Accurate molecular simulation requires computationally expensive quantum chemistry models that makes simulating complex material phenomena or large molecules intractable. The past decade has seen a revival of interatomic potentials (IPs), which are computationally cheap but traditionally inaccurate surrogate models, re-casting their construction as a “machine learning” problem.

In the first part of the talk I will explain how this problem can be formalised as an unusual infinite-dimensional approximation problem, with many structures that can be exploited to make it tractable. In particular, our initial results indicate that the curse of dimensionality can be almost completely overcome.

In the second part of the talk I will introduce a practical regression scheme which (1) realises such an approximation and (2) at the same time aims to resolves a long-standing challenge to construct high-dimensional approximations for IPs that “extrapolate well” outside of a limited training set.