Development of a machine-learning-based ionic-force correction model for quantum molecular dynamic simulations of warm dense matter

In this paper Delta learning is used to map orbital-free density functional theory (DFT) ionic forces to the corresponding Kohn-Sham (KS) DFT ionic forces. The development of the approximate force difference in terms of the ion positions is constructed and serves as a stand-in for the ground truth force difference. Descriptor vectors for ion configurations are constructed using all distances between ions in conjunction with an indexing based on a nearest neighbor ranking. It is demonstrated that such a scheme of descriptors can uniquely describe an ionic configuration up to a rotation and reflection when no ambiguity in the nearest neighbor ranking exists. How to handle the case when an ambiguity exists in the nearest neighbor ranking is discussed. As a proof of principle, the model is trained and tested on warm dense hydrogen at temperatures between 1 and 15 eV. Once tested, the model was used to perform molecular dynamic simulations of warm dense hydrogen. The resulting energies and pressures are within 1 and 2% of their respective target KS values.

Automated summary

In this paper, Delta learning is used to map orbital-free density functional theory (DFT) ionic forces to the corresponding Kohn-Sham (KS) DFT ionic forces. The approximate force difference in terms of the ion positions is developed and acts as a substitute for the ground truth force difference. Descriptor vectors are constructed for ion configurations using all distances between ions and an indexing based on nearest neighbor ranking. It is demonstrated that this descriptor scheme can uniquely describe an ionic configuration up to rotation and reflection when there is no ambiguity in the nearest neighbor ranking. The handling of ambiguous nearest neighbor ranking is also discussed. As a proof of principle, the model is trained and tested on warm dense hydrogen at temperatures ranging from 1 to 15 eV. After testing, the model is used to perform molecular dynamic simulations of warm dense hydrogen, with resulting energies and pressures within 1-2% of their respective target KS values.