Indicator configuration: An information-matching method of data reduction for training interatomic potential

Interatomic Potentials (IPs) are often trained to by fitting the IP parameters to the energies, atomic forces, or similar quantities for many atomic configurations. Typically, these training quantities are obtained from DFT calculations, and collecting data from enough unique configurations to constrain all of the IP parameters is computationally expensive. 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 constrain the predictions of an IP for target material properties. Central to our analysis is the Fisher Information Matrix (FIM), that quantifies how much information data carries about the parameters of an IP. We calculate the FIM for the target quantities of interest and for, e.g., the energy and forces of each candidate configuration. Then, we down-select from these candidate configurations so that their combined FIM matches that of the quantities of interest, 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.