Using Machine-Learning Models to Accelerate Interatomic-Force-Constant Calculations

In the last two decades, solutions of the Boltzmann transport equation for phonons based on first principles have become a mainstream tool to obtain parameter-free estimates of the thermal conductivity of crystalline solids. More recently, such approaches have been successfully extended to systems with a lower degree of translation symmetry, including crystals with defects, interfaces between bulk crystals, and heterogeneous nanostructures. The key ingredients in the basic formulation of those methods are second- and third-order interatomic force constants (IFCs), i.e., second- and third-order derivatives of the potential energy with respect to atomic displacements around the equilibrium position. Even for a single crystal and taking full advantage of symmetry, a direct calculation of all the required IFCs typically requires three orders of magnitude more computational effort than the local minimization used to find that equilibrium. IFC calculations are therefore a major limiting factor to even more widespread use of these methods. Problems can quickly become intractable when large localized defects, complex unit cells, multiple phases, collections of several materials, explicit temperature dependences or higher-order IFCs come into play, all of which are common requirements in realistic materials for technological applications.<br/><br/>In this talk, I will discuss several possible strategies to accelerate IFC calculations in realistic situations, with an analysis of their advantages and drawbacks based on experience with practical applications. Machine-learning models constitute the foundation of all of these approaches, but several clearly distinct families can be identified. A first possibility is to use first-principles data for the material under study only, trying to make more efficient use of the information than in a direct IFC calculation. Techniques in this category include high-dimensional neural-network interatomic potentials, high-order Taylor expansions, differentiable code, and regression models for the IFCs themselves. The critical issue of local vs. global approximations of the potential energy surface will be addressed in detail in connection with this family. An alternative is to exploit regularities in the IFC tensors of a family of compounds in the context of a high-throughput calculation. To conclude, I will discuss the possibility of avoiding IFC calculations altogether by switching to other families of methods, and how machine learning models shift the traditional value propositions of those.