A proof-of-concept framework for identifying molecules of unknown elemental composition and structure using experimental rotational data and probabilistic deep learning is presented. Using a minimal set of input data determined experimentally, we describe four neural network architectures that yield information to assist in the identification of an unknown molecule. The first architecture translates spectroscopic parameters into Coulomb matrix eigenspectra, as a method of recovering chemical and structural information encoded in the rotational spectrum. The eigenspectrum is subsequently used by three deep learning networks to constrain the range of stoichiometries, generate SMILES strings, and predict the most likely functional groups present in the molecule. In each model, we utilize dropout layers as an approximation to Bayesian sampling, which subsequently generates probabilistic predictions from otherwise deterministic models. These models are trained on a modestly sized theoretical dataset comprising ${sim}$83,000 unique organic molecules (between 18 and 180 amu) optimized at the $omega$B97X-D/6-31+G(d) level of theory where the theoretical uncertainty of the spectroscopic constants are well understood and used to further augment training. Since chemical and structural properties depend highly on molecular composition, we divided the dataset into four groups corresponding to pure hydrocarbons, oxygen-bearing, nitrogen-bearing, and both oxygen- and nitrogen-bearing species, training each type of network with one of these categories thus creating experts within each domain of molecules. We demonstrate how these models can then be used for practical inference on four molecules, and discuss both the strengths and shortcomings of our approach, and the future directions these architectures can take.
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