  The development of interatomic potentials that can accurately capture a wide
range of physical phenomena and diverse environments is of significant
interest, but it presents a formidable challenge. This challenge arises from
the numerous structural forms, multiple phases, complex intramolecular and
intermolecular interactions, and varying external conditions. In this paper, we
present a method to construct environment-adaptive interatomic potentials by
adapting to the local atomic environment of each atom within a system. The
collection of atomic environments of interest is partitioned into several
clusters of atomic environments. Each cluster represents a distinctive local
environment and is used to define a corresponding local potential. We introduce
a many-body many-potential expansion to smoothly blend these local potentials
to ensure global continuity of the potential energy surface. This is achieved
by computing the probability functions that determine the likelihood of an atom
belonging to each cluster. We apply the environment-adaptive machine learning
potentials to predict observable properties for Ta element and InP compound,
and compare them with density functional theory calculations.
