Applying Neural Networks to Inverse Laplace Transform Problems in Lattice QCD

从格点QCD得到的相关函数是相应谱密度函数的拉普拉斯变换。这些谱密度是理解基本物理的核心，因此从格点QCD相关函数中提取它们的问题，即反演这些拉普拉斯变换，是非常有趣的。然而，这是一个非常病态的问题，大多数方法容易受到大的数值误差的影响。该项目的目的是利用神经网络和机器学习的潜力来提高现有拉普拉斯变换反演方法的准确性和可靠性，从而能够以较低的数值误差提取相关的谱密度函数。

Correlation functions obtained from Lattice QCD are Laplace transforms of corresponding spectral density functions. These spectral densities are central to understanding the underlying physics, so the problem of extracting them from Lattice QCD correlation functions, i.e. inverting these Laplace transforms, is of great interest. This is a very ill-conditioned problem however, with most methods being susceptible to large numerical errors. The aim of this project is to use the potential of neural networks and machine learning to improve the accuracy and reliability of the existing methods for inverting Laplace transforms and thus be able to extract the associated spectral density functions with lower numerical errors.