Understanding multi-fidelity training of machine-learned force-fields

This study systematically investigates two multi-fidelity strategies used to train machine-learned force fields (MLFFs) -- pre-training/fine-tuning and multi-headed training -- and elucidates the mechanisms underpinning their success. For pre-training and fine-tuning, we uncover a log-log linear relationship between pre-trained and fine-tuned accuracies that holds across model architectures, model sizes, and quantum-chemical methods. The success of this approach hinges on the quantity and quality of available pre-training data, and, critically, the inclusion of force labels. We demonstrate that pre-trained representations are inherently method-specific, requiring adaptation of the model backbone during fine-tuning. In contrast, multi-headed models learn method-independent backbone representations, where again the heads'accuracies are log-log linearly related. Relative to pre-training and fine-tuning, these shared representations marginally reduce model performance in most cases. However, this trade-off is offset by practical advantages: multi-headed training extends naturally to multiple labelling methods and enables partial replacement of expensive labels with cheaper alternatives, paving the way towards cost-efficient universal MLFFs.