Symbolic Regression of Generalized Parton Distributions using PySR*

AI/ML informed Symbolic Regression is the next stage of scientific modeling. We utilize a highly customizable symbolic regression package "PySR" to model the x and t dependence of the flavor isovector combination H^{u-d}(x,t,ζ,Q^2) at ζ=0 and Q^2= 4 GeV^2. These PySR models were trained on various ranges of GPD pseudodata provided by both Lattice QCD and contemporary models such as GGL and VGG. In addition to PySR penalizing more complex models, PySR GPDs were also selected based on a custom loss function that both encouraged low mean-squared error and penalized expressions that failed to satisfy various physical constraints for GPDs. Mean-Squared error of PySR GPDs were compared with fits to common GPD parameterizations. Some PySR derived GPDs factorize in x and t. We also explore their consistency in the forward limit with current LHAPDF extractions.