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This work examines challenges associated with the accuracy of machine-learnedforce fields (MLFFs) for bulk solid and liquid phases of d-block elements. Inexhaustive detail, we contrast the performance of force, energy, and stresspredictions across the transition metals for two leading MLFF models: akernel-based atomic cluster expansion method implemented using sparse Gaussianprocesses (FLARE), and an equivariant message-passing neural network (NequIP).Early transition metals present higher relative errors and are more difficultto learn relative to late platinum- and coinage-group elements, and this trendpersists across model architectures. Trends in complexity of interatomicinteractions for different metals are revealed via comparison of theperformance of representations with different many-body order and angularresolution. Using arguments based on perturbation theory on the occupied andunoccupied d states near the Fermi level, we determine that the large, sharp ddensity of states both above and below the Fermi level in early transitionmetals leads to a more complex, harder-to-learn potential energy surface forthese metals. Increasing the fictitious electronic temperature (smearing)modifies the angular sensitivity of forces and makes the early transition metalforces easier to learn. This work illustrates challenges in capturing intricateproperties of metallic bonding with current leading MLFFs and provides areference data set for transition metals, aimed at benchmarking the accuracyand improving the development of emerging machine-learned approximations.

Complexity of Many-Body Interactions in Transition Metals via Machine-Learned Force Fields from the TM23 Data Set