Machine learning based energy-free structure predictions of molecules, transition states, and solids

The computational prediction of atomistic structure is a long-standing problem in physics, chemistry, materials, and biology. Within conventional force-field or {em ab initio} calculations, structure is determined through energy minimization, which is either approximate or computationally demanding. Alas, the accuracy-cost trade-off prohibits the generation of synthetic big data records with meaningful energy based conformational search and structure relaxation output. Exploiting implicit correlations among relaxed structures, our kernel ridge regression model, dubbed Graph-To-Structure (G2S), generalizes across chemical compound space, enabling direct predictions of relaxed structures for out-of-sample compounds, and effectively bypassing the energy optimization task. After training on constitutional and compositional isomers (no conformers) G2S infers atomic coordinates relying solely on stoichiometry and bond-network information as input (Our numerical evidence includes closed and open shell molecules, transition states, and solids). For all data considered, G2S learning curves reach mean absolute interatomic distance prediction errors of less than 0.2 Å for less than eight thousand training structures -- on par or better than popular empirical methods. Applicability test of G2S include meaningful structures of molecules for which standard methods require manual intervention, improved initial guesses for subsequent conventional {em ab initio} based relaxation, and input for structural based representations commonly used in quantum machine learning models, (bridging the gap between graph and structure based models).