Origin of the machine learning forces field errors across metal elements

The overall development of the machine learning force field (MLFF) has advanced rapidly, with a wide range of models emerging in recent years. However, some fundamental questions remain underexplored, such as why certain systems are intrinsically more difficult to train than others. Understanding this question can help us to propose different models and prepare appropriate datasets for different situations. We constructed Metal-43, a high-precision dataset comprising elemental structures of 43 metallic elements. Through systematic analysis, we reveal regular trends of fitting accuracies of these elemental metals in the periodic table. Unlike previous approaches that generally attribute fitting challenges to a vague notion of a “complex potential energy surface (PES)”, which is almost a synonym of the fitting difficulty, we provide a physical picture which connects the Fermi surface complexity to this complexity of PES. Furthermore, we demonstrate that current MLFF models still face clear limitations in capturing the complex PES even for elemental materials. These findings can provide a theoretical foundation and directional guidance for the development of more general and accurate MLFF models in the future.