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), fast but traditionally inaccurate surrogate models, re-casting their construction as an approximation and data-fitting problem.
I will give a short introduction to this problem, and in particular show how it can be formalised as an unusual approximation problem, but with many structures that can be exploited to make it tractable. I will then introduce two approximation schemes, both using different symmetric polynomials, targeting in particular efficiency and transferability, some preliminary simulation results, and the beginnings of a rigorous numerical analysis.
Joint work with Genevieve Dusson (Warwick), Gabor Csanyi and Cas van den Oort (Cambridge) and Markus Bachmayr (Mainz).