A device parameter extraction method and device based on Gaussian process regression

Abstract

The application discloses a device parameter extraction method and device based on Gaussian process regression, and the method comprises the following steps: calculating the parameter control range of the current iteration and the parameter control range of each previous iteration, projecting the space overlap interval formed by the parameter control range on the value selection range coordinate, and calculating the space overlap times of each space overlap interval on the value selection range coordinate; assigning the sampling probability of each space overlap interval from small to large according to the space overlap times from small to large, and obtaining the sampling rate required for the next iteration; thus, when determining the training sample required for the next iteration, the parameter information obtained by the Gaussian process regression model trained by the current training sample is considered, and the parameter information returned by all iterations is fused, and then the training sample range required for the next iteration is determined, so that the local optimal solution can be avoided.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of semiconductor integrated circuit design, and in particular to a device parameter extraction method and device based on Gaussian process regression. BACKGROUND

[0002] In the parameter extraction of MOS tube devices using simulation software, the following steps can be used: by setting the MOS tube parameters provided by the simulation software, the simulated current-voltage characteristics are obtained; the simulated current-voltage characteristics obtained are compared with the actual current-voltage characteristics of the MOS tube, and a certain set of parameters in the simulation software is extracted, so that the simulated current-voltage characteristics in the simulation software and the actual current-voltage characteristics of the MOS tube are close under the parameters.

[0003] The above steps can be realized by Gaussian process regression. The general method includes: first, by setting different parameters in the simulation software, the corresponding information between the parameters of the simulation software and the current-voltage characteristics is collected; second, the Gaussian process regression is used to model the corresponding information, and the purpose of regression of MOS tube parameters can be achieved.

[0004] Since the parameters of the simulation software for the MOS tube are generally more, and the corresponding relationship is more complex, and also due to the complexity of the Gaussian process regression calculation, when modeling, the method of multiple iterations can be used, and the range of parameters is reduced each time, and then the target parameters are extracted. However, in actual operation, there is a possibility that the modeling of the corresponding relationship between the parameters and the current-voltage is not accurate, which leads to the deviation of the returned parameter range from the target parameter, and then falls into a local optimal solution. SUMMARY

[0005] The present application aims to overcome the above-mentioned defects in the prior art, and provides a device parameter extraction method and device based on Gaussian process regression.

[0006] To achieve the above-mentioned purpose, the technical scheme of the present application is as follows:

[0007] The present application provides a device parameter extraction method based on Gaussian process regression, comprising the following steps:

[0008] Step S1: initialization, determining the parameter selection range;

[0009] Step S2: sampling the parameters according to the sampling rate of the current iteration to obtain a parameter sample set;

[0010] Step S3: device simulation, obtaining a characteristic information sample set corresponding to the parameter sample set;

[0011] Step S4: Use the characteristic information sample set as the observable input sample of Gaussian process regression, and use the parameter sample set as the observable output sample of Gaussian process regression, to train the model and obtain the Gaussian process regression model for the current iteration.

[0012] Step S5: Input the actual characteristic information of the device into the Gaussian process regression model of the current iteration to obtain the mean and standard deviation of the regressed parameters in the current iteration;

[0013] Step S6 determines whether the convergence condition is met. If it is met, proceed to step S10. If it is not met, continue to steps S7 to S9.

[0014] Step S7: Calculate the parameter control range for the current iteration based on the mean and standard deviation of the parameters in the current iteration;

[0015] Step S8: Calculate the spatial overlap interval formed by the projection of the parameter control range of the current iteration and the parameter control range of the previous iterations onto the selected value range coordinates, and the cumulative number of spatial overlap intervals on the selected value range coordinates. Assign sampling probabilities from small to large to each spatial overlap interval according to the number of spatial overlap intervals from small to large, and obtain the sampling rate of the next iteration.

[0016] Step S9: Replace the sampling rate of the current iteration with the sampling rate of the next iteration, and repeat steps S2 to S6;

[0017] Step S10: End.

[0018] Furthermore, in step S6, the convergence condition satisfies the following formula:

[0019] σ < 0.01 × (x max -x min Formula 1

[0020] Where σ represents the standard deviation, x max and x min These represent the upper and lower limits of parameter x within its range of values, respectively.

[0021] Furthermore, when the current iteration is the zeroth iteration, the sampling rate of the zeroth iteration is defined as a preset sampling rate; from the first iteration after the zeroth iteration, the sampling rate satisfies the following formula two:

[0022] Q m (x)=p0×F m-1 (x) Formula 2

[0023] Among them, Q m(x) represents a sampling rate of the mth iteration, x represents a parameter, m is a positive integer, p0 represents a minimum sampling probability of the current iteration, F m-1 (x) represents a spatial overlap rate representation function of the m-1th iteration, and satisfies the following formula three:

[0024]

[0025] Wherein, f * (x) represents a representation function of the original space, and satisfies the following formula four:

[0026]

[0027] Wherein, x max And x min Respectively represent the upper limit value and the lower limit value of the parameter x in the selected value range;

[0028] f i (x) represents a spatial representation function of the ith iteration, and satisfies the following formula five:

[0029]

[0030] Wherein, u represents the mean, sigma represents the standard deviation, and i is a natural number.

[0031] Further, the preset sampling rate includes a sampling rate under uniform sampling in the selected value range.

[0032] Further, the minimum sampling probability p0 satisfies the following formula six:

[0033]

[0034] The application also provides a device parameter extraction device based on Gaussian process regression, comprising:

[0035] The processing module is used for setting the parameter sample set obtained by sampling the acquired parameter in the selected value range according to the sampling rate of the current iteration to the simulation module for device simulation, taking the obtained characteristic information sample set corresponding to the parameter sample set as the observable input sample of the Gaussian process regression, and taking the parameter sample set as the observable output sample of the Gaussian process regression, performing model training to obtain the Gaussian process regression model of the current iteration, and inputting the actual characteristic information of the device into the Gaussian process regression model of the current iteration to obtain the parameter mean and standard deviation of the current iteration of the regression parameter;

[0036] The judging module is used for judging whether the convergence condition is met, and if yes, notifying the processing module to end the parameter extraction, and if not, sending information to the spatial overlap rate calculation module.

[0037] a space overlap rate calculation module, configured to calculate a parameter control range of the current iteration of the parameter according to the parameter mean value and the standard deviation of the current iteration of the parameter when the convergence condition is not met, and calculate a space overlap interval formed by projecting the parameter control range of the current iteration and the parameter control ranges of previous iterations on the selected value range coordinate, and a cumulative space overlap number of each space overlap interval on the selected value range coordinate;

[0038] a sampling module, configured to assign a sampling probability from small to large to each space overlap interval from small to large according to the space overlap number, calculate a sampling rate of the next iteration, replace the sampling rate of the current iteration with the sampling rate of the next iteration, perform sampling of the next iteration, and provide a parameter sample set of the next iteration to the processing module.

[0039] Further, the convergence condition satisfies the following formula one:

[0040] σ < 0.01 x (x max - x min ) Formula one

[0041] wherein σ represents the standard deviation, x max and x min represent the upper limit value and the lower limit value of the parameter x in the selected value range respectively.

[0042] Further, when the current iteration is the zeroth iteration, the sampling rate of the zeroth iteration is a preset sampling rate in the sampling module; from the first iteration after the zeroth iteration, the sampling rate satisfies the following formula two:

[0043] Q m (x) = p0 x F m-1 (x) Formula two

[0044] wherein Q m (x) represents the sampling rate of the mth iteration, x represents the parameter, m is a positive integer, p0 represents the minimum sampling probability of the current iteration, and F m-1 (x) represents a space overlap rate representation function of the (m-1)th iteration, and satisfies the following formula three:

[0045]

[0046] wherein f * (x) represents an original space representation function, and satisfies the following formula four:

[0047]

[0048] wherein x max and xmin respectively represent the upper limit value and the lower limit value of the parameter x in the selected value range;

[0049] f i (x) represents the spatial representation function of the i-th iteration, and satisfies the following formula five:

[0050]

[0051] Wherein, u represents the mean, σ represents the standard deviation, and i is a natural number.

[0052] Further, the preset sampling rate includes a sampling rate under uniform sampling in the selected value range.

[0053] Further, the minimum sampling probability p0satisfies the following formula six:

[0054]

[0055] As can be seen from the above technical solutions, the present application obtains the sampling rate required for the next iteration by calculating the spatial overlap interval formed by the projection of the parameter control range of the current iteration and the parameter control range of each previous iteration on the selected value range coordinate, and the spatial overlap times of each spatial overlap interval on the selected value range coordinate, and assigning a small-to-large sampling probability to each spatial overlap interval from small to large according to the spatial overlap times, so that when determining the training sample required for the next iteration, not only the parameter information obtained by the Gaussian process regression model trained by the current training sample is considered, but also all the parameter information returned by each iteration is fused to determine the training sample range required for the next iteration, thereby avoiding falling into a local optimal solution. BRIEF DESCRIPTION OF DRAWINGS

[0056] Figure 1 A flowchart of a device parameter extraction method based on Gaussian process regression according to the present application;

[0057] Figure 2 A method block diagram of device parameter extraction based on Gaussian process regression according to the method of Figure 1 a preferred embodiment of the present application;

[0058] Figure 3 A schematic diagram of spatial overlap rate calculation and sampling rate calculation according to a preferred embodiment of the present application. DETAILED DESCRIPTION

[0059] In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below. Obviously, the described embodiments are only some but not all of the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative efforts should fall into the scope of the present application. Unless otherwise defined, the technical terms or scientific terms used herein should be understood as their common meanings to those of ordinary skill in the art to which the present application belongs. The words such as "comprise" and the like used herein mean that the elements or objects before the words encompass the elements or objects listed after the words and their equivalents, and do not exclude other elements or objects.

[0060] The specific embodiments of the present application will be further described in detail below with reference to the accompanying drawings.

[0061] Please refer to Figure 1 , Figure 1 The flow chart of a device parameter extraction method based on Gaussian process regression of the present application is shown in FIG. 1. As shown in FIG. 1, the device parameter extraction method based on Gaussian process regression of the present application comprises the following steps: Figure 1

[0062] Step S1: initialization, determining the parameter value range.

[0063] Please refer to Figure 2 . When the device parameter extraction method based on Gaussian process regression of the present application is implemented, the parameter range initialization process is performed first to determine the parameter value range [x min , x max ].

[0064] This step can be completed by manual or automatic equipment.

[0065] Step S2: sampling the parameters according to the sampling rate of the current iteration to obtain the parameter sample set.

[0066] A simulation software, for example, SPICE simulation software, can be used to sample the parameter value x j data of the parameter x, i.e., x j ∈[x min , x max ], within the parameter value range [x min , x max ] of the device parameter x on the SPICE simulation software by the sampling module according to the calculated sampling rate of the current iteration. Wherein, x can represent a parameter, i.e., a numerical value, or multiple parameters, i.e., a vector.

[0067] The above-mentioned device can be a MOS tube. However, it is not limited thereto.​

[0068] The parameter x can be a conventional parameter of the MOS tube, such as a saturation drain current, a gate-source resistance, an opening voltage, and the like.

[0069] When the sampling is completed, a set of data samples, i.e., {x j} is obtained.

[0070] Thus, a set of parameters x, X = {x1, x2,..., x n} is obtained, where X is a set of x j , and j is 1 to n.

[0071] Step S3: Device simulation is performed to obtain a set of characteristic information samples corresponding to the set of parameter samples.

[0072] The sampled parameter x j is set to the SPICE simulation software by a processing module to perform device simulation, so that a characteristic information y j corresponding to the parameter x j is obtained, which can be a current-voltage characteristic information y j of the MOS tube.

[0073] When the data in the set X is completely set, a set of data samples {y j} corresponding to the set X output by the SPICE simulation software is obtained.

[0074] Thus, a set of parameters y, Y = {y1, y2,..., y n} is obtained, where Y is a set of y j , and j is 1 to n.

[0075] At this time, the data samples for modeling are prepared.

[0076] Step S4: The set of characteristic information samples is taken as an observable input sample of the Gaussian process regression, and the set of parameter samples is taken as an observable output sample of the Gaussian process regression, and model training is performed to obtain a Gaussian process regression model of the current iteration.

[0077] Then, the set of current-voltage information Y is taken as an observable input sample of the Gaussian process regression, and the set of parameters X is taken as an observable output sample of the Gaussian process regression, and model training is performed to obtain a Gaussian process regression model of the current iteration.

[0078] Step S5: The actual characteristic information of the device is input into the Gaussian process regression model of the current iteration to obtain a current iteration parameter mean and a standard deviation of the regressed parameter.

[0079] Then, the actual current-voltage characteristic information y of the MOS transistor can be continuously input to the processing module * to the Gaussian process regression model of the current iteration to obtain the parameter mean u and the standard deviation σ of the current iteration of the regressed parameter x, and complete one regression process.

[0080] Step S6: Determine whether the convergence condition is met. If yes, go to step S10. If no, continue with steps S7 to S9.

[0081] The convergence condition can be determined by the judging module by comparing the standard deviation σ of the regressed parameter with a set standard.

[0082] For example, the set standard can be that the convergence condition satisfies the following formula one:

[0083] σ < 0.01 x (x max - x min ) Formula one

[0084] wherein σ represents the standard deviation, x max and x min represent the upper limit value and the lower limit value of the selected value range of the parameter x on the SPICE simulation software, respectively.

[0085] When the size of the standard deviation σ of the regressed parameter satisfies formula one, it can be determined that the convergence condition is met, and the parameter extraction of the MOS transistor is completed.

[0086] On the contrary, when the size of the standard deviation σ of the regressed parameter does not satisfy formula one, it can be determined that the convergence condition is not met, a new iteration process is needed, and the following steps can be continued.

[0087] Step S7: Calculate the parameter control range of the current iteration of the parameter x according to the parameter mean and the standard deviation of the current iteration.

[0088] The parameter control range of the current iteration of the parameter x can be calculated by the space overlap rate calculation module according to the parameter mean u and the standard deviation σ of the current iteration obtained by regression when receiving the information that the convergence condition is not met sent by the judging module.

[0089] In a preferred embodiment, the space overlap rate calculation module can set the control limit as 3 times the standard deviation σ based on the parameter mean u of the current iteration obtained by regression to calculate the parameter control range of the current iteration of the parameter x. That is, the parameter control range of the current iteration of the parameter x is u-3σ to u+3σ.

[0090] Step S8: calculating the parameter control range of the current iteration and the space overlap intervals formed by the projection of the parameter control ranges of the previous iterations on the value range coordinate, and the cumulative space overlap times of each space overlap interval on the value range coordinate, assigning a sampling probability from small to large to each space overlap interval according to the space overlap times from small to large, and obtaining the sampling rate of the next iteration.

[0091] Since the model has not been built at the initial zeroth iteration, the parameter mean u and the standard deviation σ cannot be obtained. Therefore, when the current iteration is the zeroth iteration, the sampling rate of the zeroth iteration can be defined as a preset sampling rate, which can be set through the sampling module. For example, the preset sampling rate can include the sampling rate when uniform sampling is performed in the value range.

[0092] From the first iteration after the zeroth iteration, the sampling module can use the calculation result of the space overlap rate calculation module to calculate the sampling rate. Moreover, the calculation of the sampling rate can satisfy the following Formula Two:

[0093] Q m (x) = p0xF m-1 (x) Formula Two

[0094] wherein, Q m (x) represents the sampling rate of the mth iteration, x represents the parameter, m is a positive integer, p0 represents the minimum sampling probability of the current iteration, F m-1 (x) represents the space overlap rate representation function of the m-1th iteration formed by using the calculation result of the space overlap rate calculation module, and satisfies the following Formula Three:

[0095]

[0096] wherein, f * (x) represents the representation function of the original space, and satisfies the following Formula Four:

[0097]

[0098] wherein, x max and x min represent the upper limit value and the lower limit value of the parameter x in the value range, respectively;

[0099] f i (x) represents the space representation function of the ith iteration, and satisfies the following Formula Five:

[0100]

[0101] wherein, u represents the mean, σ represents the standard deviation, and i is a natural number.

[0102] Furthermore, the minimum sampling probability p0 in Formula 2 can satisfy the following Formula 6:

[0103]

[0104] Please see Figure 3 , Figure 3 The top image shows a diagram illustrating the calculation of spatial overlap rate, while the bottom image shows a diagram illustrating the corresponding sampling rate calculation. (For example...) Figure 3 As shown in the figure, the horizontal axis represents the range of values ​​for parameter x, and the vertical axis represents the sampling probability. The lengths of the four horizontal bars from bottom to top represent the range of values ​​for parameter x (the selectable range of the parameter). The left end of each bar, projected onto the horizontal axis, corresponds to the origin of the coordinate system and represents the lower limit of parameter x within its range in the SPICE simulation software. min The point where the right end of the horizontal bar falls on the horizontal axis of the coordinate system below the graph represents the upper limit of the range of values ​​for parameter x in the SPICE simulation software. max .

[0105] When performing the 0th iteration (the second horizontal bar from the bottom in the diagram, i.e., the initial modeling), since a preset sampling rate of uniform sampling within the selected value range is used, the parameter control range can be considered to coincide with the selected value range. Therefore, the parameter control range for the 0th iteration is x. min ~x max At this point, the projection of the parameter control range of the 0th iteration onto the horizontal axis of the selected value range coordinate system below the graph will form a spatially overlapping interval x. min ~ x max Among them, the spatially overlapping interval x min ~x max The parameter control range of the 0th iteration is projected separately onto the horizontal axis of the selected value range coordinate below the figure, and its spatial overlap number (cumulative spatial overlap number) is counted as "1";

[0106] When performing the first iteration (shown as the third horizontal bar from bottom to top), the parameter control range for the first iteration, u0-3σ0 to u0+3σ0, can be calculated using the spatial overlap calculation module based on the parameter mean u0 and standard deviation σ0 obtained from the regression in the 0th iteration. Thus, the three intervals formed by projecting the parameter control range for the first iteration onto the horizontal axis of the selected value range coordinate system below the graph can be calculated, namely: interval x... min ~u0-3σ0, the interval u0-3σ0~u0+3σ0 and the interval u0+3σ0~x max .

[0107] The spatial overlap calculation module projects the parameter control range of the first iteration onto the horizontal axis of the selected value range coordinate system shown in the figure, forming three intervals x. min~ u0-3σ0, u0-3σ0 ~ u0+3σ0 and u0+3σ0 ~ x max The projection of the parameter control range of the 0th iteration on the horizontal axis of the selected value range coordinate under the graph forms an interval x min ~ x max After superposition, three new spatial overlap intervals are calculated, namely x min ~ u0-3σ0, u0-3σ0 ~ u0+3σ0 and u0+3σ0 ~ x max . Among them, the spatial overlap interval x min ~ u0-3σ0 and u0+3σ0 ~ x max The projection of the parameter control range of the 0th iteration on the horizontal axis of the selected value range coordinate under the graph forms an interval x

[0108] When the 2nd iteration shown in the 4th horizontal bar from bottom to top is performed, the parameter control range u1-3σ1~u1+3σ1 of the 2nd iteration can be calculated by the spatial overlap rate calculation module according to the parameter mean u1 and the standard deviation σ1 obtained by regression in the 1st iteration. In this way, the parameter control range of the 2nd iteration on the horizontal axis of the selected value range coordinate under the graph can be calculated to form three intervals, namely: interval x min ~ u1-3σ1, interval u1-3σ1~u1+3σ1 and interval u1+3σ1~x max .

[0109] The spatial overlap rate calculation module projects the three intervals x min ~ u1-3σ1, interval u1-3σ1~u1+3σ1 and interval u1+3σ1~x max formed by the parameter control range of the 2nd iteration on the horizontal axis of the selected value range coordinate under the graph and the three intervals x min ~ u0-3σ0, u0-3σ0 ~ u0+3σ0 and u0+3σ0 ~ x max formed by the parameter control range of the 1st iteration on the horizontal axis of the selected value range coordinate under the graph are superimposed. min ~ x max After superposition, five new spatial overlap intervals are calculated, namely x min ~ u0-3σ0, u0-3σ0~u1-3σ1, u1-3σ1~u0+3σ0, u0+3σ0~u1+3σ1 and u1+3σ1~x max . Among them, the spatial overlap interval xmin ~u0-3σ0 and u1+3σ1~x max All of them are formed by projecting the parameter control range of the 0th iteration onto the horizontal axis of the selected value range coordinates below the figure, and their cumulative spatial overlap count is "1"; the spatial overlap interval u0-3σ0~u1-3σ1 is formed by superimposing the parameter control range of the 0th iteration and the parameter control range of the 1st iteration onto the horizontal axis of the selected value range coordinates below the figure, and the spatial overlap interval u0+3σ0~u1+3σ1 is formed by superimposing the parameter control range of the 0th iteration and the parameter control range of the 2nd iteration onto the horizontal axis of the selected value range coordinates below the figure, and their cumulative spatial overlap count is "2"; the spatial overlap interval u1-3σ1~u0+3σ0 is formed by superimposing the parameter control range of the 0th iteration, the parameter control range of the 1st iteration, and the parameter control range of the 2nd iteration onto the horizontal axis of the selected value range coordinates below the figure, and its cumulative spatial overlap count is "3".

[0110] The first horizontal bar from bottom to top in the figure shows the calculation results of the spatial overlap rate corresponding to the cumulative number of spatial overlaps between the 0th and 2nd iterations and the spatial overlap interval.

[0111] Based on the calculation results of the spatial overlap rate calculation module, the sampling module can use Formula 2 to calculate the sampling rate for the next iteration.

[0112] In Formulas 4 and 5, the numbers “0” and “1” represent the spatial overlap rate, which is the cumulative number of spatial overlaps after weighting. When the weight is 1, the value of the spatial overlap rate is equal to the cumulative number of spatial overlaps.

[0113] Figure 3 The figure below shows the sampling probabilities calculated by the sampling module for each spatially overlapping interval on the figure. According to Formula 2, when the spatially overlapping interval x... min ~u0-3σ0 and u1+3σ1~x max When the spatial overlap rate is 1, the sampling probability performed in the two spatially overlapping intervals is the minimum sampling probability p0.

[0114] When the spatial overlap rate of the spatial overlap intervals u0-3σ0~u1-3σ1 and u0+3σ0~u1+3σ1 is 2, the sampling probability performed in these two spatial overlap intervals is twice the minimum sampling probability p0. That is, the sampling probability performed in the spatial overlap intervals u0-3σ0~u1-3σ1 and u0+3σ0~u1+3σ1 is higher than that in the spatial overlap intervals x. min ~u0-3σ0 and u1+3σ1~x max The sampling probability is twice that of the standard sampling probability.

[0115] When the spatial overlap rate of the spatial overlap interval u1-3σ1~u0+3σ0 is 3, the sampling probability performed on the spatial overlap interval is 3 times of the minimum sampling probability p0, that is, the spatial overlap interval u1-3σ1~u0+3σ0 is performed with 3 times sampling probability higher than the spatial overlap intervals x min ~u0-3σ0 and u1+3σ1~x max .

[0116] The sampling rate of the formula two reflects a set composed of the sampling probabilities of each spatial overlap interval calculated by the sampling module.

[0117] The above sampling calculation method of the present application is described in detail below by examples.

[0118] Suppose the value range of the parameter x is x min =1, x max =3. Then:

[0119] At the 0th iteration, the sampling rate is uniform sampling, that is, in the range of values 1 to 3, the probability of each value point being sampled is equal.

[0120] Suppose the lower limit and the upper limit of the parameter control range of the 0th iteration obtained by regression calculation are respectively:

[0121] u0-3×σ0=1.5,

[0122] u0+3×σ0=2.5;

[0123] Then according to the formula five, its spatial representation function is:

[0124]

[0125] According to the formula three, its spatial overlap rate function is:

[0126] F0(x)=f * (x)+f0(x)

[0127] That is:

[0128]

[0129] When the sampling of the 1st iteration is performed, the sampling rate is calculated as follows:

[0130] Q1(x)=p0×F0(x)

[0131] That is:

[0132]

[0133] Wherein, it can be calculated by the formula six:

[0134]

[0135] The p0 can be 1 / 3, and the expression of the sampling rate is obtained.

[0136] The calculation for the first iteration is the same as the calculation for the zeroth iteration, and will not be repeated.

[0137] Different weights can be given to the cumulative spatial overlap times of different spatial overlap intervals.

[0138] In this way, by using the above-mentioned special sampling method designed by the application, not only is the sampling rate of the next iteration determined based on the current iteration result, but also the parameter information returned by all iterations is fused, so that falling into a local optimal solution can be avoided.

[0139] Step S9: The sampling rate of the next iteration is used to replace the sampling rate of the current iteration, and steps S2 to S6 are repeated.

[0140] When the mean u and the standard deviation σ of the parameter x of the zeroth iteration regression do not satisfy the convergence condition of, for example, formula one, after the sampling module calculates the sampling rate for the first iteration, sampling with different probabilities is performed on different spatial overlap intervals, and the method of steps S2 to S6 is repeated. If the mean u and the standard deviation σ of the parameter x of the first iteration regression still do not satisfy the convergence condition of formula one, steps S7 to S9 are continued to be repeated, the sampling rate for the second iteration is calculated, and steps S2 to S6 are repeated again. Until the mean u and the standard deviation σ of the parameter x of a certain iteration regression can satisfy the convergence condition, step S10: the extraction of the parameter is completed.

[0141] Next, a device parameter extraction device based on Gaussian process regression of the application will be described in detail with reference to the accompanying drawings.

[0142] The device parameter extraction device based on Gaussian process regression of the application can be used to execute the device parameter extraction method based on Gaussian process regression of the application described above. The device can include a processing module, a judgment module, a spatial overlap rate calculation module, and a sampling module, and the like.

[0143] Please refer to Figures 1-3 The processing module can be used to sample a set of parameter samples X={x1, x2,..., x min , x max} in the value range [x ndevice simulation according to step S3; and according to step S4, a set of characteristic information samples Y = {y1, y2,..., yN} corresponding to the parameter sample set X = {x1, x2,..., xN} is obtained. n The set of characteristic information samples Y = {y1, y2,..., yN} is taken as the observable input sample of the Gaussian process regression, and the parameter sample set X = {x1, x2,..., xN} is taken as the observable output sample of the Gaussian process regression, and the model training is performed to obtain the Gaussian process regression model of the current iteration; and according to step S5, the actual characteristic information of the device is input into the Gaussian process regression model of the current iteration to obtain the current iteration parameter mean u and standard deviation σ of the regression parameter x.

[0144] The simulation module is provided with simulation software, which can be SPICE simulation software. The device can be a MOS tube.

[0145] The judgment module can be used to judge whether the parameters (including the mean u and the standard deviation σ) extracted in the current iteration meet the convergence condition according to step S6. If the convergence condition is met, the processing module is informed to end the parameter extraction, and if the convergence condition is not met, the information is sent to the space overlap rate calculation module.

[0146] The convergence condition can be set to meet the above formula one.

[0147] The space overlap rate calculation module can be used to calculate the parameter control range of the current iteration parameter x, such as the parameter control range of u-3σ to u+3σ, according to the current iteration parameter mean u and standard deviation σ according to step S7 when the convergence condition is not met; and according to step S8, the space overlap interval formed by the projection of the parameter control range of the current iteration and the parameter control range of each iteration on the value range coordinate, and the cumulative space overlap number of each space overlap interval on the value range coordinate are calculated, as shown in formula two (and formula three to formula six). Figure 2

[0148] The sampling module can be used to assign a sampling probability from small to large to each space overlap interval according to the space overlap interval range and the cumulative space overlap number calculated by the space overlap rate calculation module in step S8, from small to large, to calculate the sampling rate of the next iteration according to formula two (and formula three to formula six); and according to step S9, the sampling rate of the next iteration is replaced by the sampling rate of the current iteration, and the next iteration sampling is performed according to step S2, and a new set of parameter sample sets for the next iteration is provided to the processing module for continuing to execute the loop of steps S3 to S9 until the parameter extraction is ended according to step S10 when the convergence condition is met.

[0149] ​Wherein, when the current iteration is the zeroth iteration, the sampling rate of the zeroth iteration is a preset sampling rate in the sampling module; from the first iteration after the zeroth iteration, the sampling rate is calculated according to Formula Two.

[0150] Further, the preset sampling rate includes a sampling rate under uniform sampling in the value range.

[0151] In summary, the present application obtains the sampling rate required for the next iteration by calculating the parameter control range of the current iteration, the space overlap interval formed by the projection of the parameter control range of each iteration before the current iteration on the value range coordinate, and the space overlap times of each space overlap interval on the value range coordinate, and assigning a sampling probability from small to large to each space overlap interval from small to large space overlap times, so that when determining the training sample required for the next iteration, not only the parameter information obtained by the Gaussian process regression model trained by the current training sample is considered, but also the parameter information returned by all iterations is fused to determine the training sample range required for the next iteration, so that the local optimal solution can be avoided.

[0152] Although the embodiments of the present application have been described in detail above, it is obvious to those skilled in the art that various modifications and changes can be made to these embodiments. However, it should be understood that such modifications and changes are within the scope and spirit of the present application in the claims. Moreover, the present application described herein can have other embodiments and can be implemented or realized in various ways.

Claims

1. A method for extracting device parameters based on Gaussian process regression, characterized in that, Includes the following steps: Step S1: Initialization, determining the range of parameter values; Step S2: Sample the parameters according to the sampling rate of the current iteration to obtain a parameter sample set; Step S3: Perform device simulation to obtain a characteristic information sample set corresponding to the parameter sample set; Step S4: Use the characteristic information sample set as the observable input sample of Gaussian process regression, and use the parameter sample set as the observable output sample of Gaussian process regression, to train the model and obtain the Gaussian process regression model for the current iteration. Step S5: Input the actual characteristic information of the device into the Gaussian process regression model of the current iteration to obtain the mean and standard deviation of the regressed parameters in the current iteration; Step S6: Determine whether the convergence condition is met. If it is met, proceed to step S10. If it is not met, continue to step S7 to step S9. Step S7: Calculate the parameter control range for the current iteration based on the mean and standard deviation of the parameters in the current iteration; Step S8: Calculate the spatial overlap interval formed by the projection of the parameter control range of the current iteration and the parameter control range of the previous iterations onto the selected value range coordinates, and the cumulative number of spatial overlap intervals on the selected value range coordinates. Assign sampling probabilities from small to large to each spatial overlap interval according to the number of spatial overlap intervals from small to large, and obtain the sampling rate of the next iteration. Step S9: Replace the sampling rate of the current iteration with the sampling rate of the next iteration, and repeat steps S2 to S6; Step S10: End.

2. The device parameter extraction method based on Gaussian process regression according to claim 1, characterized in that, In step S6, the convergence condition satisfies the following formula: Formula 1 in, Represents standard deviation, x max and x min They represent parameters respectively x The upper and lower limits of the selected value range.

3. The device parameter extraction method based on Gaussian process regression according to claim 1, characterized in that, When the current iteration is the zeroth iteration, the sampling rate of the zeroth iteration is defined as a preset sampling rate; from the first iteration after the zeroth iteration, the sampling rate satisfies the following formula: Formula 2 in, Q m (x) This represents the sampling rate in the m-th iteration. x The representative parameter, m, is a positive integer. p 0 represents the minimum sampling probability in the current iteration. F m-1 ( x Let represent the spatial overlap rate function for the (m-1)th iteration, and satisfy the following formula: Formula 3 in, The representation function of the original space satisfies the following formula: Formula 4 in, x max and x min They represent parameters respectively x The upper and lower limits of the selected value range; Representing the i The spatial representation function of the next iteration satisfies the following formula five: Formula 5 in, Let represent the mean of the i-th iteration. Represents the standard deviation of the i-th iteration. i This represents the number of iterations.

4. The device parameter extraction method based on Gaussian process regression according to claim 3, characterized in that, The preset sampling rate includes the sampling rate under uniform sampling within the selected range.

5. The device parameter extraction method based on Gaussian process regression according to claim 3, characterized in that, The minimum sampling probability p 0, satisfying the following formula six: Formula Six.

6. A device parameter extraction apparatus based on Gaussian process regression, characterized in that, include: The processing module is used to set the parameter sample set obtained by sampling the acquired parameters within the selected range according to the sampling rate of the current iteration into the simulation module for device simulation, use the characteristic information sample set corresponding to the parameter sample set as the observable input sample of Gaussian process regression, and use the parameter sample set as the observable output sample of Gaussian process regression to train the model, obtain the Gaussian process regression model of the current iteration, and obtain the mean and standard deviation of the regressed parameters in the current iteration by inputting the actual characteristic information of the device into the Gaussian process regression model of the current iteration; The judgment module is used to determine whether the convergence condition is met. If it is met, the processing module is notified to end parameter extraction. If it is not met, the information is sent to the spatial overlap rate calculation module. The spatial overlap rate calculation module is used to calculate the parameter control range of the current iteration based on the mean and standard deviation of the parameter in the current iteration when the convergence condition is not met, and to calculate the spatial overlap interval formed by the projection of the parameter control range of the current iteration and the parameter control range of each previous iteration onto the selected value range coordinates, as well as the cumulative number of spatial overlap intervals on the selected value range coordinates. The sampling module is used to assign sampling probabilities from small to large to each of the spatial overlap intervals according to the number of spatial overlaps from small to large, calculate the sampling rate of the next iteration, replace the sampling rate of the current iteration, perform sampling for the next iteration, and provide the obtained parameter sample set for the next iteration to the processing module.

7. The device parameter extraction device based on Gaussian process regression according to claim 6, characterized in that, The convergence condition satisfies the following formula: Formula 1 in, Represents standard deviation, x max and x min They represent parameters respectively x The upper and lower limits of the selected value range.

8. The device parameter extraction device based on Gaussian process regression according to claim 6, characterized in that, When the current iteration is the zeroth iteration, the sampling rate of the zeroth iteration is the preset sampling rate in the sampling module; from the first iteration after the zeroth iteration, the sampling rate satisfies the following formula: Formula 2 in, Q m (x) This represents the sampling rate in the m-th iteration. x The representative parameter, m, is a positive integer. p 0 represents the minimum sampling probability in the current iteration. F m-1 ( x Let represent the spatial overlap rate function for the (m-1)th iteration, and satisfy the following formula: Formula 3 in, The representation function of the original space satisfies the following formula: Formula 4 in, x max and x min They represent parameters respectively x The upper and lower limits of the selected value range; Representing the i The spatial representation function of the next iteration satisfies the following formula five: Formula 5 in, Let represent the mean of the i-th iteration. Represents the standard deviation of the i-th iteration. i This represents the number of iterations.

9. The device parameter extraction device based on Gaussian process regression according to claim 8, characterized in that, The preset sampling rate includes the sampling rate under uniform sampling within the selected range.

10. The device parameter extraction device based on Gaussian process regression according to claim 8, characterized in that, The minimum sampling probability p 0, satisfying the following formula six: Formula Six.

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