Supervised machine learning for analysing spectra of exoplanetary atmospheres

The use of machine learning is becoming ubiquitous in astronomy(1-3), but remains rare in the study of the atmospheres of exoplanets. Given the spectrum of an exoplanetary atmosphere, a multi-parameter space is swept through in real time to find the best-fit model(4-6). Known as atmospheric retrieval, this technique originates in the Earth and planetary sciences(7). Such methods are very time-consuming, and by necessity there is a compromise between physical and chemical realism and computational feasibility. Machine learning has previously been used to determine which molecules to include in the model, but the retrieval itself was still performed using standard methods(8). Here, we report an adaptation of the random forest method of supervised machine learning(9,10), trained on a precomputed grid of atmospheric models, which retrieves full posterior distributions of the abundances of molecules and the cloud opacity. The use of a precomputed grid allows a large part of the computational burden to be shifted offline. We demonstrate our technique on a transmission spectrum of the hot gas-giant exoplanet WASP-12b using a five-parameter model (temperature, a constant cloud opacity and the volume mixing ratios or relative abundances of molecules of water, ammonia and hydrogen cyanide)(11). We obtain results consistent with the standard nested-sampling retrieval method. We also estimate the sensitivity of the measured spectrum to the model parameters, and we are able to quantify the information content of the spectrum. Our method can be straightforwardly applied using more sophisticated atmospheric models to interpret an ensemble of spectra without having to retrain the random forest.