Modeling methods and usage of proxy models

Abstract

The present application discloses a modeling method and a method for using a proxy model, which includes: obtaining first sample data and its corresponding first observation value; determining an initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value; using the first sample data as a model input, determining a first output value using the initial proxy model, and determining a first true value using a true model that matches the model problem to be fitted; determining a first error between the first output value and the first true value; sampling data based on the first error to obtain second sample data, and determining a second observation value corresponding to the second sample data using the true model; and constructing a target proxy model based on the first sample data, the first observation value, the second sample data, and the second observation value, so as to enable accurate sampling, quickly capture important sample data, reduce sampling time and cost, and then reduce the amount of computation in the subsequent modeling process to improve modeling efficiency.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to a modeling method and a method for using a proxy model. Background Art

[0002] Polynomial Chaos Expansion (PCE) is an interdisciplinary method and a powerful tool that combines probability theory, orthogonal polynomial theory, and uncertainty quantification. It is primarily used to model and analyze system uncertainty, such as in simulation analysis in fields like engineering, physics, and finance. Simulation analysis, in particular, has broad application prospects in uncertainty quantification and complex system modeling. Surrogate models are simplified mathematical representations designed to replace the original computational model or simulator. In some cases, PCE can be considered a specially designed surrogate model.

[0003] In related technologies, existing sample data is often used to fit specific problems (such as engineering, physics, and finance) to generate a proxy model for the corresponding polynomial chaos expansion. To ensure modeling accuracy, a sufficiently large amount of sample data is required. However, requiring a large amount of sample data not only increases sampling time and cost, but also significantly increases the computational workload during the modeling process due to the large amount of sample data that needs to be simulated after sampling, affecting modeling efficiency. Summary of the Invention

[0004] In order to solve the above technical problems, the embodiments of the present application propose a modeling method and a usage method of a proxy model, which can accurately sample to quickly capture important sample data, reduce sampling time and cost, and then reduce the amount of calculation in the subsequent modeling process to improve modeling efficiency, while taking into account the accuracy of the constructed proxy model.

[0005] In a first aspect, an embodiment of the present application provides a method for modeling a proxy model, comprising:

[0006] Obtaining first sample data and its corresponding first observation value;

[0007] Determining an initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value;

[0008] Using the first sample data as a model input, determining a first output value using the initial proxy model, and determining a first true value using a true model that matches the model problem to be fitted;

[0009] determining a first error between the first output value and the first true value;

[0010] Sampling data based on the first error to obtain second sample data, and determining a second observation value corresponding to the second sample data using the true model;

[0011] A target proxy model is constructed based on the first sample data, the first observation value, the second sample data, and the second observation value.

[0012] Optionally, performing data sampling based on the first error to obtain second sample data includes:

[0013] Determine a sampling area according to the first error, wherein the geometric center of the sampling area is a maximum error sample point, and the maximum error sample point is a sample point corresponding to the maximum absolute value of the first error among the sample points included in the first sample data;

[0014] Data sampling is performed on the sampling area to obtain the second sample data.

[0015] Optionally, the sampling area is a circular area, wherein the center of the circular area is the maximum error sample point, and the radius of the circular area is determined based on a set ratio and a maximum absolute value of the first error, and the set ratio is less than 1 and greater than 0;

[0016] The performing data sampling on the sampling area to obtain the second sample data includes:

[0017] The circular area is uniformly sampled to obtain the second sample data.

[0018] Optionally, performing data sampling based on the first error to obtain second sample data includes:

[0019] Based on the first error, generating a corresponding first probability distribution;

[0020] Data sampling is performed based on the first probability distribution to obtain the second sample data.

[0021] Optionally, the first probability distribution includes a third probability distribution, and generating the corresponding first probability distribution based on the first error includes:

[0022] Normalizing the absolute value of the first error to generate a second probability distribution based on absolute error;

[0023] According to the second probability distribution, calculating by maximum likelihood estimation to obtain Gaussian distribution parameters;

[0024] The Gaussian distribution determined by the Gaussian distribution parameters is used as the third probability distribution.

[0025] Optionally, the first probability distribution includes a fourth probability distribution, and generating the corresponding first probability distribution based on the first error includes:

[0026] Normalizing the absolute value of the first error to generate a second probability distribution based on absolute error;

[0027] According to the second probability distribution, a probability generation model based on a neural network is used to simulate the fourth probability distribution.

[0028] Optionally, determining an initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value includes:

[0029] Determine a polynomial corresponding to the model problem to be fitted, and determine a matrix corresponding to the polynomial;

[0030] Based on the first sample data and the first observation value, the matrix corresponding to the polynomial is solved using the least squares method to obtain undetermined coefficients, so as to construct an initial proxy model of the polynomial chaotic expansion according to the undetermined coefficients.

[0031] Optionally, constructing a target proxy model based on the first sample data, the first observation value, the second sample data, and the second observation value includes:

[0032] The first sample data and the second sample data are merged to obtain new first sample data, and the first observation value and the second observation value are merged to obtain a new first observation value, thereby repeating the steps of determining the initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value and subsequent steps until the set conditions are met, and the initial proxy model determined last time is used as the target proxy model.

[0033] Optionally, the error between the second sample data and the second observation value is a second error, wherein the setting condition includes at least one of the following:

[0034] Repeating the execution a number of times reaches an adaptive number, wherein the adaptive number is preset, or the adaptive number is determined by at least one of the following: a maximum absolute value of the first error obtained for the first time, and a maximum absolute value of the second error obtained for the first time;

[0035] The accuracy of the most recently obtained initial proxy model meets the preset accuracy requirements.

[0036] In a second aspect, an embodiment of the present application provides a method for using a proxy model, including:

[0037] Obtaining data to be processed and a target proxy model, wherein the target proxy model is constructed based on any of the above-mentioned modeling methods;

[0038] The data to be processed is input into the target proxy model, so that the target proxy model performs a corresponding target operation according to the data to be processed, wherein the target operation includes at least one of the following: uncertainty quantification analysis and simulation.

[0039] In summary, the embodiments of the present application have at least the following beneficial effects:

[0040] According to an embodiment of the present application, first sample data and its corresponding first observation value are obtained; an initial proxy model corresponding to the model problem to be fitted is determined based on the first sample data and the first observation value; the first sample data is used as a model input, a first output value is determined using the initial proxy model, and a first true value is determined using a true model that matches the model problem to be fitted; a first error between the first output value and the first true value is determined; data is sampled based on the first error to obtain second sample data, and a second observation value corresponding to the second sample data is determined using the true model; a target proxy model is constructed based on the first sample data, the first observation value, the second sample data and the second observation value, so that accurate sampling can be performed to quickly capture important sample data, reduce sampling time and cost, and then reduce the amount of computation in the subsequent modeling process to improve modeling efficiency, while taking into account the accuracy of the constructed proxy model. BRIEF DESCRIPTION OF THE DRAWINGS

[0041] Figure 1 Schematic diagram of the process of modeling the proxy model provided in the embodiment of the present application;

[0042] Figure 2 is a schematic diagram of the input and output of the real model provided in the embodiment of the present application;

[0043] Figure 3 is a schematic diagram of data distribution of first sample data and its corresponding first observation value provided in an embodiment of the present application;

[0044] Figure 4 is a schematic diagram of the initial proxy model provided in an embodiment of the present application;

[0045] Figure 5 is a schematic diagram of the absolute value of the first error provided in an embodiment of the present application;

[0046] Figure 6 This is a schematic diagram of all sample points obtained by sampling according to the probability distribution obtained by error according to an embodiment of the present application;

[0047] Figure 7 is a schematic diagram of a target proxy model provided in an embodiment of the present application;

[0048] Figure 8 is another schematic diagram of the absolute value of the first error provided in an embodiment of the present application;

[0049] Figure 9 This is a schematic diagram of sample points obtained after uniform sampling provided by an embodiment of the present application;

[0050] Figure 10 is a schematic diagram of a real model of a two-dimensional problem provided by an embodiment of the present application;

[0051] Figure 11 This is a schematic diagram of all sample points obtained by sampling the two-dimensional problem according to the probability distribution obtained by error provided by an embodiment of the present application. DETAILED DESCRIPTION

[0052] The following will be combined with the drawings in the embodiments of this application to clearly and completely describe the technical solutions in the embodiments of this application. Obviously, the embodiments described are only part of the embodiments of this application, not all of the embodiments. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of this application.

[0053] In the description of this application, the terms "first", "second", "third", etc. are used for descriptive purposes only and are not to be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Thus, features defined as "first", "second", "third", etc. may explicitly or implicitly include one or more of such features. In the description of this application, unless otherwise specified, "multiple" means two or more. In the description of this application, the term "including" and its variations are open inclusions, i.e., "including but not limited to". The term "based on" means "at least partially based on". The term "according to" means "at least partially based on". The term "one embodiment" means "at least one embodiment"; the term "another embodiment" means "at least one other embodiment"; the term "some embodiments" means "at least some embodiments".

[0054] In the description of this application, it should be noted that, unless otherwise expressly specified or limited, the terms "mounted," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections; mechanical connections or electrical connections; direct connections or indirect connections through an intermediate medium; and internal connections between two components. Those skilled in the art will understand the specific meanings of the above terms in this application based on the specific circumstances.

[0055] In the description of this application, it should be noted that, unless otherwise defined, all technical and scientific terms used in this application have the same meanings as those commonly understood by those skilled in the art. The terms used in this specification are only for the purpose of describing specific embodiments and are not intended to limit this application. Those of ordinary skill in the art will understand the specific meanings of the above terms in this application in specific circumstances.

[0056] First, see Figure 1 , shows a flow chart of a modeling method of an agent model provided in an embodiment of the present application, the method includes steps S101-S106, which are specifically as follows:

[0057] S101, obtaining first sample data and its corresponding first observation value.

[0058] In one example, the first sample data and the first observation value can be a small amount of initial sample data obtained by uniform distribution or Latin hypercube sampling. and the corresponding observations ,in , is the number of sample points (i.e., initial samples) in the first sample data. It is understood that both the first sample data and the first observation value correspond to the model problem to be fitted, wherein the first sample data may be pre-sampled from each sample corresponding to the model problem to be fitted.

[0059] S102: Determine an initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value.

[0060] In one example, the model problem to be fitted may include at least one of an engineering problem, a physical problem, and a financial problem. For example, the engineering problem may include at least one of the following: problems related to artificial intelligence models, problems related to fluid mechanics, problems related to structural engineering, problems related to environmental science, problems related to control systems, etc.

[0061] In one example, the polynomial chaos expansion can be regarded as a specially designed proxy model, which can construct a description of the uncertainty in the system corresponding to the model problem to be fitted through a set of orthogonal polynomials. Here, the set of orthogonal polynomials can be fitted and calculated by using the first sample data and the first observation value as input data to construct the corresponding initial proxy model.

[0062] S103 , using the first sample data as a model input, determining a first output value using the initial proxy model, and determining a first true value using a true model that matches the model problem to be fitted.

[0063] In one example, the true model may refer to a related function constructed based on the model problem to be fitted, such as a response function.

[0064] S104: Determine a first error between the first output value and the first true value.

[0065] S105 , performing data sampling based on the first error to obtain second sample data, and using the true model to determine a second observation value corresponding to the second sample data.

[0066] It can be understood that data sampling refers to sampling from sample data corresponding to the model problem to be fitted. In this way, the first sample data and the second sample data are both samples for the model problem to be fitted.

[0067] S106: Construct a target proxy model based on the first sample data, the first observation value, the second sample data, and the second observation value.

[0068] In one example, the first sample data, the first observation value, the second sample data and the second observation value can be used to update the initial proxy model to construct a target proxy model, or the first and second sample data and the first and second observation values ​​can be merged and the target proxy model can be constructed using the relevant embodiments of step S102.

[0069] In some cases, the target proxy model is a proxy model based on polynomial chaos expansion, capable of being used for at least one of the following:

[0070] 1. Computational fluid dynamics, so as to apply it to simulation analysis of nonlinear and complex systems, thereby improving the efficiency and accuracy of simulation analysis in related fields.

[0071] 2. Research on numerical methods / calculations of numerical methods for application in corresponding simulation analysis in engineering fields, thereby improving the efficiency and accuracy of simulation analysis in related fields.

[0072] 3. Artificial intelligence, for example, in combination with machine learning and / or in combination with deep learning to improve the accuracy and efficiency of applied artificial intelligence models.

[0073] For example, aircraft design data can be obtained and input into a target proxy model for simulation to obtain simulation results of the aircraft. The simulation results may include the uncertainty of the aircraft's airfoil under different aerodynamic conditions. In addition, when ship / vehicle data is input into a target proxy model for simulation, the obtained ship / vehicle simulation results may include deviations that may occur in the manufacturing process corresponding to the ship / vehicle design plan.

[0074] In an optional implementation, the performing data sampling based on the first error to obtain second sample data includes:

[0075] A sampling area is determined according to the first error, wherein the geometric center of the sampling area is a maximum error sample point, and the maximum error sample point is a sample point corresponding to the maximum absolute value of the first error among the sample points included in the first sample data.

[0076] Data sampling is performed on the sampling area to obtain the second sample data.

[0077] In one example, the sampling area can be a regular, symmetrical area, for example, a rectangular area with the maximum error sample point as its geometric center, preferably a square area, or an elliptical area with the maximum error sample point as its geometric center. Thus, a corresponding data sampling method can be obtained based on the specific shape of the sampling area to perform data sampling on the sampling area.

[0078] It should be noted that, in this embodiment, a sample point corresponds to a first observation value, and each sample point is used as a model input to obtain a corresponding first output value and a first true value. The difference between each first output value and its corresponding first true value is the first error corresponding to the corresponding sample point.

[0079] In an optional embodiment, the sampling area is a circular area, wherein the center of the circular area is the maximum error sample point, and the radius of the circular area is determined based on a set ratio and the maximum absolute value of the first error, and the set ratio is less than 1 and greater than 0.

[0080] The performing data sampling on the sampling area to obtain the second sample data includes:

[0081] The circular area is uniformly sampled to obtain the second sample data.

[0082] In one example, the set ratio is 0.5. Here, it is assumed that the maximum absolute value of the first error is , the corresponding sample points are Then, find the sample points The absolute error near The nearest sample point on the left and right , you can define the radius .

[0083] The following combination Figures 2 to 5 To explain, see Figure 2 , showing the input and output of a real model ( Figure 2 The horizontal axis is the input of the real model, and the vertical axis is the output of the real model). For such a real model, the slope is particularly large when the input variable is equal to 0.5. More sampling points are required to obtain a good proxy model that fits the polynomial chaos expansion. At this time, see Figure 3 , shows the data distribution of the first sample data (horizontal axis) obtained by initial sampling and its corresponding first observation value (vertical axis). It can be seen that the sampling is uniform on the horizontal axis at this time. First, an initial proxy model is constructed based on this, such as Figure 4 Here, see Figure 4 , we can see that the initial proxy model ( Figure 4 The horizontal axis is the input of the model, and the vertical axis is the output of the model. The change jitter is relatively large when the input variable is equal to 0.5. Figure 5 , calculate the absolute error between the sample data of the initial proxy model and the true model (that is, the absolute value of the first error, Figure 5 The horizontal axis is the input of the two models, and the vertical axis is the absolute value of the first error. It can be seen that the error is exactly when the input variable is 0.5. Therefore, it can be seen that the resampling should be concentrated around the input variable 0.5.

[0084] See also Figure 6 and Figure 9 , Figure 6 is the sample point obtained by uniformly sampling the circular area ( Figure 6 The horizontal axis is the first sample data or the second sample data obtained by the current sampling, and the vertical axis is the first observation value or the second observation value), where the blue dot is Figure 3 The sample points of the first sample data are shown, and the orange points are the sample points of the second sample data currently obtained (it can be seen that they are mainly concentrated around the input variable 0.5). Figure 7 , is the initial proxy model constructed based on the first sample data and the currently obtained second sample data ( Figure 7 The horizontal axis is the input of the model, and the vertical axis is the output of the model). Its change jitter is compared with Figure 4 There has been a significant improvement, accordingly, Figure 8 is the absolute error between the current initial proxy model and the sample data of the true model ( Figure 8 The horizontal axis is the input of the two models, and the vertical axis is the value of the absolute error). Figure 9is the sample point obtained after uniform sampling of the circular area again ( Figure 9 The horizontal axis is the first sample data or the second sample data obtained after another uniform sampling, and the vertical axis is the first observation value or the second observation value regenerated after another uniform sampling).

[0085] See also Figure 10 and Figure 11 , which is an example corresponding to the case where this embodiment is extended to a two-dimensional problem, wherein, Figure 10 represents the true model, Figure 11 Represents the target agent model, x represents the horizontal axis of the two-dimensional problem, and y represents the vertical axis of the two-dimensional problem. It can be seen that Figure 11 The clustered sampling points are formed in the , which well captures the part with larger slope in the real model (i.e. Figure 10 the greenish part).

[0086] In an optional implementation, the performing data sampling based on the first error to obtain second sample data includes:

[0087] Based on the first error, a corresponding first probability distribution is generated.

[0088] Data sampling is performed based on the first probability distribution to obtain the second sample data.

[0089] In some cases, the various embodiments of this application related to obtaining second sample data by data sampling can be combined. That is, all second sample data can include: second sample data obtained by sampling data in the sampling area, and second sample data obtained by sampling data based on the first probability distribution. In other words, in this case, data sampling in the sampling area obtains partial second sample data, and data sampling based on the first probability distribution obtains partial second sample data.

[0090] Furthermore, all second sample data can be obtained by weighted merging "part of the second sample data obtained according to the sampling area (hereinafter referred to as the first part of the data)" and "part of the second sample data obtained according to the first probability distribution (hereinafter referred to as the second part of the data)", and the respective weights of the first part of the data and the second part of the data can be determined according to the model problem to be fitted.

[0091] In an optional embodiment, the first probability distribution includes a third probability distribution, and generating the corresponding first probability distribution based on the first error includes:

[0092] The absolute value of the first error is normalized to generate a second probability distribution based on absolute errors.

[0093] It should be noted that for the second probability distribution in this embodiment, if the "absolute value of the first error" (i.e., the absolute error) corresponding to all sample points is normalized, the resulting value is a probability. Sample points corresponding to locations with large absolute errors have higher probabilities, thus forming a second probability distribution based on absolute errors. This second probability distribution represents a higher probability for larger absolute errors and a lower probability for smaller absolute errors. Therefore, if sampling is possible based on this second probability distribution, the probability of sampling sample points in locations with large absolute errors is higher.

[0094] According to the second probability distribution, calculation is performed through maximum likelihood estimation to obtain Gaussian distribution parameters.

[0095] The Gaussian distribution determined by the Gaussian distribution parameters is used as the third probability distribution.

[0096] In one example, after obtaining the third probability distribution, sampling data based on the first probability distribution to obtain the second sample data may include: determining an important area according to the third probability distribution, drawing a corresponding circle with the important area as the geometric center, so that the drawn circle corresponds to the Gaussian distribution Confidence interval, then, data sampling is performed within the drawn circle, that is, within the selected confidence interval, preferably uniform sampling. In the two-dimensional case, important areas can be represented by drawing contour maps to represent areas at different confidence levels. Generally speaking, in a contour map, each closed curve represents the area within a given confidence level, that is, the set of all points inside the curve meets the probability coverage of the selected confidence level.

[0097] In one example, we can consider a Gaussian distribution to simulate the probability distribution represented by the absolute error. Sampling from this Gaussian distribution can yield the desired sample points near regions with large absolute errors. The mathematical description is shown below.

[0098] Assume that the initial sample points are , where the probability value obtained after the normalization of the absolute error corresponding to each point is ,in Yes The probability or weight of occurrence. Thus, the goal of this embodiment is to find a Gaussian distribution To fit these data points. The probability density function of the Gaussian distribution is:

[0099]

[0100] in mean (expected), is the variance. Here we can determine the parameters of the Gaussian distribution by maximum likelihood estimation and , so that the given point Maximize the likelihood function.

[0101] For a given set of points and the corresponding probability , the likelihood function is:

[0102]

[0103] in Each point The log-likelihood function is:

[0104]

[0105] Substituting the probability density function of the Gaussian distribution, we get:

[0106]

[0107] Simplified to:

[0108]

[0109] Finally, the Gaussian distribution parameters obtained by maximum likelihood estimation are:

[0110]

[0111]

[0112] Thus, the final Gaussian distribution is obtained.

[0113] In an optional embodiment, the first probability distribution includes a fourth probability distribution, and generating the corresponding first probability distribution based on the first error includes:

[0114] The absolute value of the first error is normalized to generate a second probability distribution based on absolute errors.

[0115] According to the second probability distribution, a probability generation model based on a neural network is used to simulate the fourth probability distribution.

[0116] In some cases, the first probability distribution may include a third probability distribution and a fourth probability distribution. In this case, sampling data based on the first probability distribution to obtain the second sample data may include: sampling data according to the third probability distribution to obtain a portion of the second sample data, and sampling data according to the fourth probability distribution to obtain a portion of the second sample data. In other words, in this case, the second sample data obtained based on the first probability distribution includes the second sample data obtained according to the third probability distribution and the second sample data obtained according to the fourth probability distribution.

[0117] In one example, the probability generation model can be built based on Normalizing Flow, a framework for probability density modeling and generative modeling that maps a simple probability distribution (such as a standard normal distribution) to a complex target through a series of reversible transformations. The core goal of this model is to be able to model complex data distributions, estimate the probability density of the data distribution, and generate samples that conform to the data distribution, i.e., samples in areas with large absolute errors, by learning this series of reversible transformations. The probability generation model can be a KRnet model, which is a real-valued non-volume-preserving model further extended by the Knothe-Rosenblatt rearrangement. The mathematical description is shown below.

[0118] First, define the initial distribution as .

[0119] Then define the multi-layer reversible transformation as .

[0120] Then the density formula is derived:

[0121]

[0122] Then, by optimizing the objective, we can use common optimization methods for neural networks, such as the adaptive moment estimation method, to maximize the log-likelihood:

[0123]

[0124] Therefore, only a relatively small number of training iterations are needed to obtain a suitable model. Sampling, then passing By generating target distribution samples, new sample points are obtained to constitute at least part of the second sample data.

[0125] In an optional implementation, determining an initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value includes:

[0126] Determine a polynomial corresponding to the model problem to be fitted, and determine a matrix corresponding to the polynomial.

[0127] Based on the first sample data and the first observation value, the matrix corresponding to the polynomial is solved using the least squares method to obtain undetermined coefficients, so as to construct an initial proxy model of the polynomial chaotic expansion according to the undetermined coefficients.

[0128] In one example, the polynomial may be a Legendre polynomial or a Hermite polynomial, and in this case, the order of the polynomial may also be determined. The mathematical description is as follows.

[0129] The polynomial can be expressed by the following formula:

[0130]

[0131] in, is the output, are the coefficients to be solved, is the chosen orthogonal polynomial basis, is the input random variable.

[0132] At this point, the matrix corresponding to the polynomial can be expressed by the following formula:

[0133]

[0134] in, yes The observation vector of . yes The matrix elements are . yes The coefficient vector corresponding to the coefficient to be solved. In order to minimize the residual sum of squares, the least squares method can be used to solve the coefficients to be determined:

[0135]

[0136] Thus, an initial proxy model of polynomial chaos expansion with general accuracy can be obtained.

[0137] In one example, the method for obtaining the true model may include: obtaining text suitable for indicating a preset sample problem, and polynomial guidance information corresponding to the text, wherein the text is suitable for indicating a preset polynomial; using the text and the polynomial guidance information as root nodes for decision tree operations; inputting the text and the polynomial guidance information into a large model, so that the large model generates a polynomial for the text according to the target polynomial features indicated by the polynomial guidance information, and obtains the polynomial generated by the large model; determining the similarity between the polynomial generated by the large model and the preset polynomial; and when the similarity is less than a preset threshold, the preset polynomial is generated. Feedback is provided to the large model, causing the large model to perform a function structure analysis on the generated polynomial and the preset polynomial, and to modify the polynomial guide information according to the function structure analysis results; the text and the modified polynomial guide information are used as splitting nodes for the decision tree operation, wherein the splitting node is used to perform operations after the root node (i.e., during the decision tree operation, the root node and the splitting node are operated in sequence); after the decision tree operation is completed, the decision parameters corresponding to each branch in the decision tree are obtained, and the target branch is determined in each branch based on the decision parameters, and the true model is determined based on the target branch in the decision tree. Because in actual applications, the mathematical expressions corresponding to many engineering problems are not obtained by strict mathematical derivation and proof, but are empirical formulas, or even the relevant mathematical expressions have not yet been summarized, in this case, in this embodiment, the decision tree model can be optimized so that the optimized decision tree model can fit a more accurate true model based on the text description of the engineering problem and its corresponding polynomial guide information (e.g., polynomial guide information generated by the corresponding empirical formula).

[0138] Continuing with the above example, the parameter value of the decision parameter corresponding to the target branch can be higher than the set parameter threshold.

[0139] Continuing with the above example, determining the true model according to the target branch in the decision tree may include: determining the branch with the highest parameter value of the decision parameter in the target branch as the true model.

[0140] In an optional implementation, constructing a target proxy model based on the first sample data, the first observation value, the second sample data, and the second observation value includes:

[0141] The first sample data and the second sample data are merged to obtain new first sample data, and the first observation value and the second observation value are merged to obtain a new first observation value, thereby repeating the steps of determining the initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value and subsequent steps until the set conditions are met, and the initial proxy model determined last time is used as the target proxy model.

[0142] In an optional embodiment, the error between the second sample data and the second observation value is a second error, wherein the setting condition includes at least one of the following:

[0143] Repeating the execution a number of times reaches an adaptive number, wherein the adaptive number is preset, or the adaptive number is determined by at least one of the following: a maximum absolute value of the first error obtained for the first time, and a maximum absolute value of the second error obtained for the first time;

[0144] The accuracy of the most recently obtained initial proxy model meets the preset accuracy requirements.

[0145] In combination with the above-mentioned relevant embodiments, this application has the following technical effects:

[0146] 1. Adaptively iteratively generating sample points by calculating absolute errors through sample evaluation, without introducing additional computational overhead. This is particularly advantageous for problems where sample acquisition is difficult. It is also simple, straightforward, easy to implement, highly efficient, and versatile.

[0147] 2. The absolute error evaluated based on the samples can quickly capture the most important singular parts of the true model, or the parts that are more difficult to fit.

[0148] 3. The sampling used for sample evaluation can also be used to calculate the unknown coefficients of the proxy model for polynomial chaos expansion without any waste of computational effort.

[0149] In a second aspect, an embodiment of the present application provides a method for using a proxy model, including:

[0150] Obtaining data to be processed and a target proxy model, wherein the target proxy model is constructed based on any of the above-mentioned modeling methods;

[0151] The data to be processed is input into the target proxy model, so that the target proxy model performs a corresponding target operation according to the data to be processed, wherein the target operation includes at least one of the following: uncertainty quantification analysis and simulation.

[0152] In one example, the data to be processed may include material strength data and / or temperature data. It should be understood that material strength data and temperature data are often not deterministic but subject to change. Such change can be represented by a random variable, which is a quantity with a probability distribution. For example, a parameter in the material strength data or temperature data may randomly vary within a range. In this case, the target operation includes uncertainty quantification analysis, which enables the target proxy model to perform corresponding uncertainty quantification analysis on the material strength data and / or temperature data, so as to accurately predict the output corresponding to the material strength data and / or temperature data based on the analysis results. In addition, the analysis results can also be used to characterize the impact of the uncertainty of the data to be processed on the model output.

[0153] In one example, the data to be processed may include engineering data, such as fluid dynamics data, structural engineering data, geological engineering data, aircraft-related data (such as aircraft wing structure data), ship-related data (such as hull structure data), vehicle-related data (such as vehicle body structure data), etc. In this case, the target operation includes simulation, that is, the target proxy model can perform corresponding simulation based on the data to be processed. For example, the target proxy model can perform aircraft design simulation based on aircraft-related data, ship design simulation based on ship-related data, vehicle design simulation based on vehicle-related data, etc.

[0154] In summary, the embodiments of the present application have at least the following beneficial effects:

[0155] According to an embodiment of the present application, first sample data and its corresponding first observation value are obtained; an initial proxy model corresponding to the model problem to be fitted is determined based on the first sample data and the first observation value; the first sample data is used as a model input, a first output value is determined using the initial proxy model, and a first true value is determined using a true model that matches the model problem to be fitted; a first error between the first output value and the first true value is determined; data is sampled based on the first error to obtain second sample data, and a second observation value corresponding to the second sample data is determined using the true model; a target proxy model is constructed based on the first sample data, the first observation value, the second sample data and the second observation value, so that accurate sampling can be performed to quickly capture important sample data, reduce sampling time and cost, and then reduce the amount of computation in the subsequent modeling process to improve modeling efficiency, while taking into account the accuracy of the constructed proxy model.

[0156] Through the description of the above implementation methods, those skilled in the art can clearly understand that the present application can be implemented by means of software plus the necessary hardware platform, and of course, it can also be implemented entirely through hardware. Based on this understanding, all or part of the contribution of the technical solution of the present application to the background technology can be embodied in the form of a software product. The computer software product can be stored in a storage medium, such as ROM (Read-Only Memory) / RAM (Random Access Memory), a disk, an optical disk, etc., and includes a number of instructions for enabling a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment of the present application or certain parts of the embodiments.

[0157] The above is a preferred embodiment of the present application. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principles of the present application. These improvements and modifications are also considered to be within the scope of protection of the present application.

Claims

1. A method for modeling an agent model, characterized in that: include: Obtaining first sample data and its corresponding first observation value; Determining an initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value; Using the first sample data as a model input, determining a first output value using the initial proxy model, and determining a first true value using a true model that matches the model problem to be fitted; determining a first error between the first output value and the first true value; Sampling data based on the first error to obtain second sample data, and determining a second observation value corresponding to the second sample data using the true model; constructing a target proxy model based on the first sample data, the first observation value, the second sample data, and the second observation value; The step of sampling data based on the first error to obtain second sample data includes: generating a corresponding first probability distribution based on the first error; and sampling data based on the first probability distribution to obtain at least part of the second sample data. The first probability distribution includes a fourth probability distribution, and generating the corresponding first probability distribution based on the first error includes: normalizing the absolute value of the first error to generate a second probability distribution based on the absolute error; and simulating the fourth probability distribution using a probability generation model based on a neural network based on the second probability distribution; The determining of the initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value includes: determining a polynomial corresponding to the model problem to be fitted and determining a matrix corresponding to the polynomial; solving the matrix corresponding to the polynomial using a least squares method based on the first sample data and the first observation value to obtain undetermined coefficients, and constructing an initial proxy model of the chaotic expansion of the polynomial according to the undetermined coefficients; The constructing of the target proxy model based on the first sample data, the first observation value, the second sample data, and the second observation value includes: merging the first sample data and the second sample data to obtain new first sample data, and merging the first observation value and the second observation value to obtain new first observation value, thereby repeatedly performing the steps of determining the initial proxy model corresponding to the model problem to be fitted based on the first sample data and the first observation value and subsequent steps until a set condition is met, and using the initial proxy model determined last as the target proxy model; The target proxy model is used for at least one of the following: Computational fluid dynamics, when the target proxy model is used for computational fluid dynamics, the first sample data includes data related to computational fluid dynamics; Numerical method research or numerical method calculation, when the target proxy model is used for numerical method research or numerical method calculation, the first sample data includes data related to the numerical method research or numerical method calculation; Artificial intelligence, when the target agent model is used for artificial intelligence, the first sample data includes data related to artificial intelligence.

2. The method for modeling a proxy model according to claim 1, wherein: The performing data sampling based on the first error to obtain second sample data further includes: Determine a sampling area according to the first error, wherein the geometric center of the sampling area is a maximum error sample point, and the maximum error sample point is a sample point corresponding to the maximum absolute value of the first error among the sample points included in the first sample data; Data sampling is performed on the sampling area to obtain part of the second sample data.

3. The modeling method of the proxy model according to claim 2, characterized in that: The sampling area is a circular area, wherein the center of the circular area is the maximum error sample point, and the radius of the circular area is determined based on a set ratio and the maximum absolute value of the first error, and the set ratio is less than 1 and greater than 0; The performing data sampling on the sampling area to obtain part of the second sample data includes: The circular area is uniformly sampled to obtain part of the second sample data.

4. The method for modeling a proxy model according to claim 1, wherein: The first probability distribution includes a third probability distribution, and generating the corresponding first probability distribution based on the first error further includes: Normalizing the absolute value of the first error to generate a second probability distribution based on absolute error; According to the second probability distribution, calculating by maximum likelihood estimation to obtain Gaussian distribution parameters; The Gaussian distribution determined by the Gaussian distribution parameters is used as the third probability distribution.

5. The method for modeling a proxy model according to claim 1, wherein: The error between the second sample data and the second observation value is a second error, wherein the setting condition includes at least one of the following: Repeating the execution a number of times reaches an adaptive number, wherein the adaptive number is preset, or the adaptive number is determined by at least one of the following: a maximum absolute value of the first error obtained for the first time, and a maximum absolute value of the second error obtained for the first time; The accuracy of the most recently obtained initial proxy model meets the preset accuracy requirements.

6. A method for using a proxy model, characterized in that: include: Obtaining data to be processed and a target proxy model, wherein the target proxy model is constructed based on the modeling method according to any one of claims 1 to 5; The data to be processed is input into the target proxy model, so that the target proxy model performs a corresponding target operation according to the data to be processed, wherein the target operation includes at least one of the following: uncertainty quantification analysis and simulation.

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