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Generalized parton distributions from symbolic regression

Andrew Dotson1,*, Zaki Panjsheeri2,†, Anusha Reddy Singireddy3, Douglas Q. Adams2, Marija Čuić2, Emmanuel Ortiz-Pacheco4, Saraswati Pandey2, Marie Boër5, Gia-Wei Chern2 et al. (EXCLAIM Collaboration)

Gia-Wei Chern2, Michael Engelhardt1, Gary R. Goldstein6, Yaohang Li3, Huey-Wen Lin4, Simonetta Liuti2,‡, and Matthew D. Sievert1 (EXCLAIM Collaboration)

  • *Contact author: adots004@nmsu.edu
  • †Contact author: zap2nd@virginia.edu
  • ‡Contact author: sl4y@virginia.edu
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Phys. Rev. D 114, 054054 – Published 29 September, 2026

DOI: https://doi.org/10.1103/ynm6-znr4

Abstract

Artificial intelligence/machine learning–informed symbolic regression is the next stage of scientific modeling. We utilize a highly customizable symbolic regression package “PySR” (python symbolic regression) to model the x and t dependence of the flavor isovector combination Hu−d(x,t,ξ) at ξ=0. These PySR models were trained on generalized parton distribution (GPD) results provided by both lattice QCD and phenomenological sources Goldstein Gonzalez Liuti, Goloskokov Kroll, and Vanderhaeghen Guichon Guidal. 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.

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Phys. Rev. D 114, 054054– Published 29 September, 2026
  • Received 2 July 2025
  • Accepted 26 May 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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