Interpreting epistemic uncertainties in PDF analyses via symbolic regression

Inverse problems are ubiquitous in hadron structure studies: quantum correlation functions such as the parton distribution functions (PDFs) are never directly observed, so their error bands entangle aleatoric, epistemic, and distributional contributions. In this new precision era of QCD, it is vital to create a physics-aware bridge with next-generation AI/ML algorithms. Leveraging evidential deep learning and symbolic regression, we not only isolate and quantify each uncertainty source but also interpret it in analytic form. I will present a new machine learning pipeline that extracts analytic surrogate models for PDF uncertainties with symbolic regression. This algorithm searches the equation space to isolate expressions which capture the epistemic spread of global-fit ensembles. Incorporating added constraints such as lattice QCD calculations refines the fidelity of PDF extractions and deepens our understanding of nonperturbative QCD. Ultimately, this integrated approach pushes the frontier of hadron structure discovery, aligning cutting-edge AI/ML progress with emerging opportunities at existing and future experimental physics facilities such as the EIC.