Title: Machine Learning Force Fields with Data Cost Aware Training. Abstract: Machine learning force fields (MLFF) have been proposed to accelerate molecular dynamics (MD) simulation, which finds widespread applications in chemistry and biomedical research. Even for the most data-efficient MLFF models, reaching chemical accuracy can require hundreds of frames of force and energy labels generated by expensive quantum mechanical algorithms, which may scale as $O(n^3)$ to $O(n^7)$, with $n$ being the number of basis functions used and typically proportional to the number of atoms.
To address this issue, we propose a multi-stage computational framework -- ASTEROID, which enjoys low training data generation cost without significantly sacrificing MLFFs' accuracy. Specifically, ASTEROID leverages a combination of both large cheap inaccurate data and small expensive accurate data. The motivation behind ASTEROID is that inaccurate data, though incurring large bias, can help capture the sophisticated structures of the underlying force field. Therefore, we first train a MLFF model on a large amount of inaccurate training data, employing a bias-aware loss function to prevent the model from overfitting the potential bias of the inaccurate training data. We then fine-tune the obtained model using a small amount of accurate training data, which preserves the knowledge learned from the inaccurate training data while significantly improving the model's accuracy. Moreover, we propose a variant of ASTEROID based on score matching for the setting where the inaccurate training data are unlabelled. Extensive experiments on MD simulation datasets show that ASTEROID can significantly reduce data generation costs while improving the accuracy of MLFFs.