"A study of applications of Physics-Informed Neural Networks"

Methods of machine learning are starting to be widely used in applications in hadronic physics. Neural networks provide a very flexible parametrization of functions to be extracted from the experimental data. They are used in hadronic physics to extract parton distribution functions and other functions that describe the internal structure of the nucleon. At the same time, the inverse problem solutions must obey physical laws encoded in differential equations, boundary conditions, etc. One of the goals of the inverse problem is reliable estimation of the errors of the extractions and the posterior probability density of the underlying parameters. The flexibility provided by the neural networks is the origin of the pitfall of the traditional neural networks, which is the extrapolation of the results. The extrapolation needed for predictions for unmeasured regions may become unphysical if the appropriate constraints or functional forms are not imposed. In our study, we will construct a neural network that describes synthetic data and demonstrate potential problems of its utilization. We will further study and apply methods of the Physics-Informed Neural Networks (PINN) to tame the behavior of the network and to guide the neural network to obey physical laws. Using comprehensive examples, we will work towards the goal of constructing a flexible PINN to handle the inverse problems that arise in hadronic physics.