  The radiation pattern within high energy quark- and gluon-initiated jets (jet
substructure) is used extensively as a precision probe of the strong force as
well as an environment for optimizing event generators with numerous
applications in high energy particle and nuclear physics. Looking at
electron-proton collisions is of particular interest as many of the
complications present at hadron colliders are absent. A detailed study of
modern jet substructure observables, jet angularities, in electron-proton
collisions is presented using data recorded using the H1 detector at HERA. The
measurement is unbinned and multi-dimensional, using machine learning to
correct for detector effects. All of the available reconstructed object
information of the respective jets is interpreted by a graph neural network,
achieving superior precision on a selected set of jet angularities. Training
these networks was enabled by the use of a large number of GPUs in the
Perlmutter supercomputer at Berkeley Lab. The particle jets are reconstructed
in the laboratory frame, using the $k_{\mathrm{T}}$ jet clustering algorithm.
Results are reported at high transverse momentum transfer $Q^2>150$ GeV${}^2$,
and inelasticity $0.2 < y < 0.7$. The analysis is also performed in sub-regions
of $Q^2$, thus probing scale dependencies of the substructure variables. The
data are compared with a variety of predictions and point towards possible
improvements of such models.
