  Machine learning potentials (MLPs) are becoming powerful tools for performing
accurate atomistic simulations and crystal structure optimizations. An approach
to developing MLPs employs a systematic set of polynomial invariants including
high-order ones to represent the neighboring atomic density. In this study, a
formulation of the polynomial invariants is extended to the case of
multicomponent systems. The extended formulation is more complex than the
formulation for elemental systems. This study also shows its application to
Ti-Al binary system. As a result, an MLP with the lowest error and MLPs with
high computational cost performance are selected from the many MLPs developed
systematically. The predictive powers of the developed MLPs for many
properties, such as the formation energy, elastic constants, thermodynamic
properties, and mechanical properties, are examined. The MLPs exhibit high
predictive power for the properties in a wide variety of ordered structures.
The present scheme should be systematically applicable to other multicomponent
systems.
