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Saudi Digital Library
Inverse problems – using measured observations to determine unknown parameters – are well motivated but challenging in many scientific problems. Mapping parameters to observables is a well-posed problem with unique solutions, and therefore can be solved with differential equations or linear algebra solvers. However, the inverse problem requires backward mapping from observ able to parameter space, which is often nonunique. Consequently, solving inverse problems is ill-posed and a far more challenging computational problem. Our motivated application in this dissertation is the inverse problems in nuclear physics that char acterize the internal structure of the hadrons. We first present a machine learning framework called Variational Autoencoder Inverse Mapper (VAIM), as an autoencoder based neural network archi tecture to construct an effective “inverse function” that maps experimental data into QCFs. In addition to the well-known inverse problems challenges such as ill-posedness, an application spe cific issue is that the experimental data are observed on kinematics bins which are usually irregular and varying. To address this ill defined problem, we represent the observables together with their kinematics bins as an unstructured, high-dimensional point cloud. The point cloud representation is incorporated into the VAIM framework. Our new architecture point cloud-based VAIM (PC VAIM) enables the underlying deep neural networks to learn how the observables are distributed across kinematics. Next, we present our methods of extracting the leading twist Compton form factors (CFFs) from polarization observables. In this context, we extend VAIM framework to the Conditional -VAIM to extract the CFFs from the DVCS cross sections on several kinematics. Connected to this effort is a study of the effectiveness of incorporating physics knowledge into machine learning. We start this task by incorporating physics constraints to the forward problem of mapping the kinematics to the cross sections. First, we develop Physics Constrained Neural Networks (PCNNs) for Deeply Virtual Exclusive Scattering (DVCS) cross sections by integrating some of the physics laws such as the symmetry constraints of the cross sections. This provides us with an inception of incorporating physics rules into our inverse mappers which will one of the directions of our future research.
Inverse problems, AI, Nuclear Physics, QCD