  This work examines challenges associated with the accuracy of machine-learned
force fields (MLFFs) for bulk solid and liquid phases of d-block elements. In
exhaustive detail, we contrast the performance of force, energy, and stress
predictions across the transition metals for two leading MLFF models: a
kernel-based atomic cluster expansion method implemented using sparse Gaussian
processes (FLARE), and an equivariant message-passing neural network (NequIP).
Early transition metals present higher relative errors and are more difficult
to learn relative to late platinum- and coinage-group elements, and this trend
persists across model architectures. Trends in complexity of interatomic
interactions for different metals are revealed via comparison of the
performance of representations with different many-body order and angular
resolution. Using arguments based on perturbation theory on the occupied and
unoccupied d states near the Fermi level, we determine that the large, sharp d
density of states both above and below the Fermi level in early transition
metals leads to a more complex, harder-to-learn potential energy surface for
these metals. Increasing the fictitious electronic temperature (smearing)
modifies the angular sensitivity of forces and makes the early transition metal
forces easier to learn. This work illustrates challenges in capturing intricate
properties of metallic bonding with current leading MLFFs and provides a
reference data set for transition metals, aimed at benchmarking the accuracy
and improving the development of emerging machine-learned approximations.
