Energy and force estimates are frequently used to relax the atomic positions on the potential energy surface in order to locate structural minima 1, 2. Elemental information and 3D coordinates of all atoms define a system’s electronic Hamiltonian, and thereby all related observables which can be estimated as expectation values of approximate solutions to the electronic Schrödinger equation. The prediction of three-dimensional (3D) structures from a molecular graph is a universal challenge relevant to many branches of the natural sciences. Applicability tests of G2S include successful predictions for systems which typically require manual intervention, improved initial guesses for subsequent conventional ab initio based relaxation, and input generation for subsequent use of structure based quantum machine learning models. G2S improves systematically with training set size, reaching mean absolute interatomic distance prediction errors of less than 0.2 Å for less than eight thousand training structures - on par or better than conventional structure generators. The numerical evidence collected includes 3D coordinate predictions for organic molecules, transition states, and crystalline solids. Exploiting implicit correlations among relaxed structures in training data sets, our machine learning model Graph-To-Structure (G2S) generalizes across compound space in order to infer interatomic distances for out-of-sample compounds, effectively enabling the direct reconstruction of coordinates, and thereby bypassing the conventional energy optimization task. This accuracy/cost trade-off prohibits the generation of synthetic big data sets accounting for chemical space with atomistic detail. Conventionally, force-fields or ab initio methods determine structure through energy minimization, which is either approximate or computationally demanding. The computational prediction of atomistic structure is a long-standing problem in physics, chemistry, materials, and biology.
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