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.

这项工作研究了与d块元素的散装固相和液相的机器学习力场 (MLFF) 准确性相关的挑战。我们详细地比较了两种领先的 MLFF 模型的过渡金属的力、能量和应力预测的性能：使用稀疏高斯过程 (FLARE) 实现的基于内核的原子簇扩展方法，以及等变消息传递神经网络网络（NequIP）。与晚期铂族和铸币族元素相比，早期过渡金属呈现出更高的相对误差，并且更难学习，并且这种趋势在模型架构中持续存在。通过比较具有不同多体阶数和角分辨率的表示的性能，揭示了不同金属原子间相互作用的复杂性趋势。使用基于费米能级附近占据和未占据d态的微扰理论的论据，我们确定早期过渡金属中费米能级上方和下方的大而尖锐的d态密度会导致更复杂、更难-了解这些金属的势能表面。增加虚拟电子温度（涂抹）会改变力的角度敏感性，并使早期过渡金属力更容易学习。这项工作说明了使用当前领先的 MLFF 捕获金属键合的复杂特性所面临的挑战，并提供了过渡金属的参考数据集，旨在对准确性进行基准测试并改进新兴机器学习近似值的开发。