Bob, together with Stefanie Kampa an undergraduate student, Dr. Florian Sammueller and Professor Matthias Schmidt (a former academic colleague in Bristol) at the University of Bayreuth, published a paper in Physical Review Letters - https://link.aps.org/doi/10.1103/PhysRevLett.134.107301 - that merited an Editor’s Suggestion.

A long-standing problem in classical statistical mechanics is how to determine the underlying (effective) interactions between atoms, molecules, ions or, at a longer length scale, between colloidal particles, from structural measurements. The liquid state is well-suited to such investigations and John Enderby, recall the Lecture Theatre named after him, pioneered some of these in the early 1970’s. Measurement of the pair-correlation function g (r) can, in principle, yield the pair-potential φ (r) between constituent particles.

The current paper takes a very different approach from earlier attempts at ‘inverting’ structural data that implemented approximate analytical theories or brute force computer simulation methods. By combining rigorous classical density functional theory (DFT) with powerful machine learning, recently introduced and tested in a recent PRX - https://journals.aps.org/prx/abstract/10.1103/PhysRevX.15.011013 -, the authors demonstrate that a neural functional provides a highly efficient means of inverting g (r) to obtain φ (r). Surprisingly, using the neural functional also implies that one-body information, namely density profiles ρ(x), appears sufficient to infer the pair potential.

Although focusing on simple model systems, the results point to potential applications in soft matter design: given certain structural information can one infer the (effective) interactions that gave rise to this input and hence predict other properties of a material?