Navigating energy landscapes for materials discovery: Integrating modeling, simulation, and machine learning

The energy landscape represents a high-dimensional mapping of the configurational states of an atomic system with their respective energies. Under isobaric conditions, enthalpy landscapes can be used to account for volumetric changes of the system. Understanding the energy or enthalpy landscape holds the key for discovering materials with targeted properties, since the landscape encapsulates the complete thermodynamic and kinetic behavior of a system, including relaxation, metastable phases, and reactivity. However, the curse of dimensionality prohibits one from enumerating and visualizing the energy landscape—the energy landscape of an N-atom system has 3N dimensions. Here, we outline the emerging computational techniques that allow the exploration of complex energy landscapes of materials in three distinct categories: the classical, metaheuristic, and machine learning approaches. We discuss the advantages and disadvantages associated with each of these methods, with a focus on the nature of problems where they can provide excellent solutions (and vice versa). Altogether, in addition to giving an overview of existing approaches, we hope the review provides an impetus to develop novel methods to explore the energy landscapes that can, in turn, provide both a fundamental understanding of the physics of materials and accelerate the discovery of novel materials.