Bayesian Neural Network Variational Autoencoder Inverse Mapper (BNN-VAIM) and its application in Compton Form Factors extraction

• Published in: Journal of instrumentation 2024-08, Vol.19 (8), p.C08003
• Main Authors: Hossen, MD Fayaz Bin, Alghamdi, Tareq, Almaeen, Manal, Li, Yaohang
• Format: Article
• Language: English
• Subjects: Analysis and statistical methods; Bayesian analysis; Data processing methods; Form factors; Ill posed problems; Inverse problems; Machine learning; Neural networks; Scattering cross sections; Uncertainty
• ISSN: 1748-0221; 1748-0221
• DOI: 10.1088/1748-0221/19/08/C08003

We extend the Variational Autoencoder Inverse Mapper (VAIM) framework for the inverse problem of extracting Compton Form Factors (CFFs) from deeply virtual exclusive reactions, such as the unpolarized Deeply virtual exclusive scattering (DVCS) cross section. VAIM is an end-to-end deep learning framework to address the solution ambiguity issue in ill-posed inverse problems, which comprises of a forward mapper and a backward mapper to simulate the forward and inverse processes, respectively. In particular, we incorporate Bayesian Neural Network (BNN) into the VAIM architecture (BNN-VAIM) for uncertainty quantification. By sampling the weights and biases distributions of the BNN in the backward mapper of the VAIM, BNN-VAIM is able to estimate prediction uncertainty associated with each individual solution obtained for an ill-posed inverse problem. We first demonstrate the uncertainty quantification capability of BNN-VAIM in a toy inverse problem. Then, we apply BNN-VAIM to the inverse problem of extracting 8 CFFs from the unpolarized DVCS cross section.