Generalized Parton Distributions from Symbolic Regression

Abstract

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 $H_{u-d}(x,t,\xi)$ at $\xi=0$. These PySR models were trained on GPD results provided by both Lattice QCD and phenomenological sources GGL, GK, and VGG. We demonstrate, for the first time, the consistency and systematic convergence of Symbolic Regression by quantifying the disparate models through their Taylor expansion coefficients. In addition to PySR penalizing models with higher complexity and mean-squared error, we implement schemes that test specific physics hypotheses, including force-factorized $x$ and $t$ dependence and Regge behavior in PySR GPDs. We show that PySR can identify factorizing GPD sources based on their response to the Force-Factorized model. Knowing the precise behavior of the GPDs, and their uncertainties in a wide range in $x$ and $t$, crucially impacts our ability to concretely and quantitatively predict hadronic spatial distributions and their derived quantities.