Raster scan measurement acceleration method

Abstract

Disclosed in an embodiment is a measurement acceleration method in which a processor executes at least one of the instructions stored in a memory, the method comprising the steps of: extracting initial data for creating an initial regression model; training regression models with the initial data; extracting first data by a preset first skip value; using the first data to construct an ensemble model and outputting a first predicted value and a first variance value as result values of ensemble variance; calculating second data with a second skip value for a section in which the first variance value is higher than a set threshold value; and updating the regression model by reflecting the second data.

Description

Raster Scan Measurement Acceleration Method

[0001] This embodiment describes a method for accelerating measurements to which a raster scan method is applied.

[0002] Raster scanning is a method that completes measurements of an irradiated area by sequentially selecting measurement locations in a highly uniform manner. As a scanning method, raster scanning is widely utilized in measurement fields requiring high-resolution imaging and data acquisition. Raster scanning is associated with the measurement of specific physical quantities regarding general variables, such as the movement of illumination light, probe movement, or external variables capable of representing physical states. A typical example is acquiring physical quantity data by moving a probe linearly in a specific sequence over a two-dimensional surface. Measuring the distribution of current passing through a device under two different gate voltages can serve as another example. Raster scanning is the most common measurement method for attempting to control external variables and scan physical quantities.

[0003] Generally, the range of variation in physical quantities due to fluctuations in external variables cannot be known before measurement. Therefore, it is not possible to know in advance which sections require high resolution. It is common practice to perform measurements sequentially on a uniform two-dimensional grid. Consequently, in many cases, raster scanning has the disadvantage that measurement time increases rapidly in high-resolution image measurements.

[0004] It is possible to utilize machine learning methods to replace conventional raster scanning. These methods allow for the identification of sections requiring high-resolution measurements during the measurement process and enable accelerated scanning overall. For example, the Gaussian Process (GP) algorithm, based on conventional Bayesian inference, can predict measurement uncertainty through regression analysis of measurement values, thereby identifying sections requiring high resolution before measurement. However, it is known that the Gaussian Process method generally consumes significant computing resources when training on large data sizes. Furthermore, acquiring high-resolution data is currently impossible with existing computer algorithms. Therefore, there is a need for measurement algorithms that can accelerate high resolution and large data sizes.

[0005] The technical problem that the present invention aims to solve is to overcome the acceleration limitations associated with large data sizes or high-resolution raster scan measurements that conventional Gaussian process methods cannot handle. To this end, the present invention proposes an ensemble variance-based raster scan measurement technique. This involves utilizing multiple regression models simultaneously and training each model independently to create a single ensemble model. This ensemble model can obtain the mean and variance of predictions from the independent predictions of the multiple models. The variance of the ensemble model represents the uncertainty of the measurement. Therefore, since the uncertainty of the measurement can be evaluated at an intermediate stage, sections requiring selective high-resolution measurement can be determined midway through the entire measurement process. The machine learning method presented in the present invention accelerates the entire measurement process, even when using very large training data or performing high-resolution measurements. Specifically, multiple different k-nearest neighbors (KNN) regression models are utilized simultaneously. Training these multiple regression models has a computational complexity [O(n)] that depends linearly on the data size. This is a computational complexity [O(n²)²] proportional to the cube of the data size obtainable from existing Gaussian Process (GP) methods. 3 It compares very well with )]. In this invention, the uncertainty of the measurement can be determined during the measurement by utilizing ensemble variance with computational complexity [O(n)]. In addition, the entire measurement process is set as a multi-stage process. As the measurement stage changes, the grid interval size is varied from a large value to a small value. While utilizing multi-stage measurement, measurement / training / ensemble model construction is continuously carried out.

[0006] The problems intended to be solved in the embodiments are not limited thereto, and may also include objectives or effects that can be identified from the means of solving the problems or the forms of implementation described below.

[0007] A measurement acceleration method according to an embodiment of the present invention starts at a first-stage grid system (first skip value). Measurements are completed sequentially for all grid points belonging to the first-stage measurement grid system. The measurement points and the measured results are stored sequentially in separate files. Once all measurements are completed, multiple regression models are trained independently. The models are combined to complete an initial ensemble model. In the second stage, a new measurement grid is provided by a new skip value (second skip value). For the newly provided grid points, measurement value prediction and variance value prediction are first performed using the ensemble model. If the variance at a specific grid point is smaller than a threshold variance value, an actual measurement is not performed at that grid point. Otherwise, an actual measurement is performed at that grid point. If an actual measurement is performed, the measurement data is added to the file storing the previous measurement data. All regression models are retrained using this file. The ensemble model is updated. Once the second-stage measurement / ensemble model is constructed, a third-stage measurement is attempted. In Step 3, a new measurement grid is provided based on a new skip value (the third skip value). Predicting the ensemble variance and proceeding sequentially with measurement, training, and building the ensemble model are performed in the same manner as described in Step 2. Upon reaching the final step, all measured data will be saved to the measurement data archive file. Additionally, the ensemble model building is completed. You can directly verify the number of grid points where actual measurements were taken. For grid points where actual measurements were not taken, the predicted values ​​from the ensemble regression model are utilized.

[0008] One embodiment of the present invention enables the identification of a plurality of control parameter combinations necessary for efficiently measuring a specific physical state, thereby realizing acceleration of raster scan measurements. Scan sections requiring precise measurement are identified in the middle of the measurement. High-resolution raster measurements can be accelerated.

[0009] In addition, one embodiment of the present invention can perform uncertainty inference based on ensemble variance even when using very large training data and has a corresponding computational complexity [O(n)]. The computation time associated with machine learning does not take longer than the time to actually perform a measurement at a single grid point.

[0010] The various and beneficial advantages and effects of the present invention are not limited to those described above and may be more easily understood in the process of explaining specific embodiments of the present invention.

[0011] FIG. 1 is a flowchart of a raster scan measurement acceleration method according to one embodiment of the present invention.

[0012] FIG. 2 is a flowchart of a procedure applied to physical scanning in a raster scan measurement acceleration method according to one embodiment of the present invention.

[0013] FIG. 3 is a graph showing the shape and resolution of a grid system according to a skip value in a measurement acceleration method according to one embodiment of the present invention.

[0014] FIG. 4 is a graph visualizing the function prediction results on a two-dimensional grid by applying a KNN regression model and a GP regression model, respectively, according to an embodiment of the present invention.

[0015] Figure 5 is a graph showing the relationship between the CPU time consumed and the data size of each algorithm of the KNN-based method and the GP-based method according to one embodiment of the present invention.

[0016] FIG. 6 is a graph showing the standard deviation distribution according to the calculated function, sample location, error, and ensemble model in an example of application of a KNN-based method according to one embodiment of the present invention.

[0017] FIG. 7 is a graph visually representing the results of performing Bayesian inference using a GP-based regression model according to an embodiment of the present invention.

[0018] Figure 8 is a graph visualizing the results of comparing the mean squared error (MSE) and computation time as the number of grid points increases by applying a KNN-based method as an embodiment of the present invention.

[0019] The present invention is capable of various modifications and may have various embodiments, and specific embodiments are illustrated and described in the drawings. However, this is not intended to limit the invention to specific embodiments, and it should be understood that the invention includes all modifications, equivalents, and substitutions that fall within the spirit and scope of the invention.

[0020] Terms including ordinal numbers, such as second, first, etc., may be used to describe various components, but said components are not limited by said terms. Such terms are used solely for the purpose of distinguishing one component from another. For example, without departing from the scope of the present invention, the second component may be named the first component, and similarly, the first component may be named the second component. The term "and / or" includes a combination of a plurality of related described items or any of a plurality of related described items.

[0021] When it is stated that one component is "connected" or "connected" to another component, it should be understood that while it may be directly connected or connected to that other component, there may also be other components in between. On the other hand, when it is stated that one component is "directly connected" or "directly connected" to another component, it should be understood that there are no other components in between.

[0022] The terms used in this application are used merely to describe specific embodiments and are not intended to limit the invention. The singular expression includes the plural expression unless the context clearly indicates otherwise. In this application, terms such as "comprising" or "having" are intended to indicate the presence of the features, numbers, steps, actions, components, parts, or combinations thereof described in the specification, and should be understood as not precluding the existence or addition of one or more other features, numbers, steps, actions, components, parts, or combinations thereof.

[0023] Unless otherwise defined, all terms used herein, including technical or scientific terms, have the same meaning as generally understood by those skilled in the art to which the present invention pertains. Terms such as those defined in commonly used dictionaries should be interpreted as having a meaning consistent with their meaning in the context of the relevant technology, and should not be interpreted in an ideal or overly formal sense unless explicitly defined in this application.

[0024] Additionally, some embodiments may be represented by functional block configurations and various processing steps. Some or all of these functional blocks may be implemented by various numbers of hardware and / or software configurations that execute specific functions. For example, the functional blocks of the present disclosure may be implemented by one or more processors or microprocessors, or by circuit configurations for performing the intended functions. Additionally, for example, the functional blocks of the present disclosure may be implemented in various programming or scripting languages. The functional blocks may be implemented as algorithms executed on one or more processors. Furthermore, the present disclosure may employ prior art for electronic configuration, signal processing, and / or data processing, etc. Terms such as modules and configurations may be used broadly and are not limited to mechanical and physical configurations.

[0025] Hereinafter, embodiments will be described in detail with reference to the attached drawings, provided that identical or corresponding components are given the same reference number regardless of the drawing symbols, and redundant descriptions thereof will be omitted.

[0026] The measurement of physical quantities through raster scanning is utilized in various fields, such as MRI (magnetic resonance imaging), CT (computed tomography), SEM (scanning electron microscope), AFM (atomic force microscopy), and STM (scanning tunneling microscopy / spectroscopy).

[0027] In this embodiment, a measurement acceleration method is proposed for various fields where the raster scan method is applied. Additionally, a computational method capable of efficiently identifying a specific combination of multiple control parameters required to realize a specific physical state is also proposed. One embodiment of the present invention operates by simultaneously implementing multiple regression models based on measurement data. Basically, measurements begin in a very coarse grid system. The measurement data obtained in this way is used to train multiple regression models. The ultimate goal is to construct a regression model that can be utilized in a fine grid. Regression is a general term for techniques that model the correlation between multiple independent variables and a single dependent variable. It is a method of performing additional measurements when the prediction by the regression model is not sufficiently precise. Measurements are repeated progressively in the fine grid system. The aforementioned repetition process can be applied identically to the measurement acceleration method described below. Furthermore, this method can be implemented as a device capable of automatically selecting areas where measurement is required and areas where it is not required during the entire measurement process.

[0028] In this embodiment, a measurement method based on uncertainty inference according to ensemble variance is proposed. This method is a machine learning method based on training on data measured at specific grid points. The ensemble model provides both the predicted value and the uncertainty regarding the predicted value. An embodiment of the present invention infers uncertainty by utilizing ensemble variance. Grid points requiring additional measurement and grid points that do not require additional measurement can be selected. An embodiment of the present invention obtains the mean and variance of the regression model's predictions simultaneously by training and using multiple KNN (k-nearest neighbors) regression models simultaneously. Since multiple KNN regression models are trained and used simultaneously, epistemological uncertainty can be quantified.

[0029] In many measurements, there are cases where areas requiring high resolution are distinguished a priori from areas that do not. One embodiment of the present invention provides a computer algorithm that complements raster scanning to perform many measurements in areas requiring more precise measurements and to refrain from measurements in areas where many measurements are not needed. Furthermore, one embodiment of the present invention provides a computer algorithm that can fundamentally resolve the problem of computational complexity regarding data size. In one embodiment of the present invention, a measurement method for points distributed in a spiral form is employed to increase measurement efficiency. Preemptive measurements can be performed on a coarse grid. The multiple regression models used in this embodiment generally output different regression results. The regression results of multiple regression models can serve as a criterion for selecting areas requiring new measurements. If all regression models present nearly similar predicted values, the variance can be very small. In this case, actual measurements are not performed on previously measured locations because there is no uncertainty in the regression models.

[0030] In addition, this embodiment presents a method for performing uncertainty inference based on ensemble variance even when using very large training data. For example, when the data size required to build a regression model is n, the complexity of the method according to this embodiment is O(n). That is, the method according to the embodiment can perform more measurements at grid points where the data changes rapidly and reduce the number of measurements at grid points where it does not.

[0031] FIG. 1 is a flowchart of a raster scan measurement acceleration method according to one embodiment of the present invention, FIG. 2 is a flowchart of a procedure applied to physical scanning in a raster scan measurement acceleration method according to one embodiment of the present invention, and FIG. 3 is a graph showing the shape and resolution of a grid system according to a skip value in a measurement acceleration method according to one embodiment of the present invention.

[0032] Referring to FIG. 1, a measurement acceleration method according to an embodiment of the present invention, wherein a processor executes at least one of the instructions stored in memory, may include the steps of: extracting initial data to create an initial regression model (S110); training regression models with the initial data (S120); extracting first data by a preset first skip value (S130); utilizing the first data to build an ensemble model and outputting a first predicted value and a first variance value as the result of the ensemble variance (S140); calculating second data by a second skip value for a range in which the first variance value is higher than a preset threshold (S150); and updating the regression model by reflecting the second data in the regression model (S160). Each step below may be implemented by hardware such as a processor, and the subject below may be omitted.

[0033] In the step (S110) of extracting initial data to create an initial regression model, the processor (100) may collect initial data to perform a prediction for the first time using a machine learning regression model. The collection of initial data may be based on a sampling method. The sampling method may include spiral sampling, random sampling, or coarse grid sampling. The sampling method in this step may be performed completely independently of the skip value-based hierarchical sampling performed later.

[0034] Initial data can be collected from the entire or partial grid area. Measurement data is always stored in a file. The initial regression model can be configured to train based on the initial data.

[0035] Referring to FIG. 2, the step of extracting initial data (S110) corresponds to the step of setting a target fine grid to perform a final prediction (S210) and the step of spiral sampling (S220). For example, the processor (100) may set the target fine grid to a 300×300 grid. The processor (100) obtains initial data from measurements from the entire 300×300 grid or a portion of the grid. All measured data is stored in a file.

[0036] In the step of training regression models with initial data (S120), the processor (100) may train at least one k-Nearest Neighbors Regression (KNN) regression model based on the aforementioned initial data. The step of training regression models with initial data (S120) corresponds to the step of training regression models (S220) in FIG. 2. The terms regressor and regression model are used with the same meaning in this specification.

[0037] The KNN regression model finds the k nearest neighbor data points for an input coordinate (x, y) and calculates a predicted value through the average of the measurements of those neighbors or a distance-based weighted average. Using a non-parametric algorithm, the KNN regression model does not pre-learn a separate function form; instead, it stores data and calculates the predicted value on the fly by calculating the distance at the time of prediction. Various distances can be applied in this calculation. For example, the distance refers to the Manhattan distance when p=1 and the Euclidean distance when p=2. Median values ​​such as p=1.5 can also be used in the aforementioned distance calculation. Additionally, the processor can utilize spatial partitioning index structures, such as kd-trees or ball-trees, during the nearest neighbor search process of KNN regression.

[0038] In one embodiment of the present invention, the processor may configure multiple KNN regression models in an ensemble form rather than as a single model. The processor may configure up to 12 regression models by setting the k value to an integer from 4 to 9 and p in the distance definition to multiple values ​​such as 1.5 and 2. The configured regression models can simultaneously calculate the mean and variance of the predicted values. The regression models are not trained only during the initial sampling phase, but may be repeatedly updated throughout the hierarchical sampling process performed by adjusting skip values ​​other than the initial sampling phase.

[0039] In the step (S130) of extracting first data by a preset first skip value, the processor (100) sets a new prediction target area by selecting data at specific intervals from the entire grid where predictions are performed by an initial regression model. Here, the skip value refers to the interval between data points; for example, if the skip value is 30, only points sampled every 30 cells are selected from the entire 500×500 grid. When the skip value is 30, only points corresponding to approximately 1.33% of the entire fine grid are extracted. Referring to FIG. 2, the skip value set to skip=30 becomes the first skip value. Each point of the extracted grid can be applied to the ensemble variance.

[0040] In the step (S140) of utilizing the first data to construct an ensemble model and outputting the first predicted value and the first variance value as the result of the ensemble variance, the processor calculates a predicted value for each grid point based on a KNN regression model ensemble and estimates uncertainty by calculating the variance of the predicted values ​​between models. The mean of the predicted values ​​is defined as the first predicted value, and the variance between the predicted values ​​is defined as the first variance value. If the variance is low, the predicted value can be trusted, and if the variance is high, it can be identified as a point requiring additional measurement. The mean of the predicted values ​​can correspond to the predicted value or mean of the posterior distribution based on the ensemble model. The variance of the predicted values ​​can correspond to uncertainty or variance based on ensemble model inference. That is, the processor can perform inference for each location of the entire grid system. The step (S140) of utilizing the first data to build an ensemble model and outputting the first predicted value and the first variance value as the result of the ensemble variance corresponds to the step (S240) of predicting on a coarse grid, grid sampling when the variance is large, and training regression models after the skip=30 setting (S230) presented in FIG. 2.

[0041] In the step (S150) of calculating second data with a second skip value for a range where the first variance value is higher than a set threshold, the processor (100) may identify a first region among the previously calculated variance values ​​that is greater than a preset threshold, and perform additional sampling by setting a second skip value that is less than or equal to the first skip value for the identified first region. The processor (100) may reset the preset threshold according to the update of the data. In FIG. 2, the step (S150) of calculating second data with a second skip value for a range where the first variance value is higher than a set threshold corresponds to the step (S250) of changing the skip value to skip = skip-1. In FIG. 2, a method of decreasing the skip value by 1 was used, but the value of 1 can vary depending on the setting. The skip value can be decreased until it is 2 or more.

[0042] In the step (S160) of updating the regression model by reflecting the second data into the regression model, the processor (100) adds the newly collected second data to the existing dataset and retrains a plurality of KNN regression model ensembles. The processor reconstructs each model based on the updated entire dataset. Each model is trained by the processor (100) based on the k value and p value according to the distance definition described above.

[0043] In the step (S170) of re-outputting the second predicted value and the second variance value for the grid calculated by extracting initial data using the updated regression model, the processor (100) recalculates the second predicted value and the second variance value for the entire grid or within the region of interest using the updated regression model. At this time, the calculated predicted value may reflect more data than the step of outputting the first predicted value and the first variance value. If the most recently measured data is the second data, the second variance value provides uncertainty information based on the most recent prediction. Referring to FIG. 2, this step is included in the process of predicting on the grid by iteration (S240).

[0044] Referring again to FIG. 1, according to one embodiment of the present invention, the steps of extracting first data by a preset first skip value (S130), utilizing the first data to build an ensemble model and outputting a first predicted value and a first variance value as the result of the ensemble variance (S140), calculating second data with a second skip value for a range where the first variance value is higher than a set threshold value (S150), reflecting the second data in the regression model to update the regression model (S160), and extracting initial data using the updated regression model and re-outputting a second predicted value and a second variance value for the calculated grid (S170) may be repeated. For example, in one embodiment of the present invention, the processor (100) may further include, in addition to the steps described above, a step of calculating third data with a third skip value for a range where the second variance value is higher than a threshold value, and a step of re-updating the regression model by reflecting the third data in the regression model that was updated by reflecting the second data in the regression model. The processor (100) can stop the repetition of the preceding step based on information including the predicted value and variance value calculated by each measurement. For example, the processor (100) can perform a prediction in the final target fine grid using as one piece of information that the most recently outputted variance values ​​do not all exceed a threshold value.

[0045] In one embodiment of the present invention, the third skip value may be smaller than the second skip value. In one embodiment of the present invention, the second skip value may be smaller than the first skip value. The skip value may vary during the process of updating the result value measured by the processor (100) to the regression model.

[0046] The processor (100) can perform a prediction on the final target fine grid when the skip value is less than 2.

[0047] According to one embodiment of the present invention, when the process performed by the processor (100) completes a precise prediction for all uncertainty intervals by repeating as in FIG. 2 and reaches a fine grid prediction step (S270), the processor (100) can output a measured value or a predicted value at each position of the grid in the entire grid.

[0048] Referring to FIG. 3, a part of the procedure for a processor (100) to perform a prediction on a target fine grid of 500×500 according to an embodiment of the present invention can be observed. The processor (100) extracts data into a coarse grid with an initial skip value set to 30. A grid with a skip value of 30 is a combination of square-shaped points (30). The processor (100) can collect additional data by sequentially reducing the skip value to 20, 10, and 5 in areas where the variance value is higher than a preset threshold, so that the interval becomes a finer grid than when the skip value was earlier. A grid with a skip value of 20 is a set of points of the largest size circle (20), a grid with a skip value of 10 is a set of medium-sized circles (10), and a grid with a skip value of 5 is a set of the smallest size circles (5). Here, a smaller skip value may imply higher resolution. Furthermore, the method according to the embodiment can provide the effect of improving overall prediction accuracy while reducing the total amount of measurements by changing the skip value only for the interval with high variance and increasing the measurement density.

[0049] The advantages and effects according to one embodiment of the present invention are described below with reference to the drawings.

[0050] Figure 4 is a graph visualizing function prediction results on a two-dimensional grid by applying a KNN regression model and a GP regression model, respectively, according to an embodiment of the present invention. A comparison was performed on a grid composed of 200×200 pixels. Figures 4(a), 4(b), and 4(c) show the prediction results based on KNN regression according to an embodiment of the present invention, while Figures 4(d), 4(e), and 4(f) show the prediction results based on GP regression, respectively. Looking at Figure 4(a), the distribution of function values ​​predicted by the KNN model is represented by brightness, and the range of function values ​​is set to (-1, 1). The brighter the brightness, the closer the value is to 1, and the darker the brightness, the closer the value is to -1. Figure 4(b) shows the prediction standard deviation output by the KNN model, and the maximum range of the value is approximately 0.009. Brightness represents prediction uncertainty. The darker the value, the smaller the standard deviation. The brighter the value, the larger the standard deviation. A larger standard deviation indicates lower prediction reliability. Figure 4(c) shows the error [f between the KNN predicted value and the actual function value. KNN [(x, y) - f(x, y)] is represented. The error range is (-0.0177, 0.0177). The darker the area, the smaller the error. Fig. 4(d) shows the distribution of the predicted function values ​​of the GP model, with a range of (-1, 1). Fig. 4(e) shows the prediction standard deviation of GP; the maximum value is approximately 0.009, which is similar to KNN but shows a more uniform distribution overall. Fig. 4(f) shows the error [f between the GP predicted value and the actual function value. GPIt represents [(x, y) - f(x, y)]. The error range is (-0.0177, 0.0190), which is smaller than the error of KNN and shows almost no structural noise. The even appearance of brightness and contrast in the image demonstrates that the GP model made generally more accurate predictions than KNN. In summary, the KNN method is a prediction method based on locality, making it sensitive to local characteristics and exhibiting diverse uncertainty distributions. On the other hand, the GP method is a global model that considers the entire dataset, showing characteristics such as a more uniform distribution of errors and standard deviations and higher prediction accuracy. However, due to covariance matrix operations, the computational complexity of GP is O(n²). 3 It is very high, making it disadvantageous for processing large-scale data, whereas KNN has the advantage of being more suitable for large-scale datasets with a linear complexity of O(n).

[0051] The KNN method and the GP method are compared in more detail through the table below.

[0052] Function, f(x, y) Model Number of sampled points Percentage (%) Calculation time (CPU) (min) Normalized error, Δ (scaled error, Δ) cos(0.1x) sin(0.2y) KNN 15,21738 14.7 1.9 × 10 -2 GP5,1421341.52.3 × 10 -4 sin²(0.1x) + cos²(0.2y)KNN15,4373915.11.5 × 10 -2 GP5,1421341.53.7 × 10 -4 cos{0.1x + sin(0.2y)}KNN14,6753713.92.6 × 10 -2 GP5,1421342.45.7 × 10 -4 cos(0.1x) + sin(0.2y)KNN15,4713915.41.3 × 10 -2 GP5,1421345.54.3 × 10 -4sin(√x² + y²) / √x² + y²KNN13,0883311.94.1 × 10 -2 GP5,1421345.61.6 × 10 -5

[0053] Table 1 presents five periodic target functions. The sampling space is [-20, 20] × [-20, 20], and it is assumed that a uniform grid system consisting of 200 × 200 points was used for evaluation. For each function, the number of sampled grid points is expressed as a percentage of the total number of grids (= 40,000), and f predicted by the model ML Since both (x, y) and the actual function f(x, y) are known, a direct performance comparison between the two is possible. The normalized error (Δ) is calculated based on the following equation. [Equation 1]

[0054] Δ ML = max{|f ML (x, y) - f(x, y)|} / max{|f(x, y)|}

[0055] Equation 1 represents the value obtained by normalizing the maximum error of a function to the maximum function value. In the table, KNN refers to the k-nearest neighbors regression model according to one embodiment of the present invention, and GP refers to Gaussian process regression. In GP, ​​a radial basis function kernel (RBF kernel, or squared exponential kernel) is used, which is based on a function implemented in the scikit-learn library. Overall, the GP method shows higher prediction accuracy compared to KNN because the Δ value is smaller, but it uses fewer sample points and takes relatively longer computation time. On the other hand, the KNN method according to one embodiment of the present invention utilizes more data and has the advantages of short computation time and excellent scalability even in large-scale datasets.

[0056] Function without Gaussian Model Sampled points Percentage (%) CPU time (min.) Scaled error, Δ McCormickKNN35773.96.13.0 × 10 -2 GP53495.955.34.2 × 10 -8 AckleyKNN41864.66.41.3 × 10 -1 GP53495.953.21.0 × 10 0 Goldstein-PriceKNN1626418.119.52.6 × 10 -2 GP53495.952.48.1 × 10 -8 Himmelblau'sKNN79118.88.63.0 × 10 -2 GP53495.952.81.0 × 10 -7 Styblinski-TangKNN73638.18.22.9 × 10 -2 GP53495.952.81.1 × 10 -7

[0057] Table 2 presents five localized objective functions. Target functions modified into more local forms were generated by multiplying the following Gaussian functions by the McCormick, Ackley, Goldstein-Price, Himmelblau's, and Styblinski-Tang functions, which are frequently used as benchmarks for global optimization methods with variables used without Gaussians.

[0058] [Mathematical Formula 2]

[0059] exp{-(x / 4) 2 - (y / 2) 2}

[0060] The sampling target space is [-20, 20] × [-20, 20], and a fine grid consisting of 300 × 300 points is used for accuracy estimation. The definitions of the basic evaluation items are the same as those in Table 1. The prediction performance of the KNN model and the GP model according to one embodiment of the present invention is compared based on the number of sampled points, CPU time, and normalization error (Δ). In particular, the function f(x, y) is explicitly given. This experimental setup demonstrates that for a target function having a local structure according to one embodiment of the present invention, the Bayesian inference-based KNN ensemble method can achieve efficient prediction performance even with a small number of samples.

[0061] Figure 5 is a graph showing the relationship between CPU time consumed by each algorithm of the KNN-based method and the GP-based method according to an embodiment of the present invention and the data size. The x-axis of the graph shows the relationship between data size and computation time, and the y-axis shows the relationship between them. Circular markers represent the computation time of the KNN algorithm, and square markers represent the computation time of the GP algorithm. The horizontal axis represents the data size from 1,000 to 33,000, and the vertical axis represents the processing time. It can be confirmed through the graph in Figure 5 that the computational complexity of the KNN algorithm is linear and has a time complexity of O(n). The GP algorithm has a computational complexity of O(n 3 It has a time complexity of ). In conclusion, it shows that for large-scale data, the KNN according to one embodiment of the present invention can be advantageous in terms of computational resources.

[0062] FIG. 6 is a graph showing the distribution of the calculated function, sample location, error, and standard deviation according to the ensemble model in an application example of a KNN-based method according to an embodiment of the present invention. The target area for sampling is [-20, 20] × [-20, 20]. A precise grid system consisting of 500 × 500 points is used for accuracy estimation. FIG. 6(a) visualizes the function results obtained through KNN-based inference as a 2D map with distinguished brightness. Two ring shapes of bright brightness are observed near the center, which is f KNN It shows the peak and valley structure of the (x,y) function. Brightness represents the magnitude of the function values. Brighter values ​​indicate higher function values, while darker values ​​indicate lower values. The range of function values ​​is from -1.2 to 7.4. Fig. 6 (b) is a scatter plot showing data sample locations as points. The concentration of these points suggests that a more precise approximation was required in certain areas. Fig. 6 (c) shows the error [f between the function calculated by the KNN method and the actual function. KNN This is a map visualizing the distribution of [x,y] - f(x,y) by distinguishing between brightness levels. As seen in the two bright rings in the center of the graph in Fig. 6(c), brighter areas may indicate a larger difference between the prediction and the actual value. Conversely, the darker area inside these two bright rings may signify a value closer to the actual value. The error range is from -0.18 to 0.15. While the error is small in most areas, a somewhat structural difference appears at the center of the graph. This suggests that the model's accuracy may decrease in complex terrain. Fig. 6(d) is a histogram representing the distribution of standard deviation values ​​obtained from Bayesian inference results. The y-axis is displayed on a logarithmic scale (from 10¹ to 10 5The x-axis represents the standard deviation values ​​(from 0 to 0.08). This histogram shows that most estimates have low standard deviations, and that the frequency decreases as the standard deviation increases. While the majority of predictions are low, with standard deviations of 0.02 or less, it indicates that there are also predictions with uncertainty, such as some reaching 0.06 or higher. Large standard deviations with low frequency are also visually represented using a logarithmic scale.

[0063] Function without Gaussian Model Sampled points Percentage (%) CPU time (min.) Scaled error, Δ McCormickKNN(12)87173.519.12.4 × 10 -2 KNN(6)87063.510.82.1 × 10 -2 GP55142.280.34.5 × 10 -8 AckleyKNN(12)102064.120.85.1 × 10 -2 KNN(6)102074.112.05.1 × 10 -2 GP55142.279.16.3 × 10 -1 Goldstein-PriceKNN(12)4364417.4118.91.5 × 10 -2 KNN(6)4362417.478.01.5 × 10 -2 GP55142.279.43.3 × 10 -8 Himmelblau'sKNN(12)203188.136.42.1 × 10 -2 KNN(6)202908.123.11.9 × 10 -2 GP55142.278.54.9 × 10 -8 Styblinski-TangKNN(12)185597.432.92.7 × 10 -2 KNN(6)185187.420.52.6 × 10 -2GP55142.278.66.6 × 10 -8

[0064] Table 3 uses the same five test functions as Table 2, and the comparison items in the column configuration are identical. The difference between Table 2 and Table 3 is that Table 3 features various model configurations, such as KNN (12) and KNN (6), and is based on a denser 500 × 500 fine grid. Here, KNN (12) and KNN (6) refer to a model based on 12 KNN regression units and a model based on 6 KNN regression units, respectively. KNN (12) uses 12 regression models, resulting in high prediction accuracy, but the CPU time may be somewhat high. KNN (6) maintains similar performance even when the number of models is halved, and the computation time is reduced by half. The GP method has an error of nearly 10 -8 It has a level of prediction accuracy and a computation time of 70 to 80 minutes. The KNN method according to one embodiment of the present invention has a prediction error of 10 - Although it can be judged that there is a slight error compared to GP at the level of 2, it is more efficient than GP in terms of calculation speed. Figure 7 is a graph visually representing the results of performing Bayesian inference using a GP-based regression model according to an embodiment of the present invention.

[0065] Referring to FIG. 7, FIG. 7(a) shows the function value [f predicted by the GP regression model. GP (x,y)] and [f GP[(x, y) - f(x,y)] is represented as a map distinguished by brightness. The predicted function values ​​range from -1.2 to 7.4. In the center of the graph in Fig. 7(a), one can observe two interconnected rings that are brighter than their surroundings, and a circle located between the two preceding rings that is darker than its surroundings. The background surrounding the two rings and the dark circle may represent areas with low function values. The area of ​​the two rings in the center of the graph may represent an area with median function values. The circle located between the two preceding rings that is darker than its surroundings may represent areas with high function values. Fig. 7(b) displays the actual measured points, i.e., the sample locations used as input data, in the form of a scatter plot. The two axes are configured based on the grid index. Fig. 7(c) [f GP [(x, y)] and [f GP It is a visualization of [(x, y) - f(x, y)] as a grayscale map. The error range is -3.2×10 -7 From 1.79×10 -7 This indicates a very low level of error. A very low error can appear almost uniform in a graph distinguished by brightness. The graph in Fig. 7(c) shows almost no variation in brightness and exhibits a uniform brightness overall, which supports the fact that the GP-based prediction achieved very high accuracy. Fig. 7(d) is a histogram representing the distribution of standard deviations calculated through Bayesian inference during the prediction process in Figs. 7(a) to 7(c). The x-axis represents the value of the standard deviation, and the y-axis represents the frequency of that value on a logarithmic scale. Most standard deviations are distributed at less than 0.001, which means that the overall prediction has very high reliability. Although there are rare cases where high standard deviations occur, they are expressed on a logarithmic scale, confirming that their frequency is very low.

[0066] FIG. 8 is a graph visualizing the results of comparing the Mean Squared Error (MSE) and computation time according to an increase in the number of grid points by applying a KNN-based method as an embodiment of the present invention. In the experiment, the Mean Squared Error (MSE) was calculated using only KNN-based predicted values ​​without using explicit actual measurement data in a 500×500 grid system. This is consistent with the configuration proposed in an embodiment of the present invention and implies that output is possible across the entire grid by utilizing the predicted values ​​of the regression model even when actual measurements do not exist. Furthermore, in an embodiment of the present invention, the processor (100) can configure the values ​​by applying a KNN-based method to automatically output actual measured values ​​at locations where actual measurements exist and predicted values ​​at other points. FIG. 8(a) shows a tendency for the MSE to decrease as the number of grid points in the x-axis direction increases. FIG. 8(b) shows that as the number of grid points in the x-axis direction increases, the computation time also increases linearly.

[0067] The term "part" as used in this embodiment refers to a software or hardware component, such as a field-programmable gate array (FPGA) or an ASIC, and the "part" performs certain roles. However, the meaning of "part" is not limited to software or hardware. The "part" may be configured to reside in an addressable storage medium or configured to run one or more processors. Thus, as an example, the "part" includes components such as software components, object-oriented software components, class components, and task components, as well as processes, functions, attributes, procedures, subroutines, segments of program code, drivers, firmware, microcode, circuits, data, databases, data structures, tables, arrays, and variables. The functions provided within the components and "parts" may be combined into a smaller number of components and "parts" or further separated into additional components and "parts." In addition, the components and '~parts' may be implemented to play one or more CPUs within the device or secure multimedia card.

[0068] Each step of the aforementioned measurement acceleration method can be implemented by a control unit. The control unit may be the software described above or a hardware component such as a field-programmable gate array (FPGA) or an ASIC.

[0069] Although the invention has been described above with reference to embodiments, this is merely illustrative and does not limit the invention. Those skilled in the art will understand that various modifications and applications not exemplified above are possible within the scope of the essential characteristics of the embodiments. For example, each component specifically shown in the embodiments may be modified and implemented. Furthermore, differences related to such modifications and applications should be interpreted as being included within the scope of the invention as defined in the appended claims.

Claims

1. A measurement acceleration method in which a processor executes at least one of the instructions stored in memory, Step of extracting initial data to create an initial regression model; A step of training regression models with the above initial data; A step of extracting first data by a preset first skip value; A step of utilizing the above-mentioned first data to construct an ensemble model, and outputting a first predicted value and a first variance value as the result of the above-mentioned ensemble variance; A step of calculating second data as a second skip value for a range in which the first variance value is higher than a set threshold value; and A measurement acceleration method comprising the step of updating the regression model by reflecting the second data.

2. In Paragraph 1, A step of re-outputting a second predicted value and a second variance value for a grid calculated by extracting the initial data using the updated regression model; A measurement acceleration method further comprising the step of calculating third data as a third skip value for intervals where the second variance value is higher than the threshold value.

3. In Paragraph 2, A measurement acceleration method further comprising the step of re-updating the regression model by reflecting the third data in the second data.

4. In Paragraph 2, A measurement acceleration method in which the third skip value is smaller than the second skip value.

5. In Paragraph 1, A measurement acceleration method in which the second skip value is smaller than the first skip value.

6. In Paragraph 1, A measurement acceleration method that outputs a measured value or a predicted value at each position of the grid in the entire grid.

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