Data enhancement method based on automatic derivation and Taylor series expansion

Abstract

The invention provides a data enhancement method based on automatic derivation and Taylor series expansion. The method comprises the following steps: S1, firstly determining a primary function for a given differential (product) equation; s2, determining data points of a direct numerical solution given differential (product) equation; s4, on the premise of S1, S2 and S3, determining data enhancement hyper-parameters: the highest expansion order, the value of the displacement amplitude delta x and the distribution and parameters of the displacement coefficients, and determining the number of new data points generated for each data point obtained through expensive calculation; and distribution of random reckoning parameters of omission order contribution and determination of the number of the random reckoning parameters. According to the technology, training data required by fitting a complex differential (product) equation solution function by the neural network can be greatly reduced, computing resources are remarkably saved under the condition that the given fitting precision requirement is met, or the fitting precision is greatly improved by increasing training data supply under the given computing resources.

Description

technical field [0001] The invention relates to the technical field of data enhancement, in particular to a data enhancement method based on automatic derivation and Taylor series expansion. Background technique [0002] Since translation, rotation and permutation invariance (translation, rotation and permutation invariance) in quantum chemistry and solid-state physics calculations are generally realized by some functions with specific symmetries, the random rotation data enhancement method usually used in the field of image recognition no value. In addition, other commonly used data augmentation methods in the field of image recognition such as random scaling (zoom), flip (flip), and brightness (brightness) adjustment techniques are not helpful for the typical expensive data generation process in scientific computing. Although the addition of Gaussian noise may be used to enhance the data obtained through expensive calculations, adding too much noise will obviously affect ...

AI Technical Summary

Problems solved by technology

[0002] Since translation, rotation and permutation invariance (translation, rotation and permutation invariance) in quantum chemistry and solid-state physics calculations are generally realized by some functions with specific symmetries, the random rotation data enhancement method usually used in the field of image recognition no value

In addition, other commonly used data augmentation methods in the field of image recognition such as random scaling (zoom), flip (flip), and brightness (brightness) adjustment techniques are not helpful for the typical expensive data generation process in scientific computing.

Although the addition of Gaussian noise may be used to enhance the data obtained through expensive calculations, adding too much noise will obviously affect the accuracy of the fitting, and it is difficult to increase the training data on a large scale with a small amount of noise data

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