DGLAP evolution of parton distributions at approximate N${}^3$LO

We present recent progress towards a global determination of parton distribution functions (PDFs) at approximate N${}^3$LO (aN${}^3$LO) accuracy within the NNPDF framework. We construct a parametrisation of the $\mathcal{O}({\alpha }_s^4)$ QCD splitting functions and anomalous dimensions reproducing all known exact results, estimate the associated missing and incomplete higher order uncertainties (MHOU and IHOU, respectively), and implement it in the open-source DGLAP code EKO enabling PDFs to be evolved at aN${}^3$LO accuracy in the NNPDF fitting framework. We compare aN${}^3$LO calculation of splitting functions with the results of lower perturbative orders and quantify the impact of the various sources of theoretical uncertainties.