Applying Neural Networks to Inverse Laplace Transform Problems in Lattice QCD

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.