter fitting method based on a neural network according to claim 1, characterized in that, The frequency densification index is calculated based on the changes in adjacent frequency points, the second-order changes, and the model uncertainty. The frequency densification index satisfies the following: ; In the formula For the first The S-parameter at the i-th frequency point is relative to the i-th frequency point. First-order difference at each frequency point For the first The second-order difference of the S-parameters at each frequency point For the first Model prediction uncertainty at each frequency point , as well as These are weighting coefficients; the weighting coefficients , as well as satisfy Based on the frequency point encryption index, the frequency intervals within the target frequency range are sorted from largest to smallest, and the frequency points to be supplemented are inserted in the first 30% of the frequency intervals.

6. The S-parameter fitting method based on a neural network according to claim 1, characterized in that, Constructing a variational autoencoder, which includes an encoder and a decoder, involves: The encoder includes multiple levels of one-dimensional convolutional layers, batch normalization layers, and SiLU activation functions; the operations of the one-dimensional convolutional layers satisfy: ; In the formula These are the convolution kernel weight parameters. For bias parameters, Let be the SiLU activation function, and the SiLU activation function satisfies ; The decoder includes multiple fully connected layers, the output dimension of which is equal to twice the total number of frequency points within the target frequency range, corresponding to the real and imaginary parts of the S-parameters, respectively.

7. The S-parameter fitting method based on a neural network according to claim 1, characterized in that, Performing a reparameterization operation on the mean vector and the variance vector to obtain latent variables includes: the approximate posterior distribution of the latent variables is represented as follows: In the formula Let the mean vector be... Let Variance be the variance vector; the reparameterization operation satisfies: In the formula To obtain from the standard normal distribution Random variables obtained from sampling For the latent variables.

8. The S-parameter fitting method based on a neural network according to claim 1, characterized in that, Adding causality constraints, passivity constraints, and reciprocity constraints to the loss function includes: the loss function being a joint loss function, which satisfies the following: ; In the formula To reconstruct the loss term, For KL divergence regularization, For causal loss items, For passive loss terms, For reciprocity loss items, For smoothness loss term, , , as well as The weighting coefficients for each loss are: the reconstructed loss term calculates the mean square error between the predicted real part and the true value of the S-parameter and the mean square error between the predicted imaginary part and the true value of the S-parameter; the passive loss term constrains the maximum singular value of the S-parameter matrix at each frequency point to be no greater than 1; the reciprocity loss term constrains the L2 norm of the difference between the predicted values ​​of the S12 and S21 parameters.

9. The S-parameter fitting method based on a neural network according to claim 1, characterized in that, Iterative updates to the weights of the variational autoencoder based on the augmented dataset include: The variational autoencoder was trained end-to-end using the Adam optimizer. A gradient clipping operation is performed during backpropagation, which restricts the gradient norm to below 1.0; Training is stopped when the loss value on the validation set does not decrease after 20 consecutive training iterations. When the amplitude error of the S-parameters on the validation set exceeds 0.5dB or the maximum singular value of the S-parameter matrix at a frequency point is greater than 1, return to the frequency point encryption index calculation step, redetermine the frequency points to be supplemented, and retrain the variational autoencoder.

10. The S-parameter fitting method based on a neural network according to claim 1, characterized in that, Obtaining the discrete S-parameter data of the radio frequency network to be fitted within the target frequency range includes: The measured S-parameter data can be obtained by sweeping the frequency of the RF network to be fitted using a vector network analyzer; or, the simulated S-parameter data can be obtained by calling a full-wave electromagnetic solver in an electronic design automation environment to perform electromagnetic simulation on the parameterized layout structure. Alternatively, the measured S-parameter data and the simulated S-parameter data can be merged in the frequency dimension to obtain combined S-parameter data; The radio frequency network to be fitted includes on-chip inductors, radio frequency filters, connectors, packaged interconnect structures, and high-speed transmission channels.

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