The use of machine learning is becoming ubiquitous in astronomy1,2,3, 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 model4,5,6. Known as atmospheric retrieval, this technique originates in the Earth and planetary sciences7. 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 methods8. Here, we report an adaptation of the ‘random forest’ method of supervised machine learning9,10, 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.
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Banerji, M. et al. Galaxy Zoo: reproducing galaxy morphologies via machine learning. Mon. Not. R. Astron. Soc. 406, 342–353 (2010).
Graff, P., Feroz, F., Hobson, M. P. & Lasenby, A. SKYNET: an efficient and robust neural network training tool for machine learning in astronomy. Mon. Not. R. Astron. Soc. 441, 1741–1759 (2014).
Pearson, K. A., Palafox, L. & Griffith, C. A. Searching for exoplanets using artificial intelligence. Mon. Not. R. Astron. Soc. 474, 478–491 (2018).
Madhusudhan, N. & Seager, S. A temperature and abundance retrieval method for exoplanet atmospheres. Astrophys. J. 707, 24–39 (2009).
Benneke, B. & Seager, S. Atmospheric retrieval for super-Earths: uniquely constraining the atmospheric composition with transmission spectroscopy. Astrophys. J. 753, 100 (2012).
Line, M. R. et al. Information content of exoplanetary transit spectra: an initial look. Astrophys. J. 749, 93 (2012).
Rodgers, C. D. Inverse Methods for Atmospheric Sounding: Theory and Practice (World Scientific, Singapore, 2000).
Waldmann, I. P. Dreaming of atmospheres. Astrophys. J. 820, 107 (2016).
Ho, T. K. The random subspace method for constructing decision forests. IEEE Trans. Pattern Anal. Mach. Intell. 20, 832–844 (1998).
Breiman, L. Random forests. Mach. Learn. 45, 5–32 (2001).
Heng, K. & Kitzmann, D. The theory of transmission spectra revisited: a semi-analytical method for interpreting WFC3 data and an unresolved challenge. Mon. Not. R. Astron. Soc. 470, 2972–2981 (2017).
Kreidberg, L. et al. A detection of water in the transmission spectrum of the hot Jupiter WASP-12b and implications for its atmospheric composition. Astrophys. J. 814, 66 (2015).
Breiman, L., Friedman, J., Stone, C. J. & Olshen, R. A. Classification and Regression Trees (Chapman & Hall/CRC, Boca Raton, 1984).
Kelleher, J. D., Mac Namee, B. & D’Arcy, A. Fundamentals of Machine Learning for Predictive Data Analytics (MIT Press, Cambridge, MA, 2015).
Criminisi, A., Shotton, J. & Konukoglu, E. Decision Forests for Classification, Regression, Density Estimation, Manifold Learning and Semi-Supervised Learning Technical Report TR-2011-114 (Microsoft Research, 2011).
Trotta, R. Bayes in the sky: Bayesian inference and model selection in cosmology. Contemp. Phys. 49, 71–104 (2008).
Skilling, J. et al. Nested sampling for general Bayesian computation. Bayesian Anal. 1, 833–859 (2006).
Feroz, F. & Hobson, M. P. Multimodal nested sampling: an efficient and robust alternative to Markov Chain Monte Carlo methods for astronomical data analyses. Mon. Not. R. Astron. Soc. 384, 449–463 (2008).
Batalha, N. E. & Line, M. R. Information content analysis for selection of optimal JWST observing modes for transiting exoplanet atmospheres. Astron. J. 153, 151 (2017).
Howe, A. R., Burrows, A. & Deming, D. An information-theoretic approach to optimize JWST observations and retrievals of transiting exoplanet atmospheres. Astrophys. J. 835, 96 (2017).
Hastie, T., Tibshirani, R. & Friedman, J. The Elements of Statistical Learning (Springer, New York, 2001).
Sznitman, R., Becker, C., Fleuret, F. & Fua, P. Fast object detection with entropy-driven evaluation. In Proc. 2013 IEEE Conference on Computer Vision and Pattern Recognition 3270–3277 (IEEE, 2013).
Zikic, D., Glocker, B. & Criminisi, A. Encoding atlases by randomized classification forests for efficient multi-atlas label propagation. Med. Image Anal. 18, 1262–1273 (2014).
Rieke, N. et al. Surgical tool tracking and pose estimation in retinal microsurgery. In Proc. 18th International Conference on Medical Image Computing and Computer-Assisted Intervention (eds Navab, N. et al.) 266–273 (Lecture Notes in Computer Science 9349, Springer, 2015).
Zhang, L., Varadarajan, J., Suganthan, P. N., Ahuja, N. & Moulin, P. Robust visual tracking using oblique random forests. Proc. 2017 IEEE Conference on Computer Vision and Pattern Recognition, 5825–5834 (IEEE, 2017).
Greene, T. P. et al. Characterizing transiting exoplanet atmospheres with JWST. Astrophys. J. 817, 17 (2016).
Marley, M. S. et al. Atmospheric, evolutionary, and spectral models of the brown dwarf Gliese 229 B. Science 272, 1919–1921 (1996).
Burrows, A. et al. A non-gray theory of extrasolar giant planets and brown dwarfs. Astrophys. J. 491, 856–875 (1997).
Baraffe, I., Chabrier, G., Allard, F. & Hauschildt, P. H. Evolutionary models for low-mass stars and brown dwarfs: uncertainties and limits at very young ages. Astron. Astrophys. 382, 563–572 (2002).
Kitzmann, D. & Heng, K. Optical properties of potential condensates in exoplanetary atmospheres. Mon. Not. R. Astron. Soc. 475, 94–107 (2018).
Feroz, F., Hobson, M. P. & Bridges, M. MultiNest: an efficient and robust Bayesian inference tool for cosmology and particle physics. Mon. Not. R. Astron. Soc. 398, 1601–1614 (2009).
Buchner, J. et al. X-ray spectral modelling of the AGN obscuring region in the CDFS: Bayesian model selection and catalogue. Astron. Astrophys. 564, A125 (2014).
Barber, R. J., Tennyson, J., Harris, G. J. & Tolchenov, R. N. A high-accuracy computed water line list. Mon. Not. R. Astron. Soc. 368, 1087–1094 (2006).
Barber, R. J. et al. ExoMol line lists—III. An improved hot rotation-vibration line list for HCN and HNC. Mon. Not. R. Astron. Soc. 437, 1828–1835 (2014).
Yurchenko, S. N., Barber, R. J. & Tennyson, J. A variationally computed line list for hot NH3. Mon. Not. R. Astron. Soc. 413, 1828–1834 (2011).
Yurchenko, S. N., Tennyson, J., Barber, R. J. & Thiel, W. Vibrational transition moments of CH4 from first principles. J. Mol. Spectrosc. 291, 69–76 (2013).
Yurchenko, S. N. & Tennyson, J. ExoMol line lists—IV. The rotation-vibration spectrum of methane up to 1500 K. Mon. Not. R. Astron. Soc. 440, 1649–1661 (2014).
Rothman, L. S. et al. The HITRAN molecular spectroscopic database and HAWKS (HITRAN atmospheric workstation): 1996 edition. J. Quant. Spectrosc. Radiat. Transf. 60, 665–710 (1998).
Grimm, S. L. & Heng, K. HELIOS-K: an ultrafast, open-source opacity calculator for radiative transfer. Astrophys. J. 808, 182 (2015).
Hebb, L. et al. WASP-12b: the hottest transiting extrasolar planet yet discovered. Astrophys. J. 693, 1920–1928 (2009).
Burrows, A. & Sharp, C. M. Chemical equilibrium abundances in brown dwarf and extrasolar giant planet atmospheres. Astrophys. J. 512, 843–863 (1999).
Heng, K. & Tsai, S.-M. Analytical models of exoplanetary atmospheres. III. Gaseous C-H-O-N chemistry with nine molecules. Astrophys. J. 829, 104 (2016).
Line, M. R. et al. A systematic retrieval analysis of secondary eclipse spectra. I. A comparison of atmospheric retrieval techniques. Astrophys. J. 775, 137 (2013).
Waldmann, I. P. et al. Tau-REx I: a next generation retrieval code for exoplanetary atmospheres. Astrophys. J. 802, 107 (2015).
Lavie, B. et al. HELIOS–RETRIEVAL: an open-source, nested sampling atmospheric retrieval code; application to the HR 8799 exoplanets and inferred constraints for planet formation. Astron. J. 154, 91 (2017).
Sharp, C. M. & Burrows, A. Atomic and molecular opacities for brown dwarf and giant planet atmospheres. Astrophys. J. 168, 140–166 (2007).
We acknowledge partial financial support from the Center for Space and Habitability (P.M.-N. and K.H.), the University of Bern International 2021 PhD Fellowship (C.F.), the PlanetS National Center of Competence in Research (K.H.), the Swiss National Science Foundation (R.S., C.F. and K.H.), the European Research Council via a Consolidator Grant (K.H.) and the Swiss-based MERAC Foundation (K.H.).
P.M.-N. led the development of computer codes used for this study, performed the machine-learning-related calculations, participated in the experimental design and made the majority of the figures. C.F. computed the grid of atmospheric models used as the training set, participated in the experimental design and performed the nested-sampling retrievals. R.S. co-led the scientific vision and experimental design and co-wrote the manuscript. K.H. co-led the scientific vision and experimental design and led the writing and typesetting of the manuscript.
Supplementary Table 1, Supplementary Figures 1–3