Indicator configurations: An information-matching method for efficient data selection in interatomic potential training

Interatomic potentials (IPs) are typically trained using energy and atomic forces data obtained from computationally expensive DFT calculations. The development process often requires a large number of atomic configurations and data to be generated to effectively constrain all IP parameters. A critical problem is identifying when the training data is sufficient to constrain the predictions of the IP for material properties of interest. We present an information-matching method for selecting a minimal set of configurations, i.e. indicator configurations, that effectively constrain the predictions of an IP with respect to specific target material properties. Central to our analysis is the Fisher Information Matrix (FIM), which quantifies the information that data carries about the parameters of an IP. We calculate the FIM for the target quantities of interest (QoI) and for, e.g., the energy and forces of each candidate configuration. Then, we down-select from these candidate configurations such that their combined FIM matches that of the QoI, i.e., the indicator configurations are those whose information content is the same as the target predictions. We demonstrate this method on the Stillinger--Weber potential for several systems and target materials properties. In addition to improving the efficiency of the data-generation process, the indicator configurations reveal the physics and mechanisms relevant to the materials properties of interest.