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CN-121579961-B - Virtual sample generation method and system based on non-stationary neural network Gaussian process

CN121579961BCN 121579961 BCN121579961 BCN 121579961BCN-121579961-B

Abstract

The invention provides a virtual sample generation method and a system based on a non-stationary neural network Gaussian process, wherein the method comprises the steps of obtaining original data, judging non-stationary property, judging whether statistical properties change along with input positions, if not stationary, constructing an hidden variable model fusing the neural network and the Gaussian process, training to obtain a hidden variable space representing non-stationary distribution, and sampling based on hidden variable space probability distribution Generating by model through non-stable high-dimensional mapping = ( ,Z) (Z, Z) ‑1 X, where Z is a low-dimensional hidden variable, and X is an input variable; the method can generate high-quality and high-diversity virtual samples under the conditions of small samples and non-stable scenes.

Inventors

  • HU MIN
  • CHEN KAI

Assignees

  • 中南大学

Dates

Publication Date
20260505
Application Date
20260129

Claims (8)

  1. 1. The virtual sample generation method based on the non-stationary neural network Gaussian process is applied to material performance prediction and is characterized by comprising the following steps: S1, acquiring an original physical and chemical attribute data set for battery material design, and judging the original sample data to judge whether the sample statistical characteristics change along with the input position; S2, under the condition that the original sample data is judged to have non-stationarity, constructing a Gaussian process hidden variable model for describing the relevant change characteristics of the sample distribution position, wherein the Gaussian process hidden variable model is a non-stationary Gaussian process hidden variable model, and a non-stationary kernel function is constructed by embedding a neural network into a stationary kernel function so as to realize self-adaptive modeling of sample characteristics of different input areas, wherein the non-stationary kernel function is used for generating a non-stationary model of the sample distribution position The construction mode of (a) is as follows: Using neural networks Non-linearly mapping the original input coordinates x to the hidden space phi (x) and calculating the distance in the hidden space by a stationary kernel function K, i.e ; Wherein, the Representing coordinates or feature vectors of the ith and jth original input samples, respectively; mapping functions for a neural network; , respectively the original inputs A representation in hidden space after mapping via a neural network; K is a stable kernel function; Is a non-stationary kernel function; training the original sample data by fusing a neural network and a Gaussian process by the Gaussian process hidden variable model to obtain a hidden variable space for representing the non-stationary distribution characteristic of the sample; s3, sampling based on probability distribution of the hidden variable space to obtain a hidden variable virtual sample ; S4, carrying out non-stationary high-dimensional mapping on the hidden variable virtual sample by utilizing the Gaussian process hidden variable model to generate a material high-dimensional virtual sample with physical consistency Wherein Z is a low-dimensional hidden variable, and X is an input variable; S5, carrying out consistency test on the high-dimensional virtual sample and the original sample data, and screening based on a consistency test result to obtain a virtual sample set meeting the physical essence and statistical consistency of the material, wherein the virtual sample set is used for expanding a battery material training data set.
  2. 2. The method for generating a virtual sample based on a non-stationary neural network gaussian process according to claim 1, wherein when the original sample data is a labeled sample, the high-dimensional virtual sample is generated based on the gaussian process hidden variable model or gaussian process regression model Generating corresponding virtual tags 。
  3. 3. The virtual sample generation method based on a non-stationary neural network gaussian process according to claim 1 or 2, characterized in that in step S1 the non-stationary decision comprises any one or more of the following: dividing a sample space into a plurality of overlapped areas and calculating statistic difference of each area; comparing and analyzing the nuclear function hyper-parameter distribution of samples at different positions; or evaluating the variation of the sample distribution with the input position through an empirical distribution function.
  4. 4. The virtual sample generation method based on a non-stationary neural network gaussian process according to claim 1 or 2, wherein model parameters are initialized and a scaled conjugate gradient class optimization algorithm is adopted to perform optimization training on the model when constructing the hidden variable space.
  5. 5. The method of generating virtual samples based on a non-stationary neural network gaussian process according to claim 1 or 2, characterized in that said consistency check comprises any one or more of the following: visual comparison of the virtual sample and the original sample in a hidden variable space or a characteristic space; a two-sample consistency test based on a statistical hypothesis test; or global consistency assessment based on a distribution difference metric.
  6. 6. The virtual sample generation method based on a non-stationary neural network gaussian process according to claim 1 or 2, wherein the probability distribution of the hidden variable space is expressed as: ; Sampling And calculating: ; Wherein, the Represents the ith hidden variable; representing hidden variables Probability distribution of (1), assuming a multivariate normal distribution ; Is a hidden variable The average value vector obeying normal distribution; Is a hidden variable Covariance matrix obeying normal distribution; is a noise term sampled from a standard normal distribution N (0,I), I is an identity matrix; Is a new hidden variable obtained after re-parameterization.
  7. 7. The virtual sample generation method based on a non-stationary neural network gaussian process according to claim 1 or 2, characterized in that in step S4 the probability space of the non-stationary high-dimensional map is expressed as: ; Thus, according to the above equation, a high-dimensional virtual sample is obtained as follows: , Wherein, the Representing the generated high-dimensional virtual samples, As a non-stationary kernel function, Z is the original set of low-dimensional hidden variables for the new hidden variables, Representing a kernel matrix between the new hidden variable and the original hidden variable; Is the inverse of the original hidden variable kernel matrix, Is a matrix of nuclei between new hidden variables.
  8. 8. A virtual sample generation system based on a non-stationary neural network gaussian process, employing the virtual sample generation method based on a non-stationary neural network gaussian process according to any of claims 1 to 7, comprising: the non-stationarity judging module is used for carrying out non-stationarity analysis on the original physicochemical attribute data set of the battery material; the hidden variable modeling module is used for constructing and training a Gaussian process hidden variable model to form a hidden variable space; the hidden variable sampling module is used for carrying out probability sampling in a hidden variable space; the high-dimensional mapping module is used for mapping the hidden variable virtual sample into a material high-dimensional virtual sample with physical consistency; and the consistency test module is used for carrying out consistency evaluation on the generated high-dimensional virtual samples and screening to obtain a virtual sample set meeting the physical essence and statistical consistency of the materials.

Description

Virtual sample generation method and system based on non-stationary neural network Gaussian process Technical Field The invention relates to the technical field of virtual sample generation, in particular to a virtual sample generation method and system based on a non-stationary neural network Gaussian process. Background When applying machine learning (MACHINE LEARNING, ML) to the real world, "less data, high model requirements" is a large core bottleneck. To solve this problem, a virtual sample generation technique is commonly used in the industry, which aims to expand the scale of the training data set by mining the inherent distribution rule and characteristic association from the existing small number of real samples, and further synthesizing new virtual samples with the same statistical characteristics as the real samples. A large number of research results show that the virtual sample generation method can effectively relieve the problem of overfitting under the condition of a small sample, and the performance of a downstream prediction model is obviously improved. However, the conventional virtual sample generation method generally has a fundamental theoretical limitation that the conventional virtual sample generation method is mostly built on the basis of the strong assumption that the data distribution satisfies the 'stationarity'. In particular, this assumption considers that the covariance between any two sample points depends only on their absolute distance in the feature space, and is independent of the physicochemical properties or other semantic information inherent to the sample points themselves. Although the stationarity assumption simplifies the mathematical complexity of model construction, it is often difficult to establish when dealing with highly dimensional, multi-source heterogeneous, strongly non-linear datasets that are widely encountered in today's practical applications. For example, in the task of predicting material performance, basic properties such as atomic number and electronegativity are intrinsic factors determining macroscopic properties of the material, and neglecting these information only measures correlation according to the geometric distance of the sample points, which inevitably leads to erroneous judgment on the intrinsic structure of the data. Many academic studies have clearly indicated that models relying on stationarity assumptions are extremely prone to cause serious problems, firstly, leading to significant degradation of predictive performance and secondly, quantitative misalignments of model prediction uncertainty, which are fatal defects for risk assessment and safety critical applications. Furthermore, the stationarity assumption is naturally better suited for describing continuous, smoothly varying data processes, and the assumption is frustrating with respect to the discontinuities, mutability, and local heterogeneity characteristics that are prevalent in actual data. Therefore, the virtual samples generated by the conventional method often have the problems of mode distortion, lack of diversity and the like, so that the generalization capability of the target model is difficult to be substantially improved, and even the model performance can be damaged due to the introduction of noise samples. Therefore, a method and a system for generating a virtual sample based on a non-stationary neural network gaussian process are needed, which can generate a high-quality and high-diversity virtual sample under a small sample and a non-stationary scene. Disclosure of Invention Aiming at the defects in the prior art, the invention aims to provide a virtual sample generation method and a virtual sample generation system based on a non-stationary neural network Gaussian process, aiming at solving the technical problems of virtual sample distortion, insufficient diversity and poor model generalization caused by traditional stationary assumption in small sample learning. To achieve the above object, in a first aspect, the present invention provides a virtual sample generating method based on a non-stationary neural network gaussian process, including the steps of: S1, acquiring original sample data, and carrying out non-stationarity judgment on the original sample data to judge whether the statistical properties of a sample change along with an input position; S2, under the condition that the original sample data is judged to have non-stationarity, constructing a Gaussian process hidden variable model (Gaussian Process Latent Variable Model, GPLVM) for describing the relevant change characteristics of the sample distribution position, and training the original sample data by fusing a neural network and a Gaussian process to obtain a hidden variable space for representing the non-stationary distribution characteristics of the sample; s3, sampling based on probability distribution of the hidden variable space to obtain a hidden variable virtual sample ; S4, performin