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Register a new userAn Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval
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Machine learning is now used in many areas of astrophysics, from detecting exoplanets in Kepler transit signals to removing telescope systematics. Recent work demonstrated the potential of using machine learning algorithms for atmospheric retrieval by implementing a random forest to perform retrievals in seconds that are consistent with the traditional, computationally-expensive nested-sampling retrieval method. We expand upon their approach by presenting a new machine learning model, texttt{plan-net}, based on an ensemble of Bayesian neural networks that yields more accurate inferences than the random forest for the same data set of synthetic transmission spectra. We demonstrate that an ensemble provides greater accuracy and more robust uncertainties than a single model. In addition to being the first to use Bayesian neural networks for atmospheric retrieval, we also introduce a new loss function for Bayesian neural networks that learns correlations between the model outputs. Importantly, we show that designing machine learning models to explicitly incorporate domain-specific knowledge both improves performance and provides additional insight by inferring the covariance of the retrieved atmospheric parameters. We apply texttt{plan-net} to the Hubble Space Telescope Wide Field Camera 3 transmission spectrum for WASP-12b and retrieve an isothermal temperature and water abundance consistent with the literature. We highlight that our method is flexible and can be expanded to higher-resolution spectra and a larger number of atmospheric parameters.
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Over the past decade, the study of extrasolar planets has evolved rapidly from plain detection and identification to comprehensive categorization and characterization of exoplanet systems and their atmospheres. Atmospheric retrieval, the inverse modeling technique used to determine an exoplanetary atmospheres temperature structure and composition from an observed spectrum, is both time-consuming and compute-intensive, requiring complex algorithms that compare thousands to millions of atmospheric models to the observational data to find the most probable values and associated uncertainties for each model parameter. For rocky, terrestrial planets, the retrieved atmospheric composition can give insight into the surface fluxes of gaseous species necessary to maintain the stability of that atmosphere, which may in turn provide insight into the geological and/or biological processes active on the planet. These atmospheres contain many molecules, some of them biosignatures, spectral fingerprints indicative of biological activity, which will become observable with the next generation of telescopes. Runtimes of traditional retrieval models scale with the number of model parameters, so as more molecular species are considered, runtimes can become prohibitively long. Recent advances in machine learning (ML) and computer vision offer new ways to reduce the time to perform a retrieval by orders of magnitude, given a sufficient data set to train with. Here we present an ML-based retrieval framework called Intelligent exoplaNet Atmospheric RetrievAl (INARA) that consists of a Bayesian deep learning model for retrieval and a data set of 3,000,000 synthetic rocky exoplanetary spectra generated using the NASA Planetary Spectrum Generator. Our work represents the first ML retrieval model for rocky, terrestrial exoplanets and the first synthetic data set of terrestrial spectra generated at this scale.
The high-contrast imaging technique is meant to provide insight into those planets orbiting several astronomical units from their host star. Space missions such as WFIRST, HabEx, and LUVOIR will measure reflected light spectra of cold gaseous and rocky planets. To interpret these observations we introduce ExoReL$^Re$ (Exoplanetary Reflected Light Retrieval), a novel Bayesian retrieval framework to retrieve cloud properties and atmospheric structures from exoplanetary reflected light spectra. As a unique feature, it assumes a vertically non-uniform volume mixing ratio profile of water and ammonia, and use it to construct cloud densities. In this way, clouds and molecular mixture ratios are consistent. We apply ExoReL$^Re$ on three test cases: two exoplanets ($upsilon$ And e and 47 Uma b) and Jupiter. We show that we are able to retrieve the concentration of methane in the atmosphere, and estimate the position of clouds when the S/N of the spectrum is higher than 15, in line with previous works. Moreover, we described the ability of our model of giving a chemical identity to clouds, and we discussed whether or not we can observe this difference in the planetary reflection spectrum. Finally, we demonstrate how it could be possible to retrieve molecular concentrations (water and ammonia in this work) below the clouds by linking the non-uniform volume mixing ratio profile to the cloud presence. This will help to constrain the concentration of water and ammonia unseen in direct measurements.
Atmospheric retrievals of exoplanetary transmission spectra provide important constraints on various properties such as chemical abundances, cloud/haze properties, and characteristic temperatures, at the day-night atmospheric terminator. To date, most spectra have been observed for giant exoplanets due to which retrievals typically assume H-rich atmospheres. However, recent observations of mini-Neptunes/super-Earths, and the promise of upcoming facilities including JWST, call for a new generation of retrievals that can address a wide range of atmospheric compositions and related complexities. Here we report Aurora, a next-generation atmospheric retrieval framework that builds upon state-of-the-art architectures and incorporates the following key advancements: a) a generalised compositional retrieval allowing for H-rich and H-poor atmospheres, b) a generalised prescription for inhomogeneous clouds/hazes, c) multiple Bayesian inference algorithms for high-dimensional retrievals, d) modular considerations for refraction, forward scattering, and Mie-scattering, and e) noise modeling functionalities. We demonstrate Aurora on current and/or synthetic observations of hot Jupiter HD209458b, mini-Neptune K218b, and rocky exoplanet TRAPPIST1d. Using current HD209458b spectra, we demonstrate the robustness of our framework and cloud/haze prescription against assumptions of H-rich/H-poor atmospheres, improving on previous treatments. Using real and synthetic spectra of K218b, we demonstrate the agnostic approach to confidently constrain its bulk atmospheric composition and obtain precise abundance estimates. For TRAPPIST1d, 10 JWST NIRSpec transits can enable identification of the main atmospheric component for cloud-free CO$_2$-rich and N$_2$-rich atmospheres, and abundance constraints on trace gases including initial indications of O$_3$ if present at enhanced levels ($sim$10-100x Earth levels).
This brief review focuses on methods and applications of modeling exoplanetary atmospheres. We discuss various kinds of state of the art self-consistent and retrieval models in 1D and multi-D with a focus on open questions and short- and long-term goals in the field. Expertise previously developed in modeling cool stellar atmospheres and in modeling solar system planetary atmospheres has proven valuable to the field, and will continue to do so. We described upcoming opportunities for making progress in our understanding of atmospheres, and close with what we see as the fields challenges.
We develop variational Laplace for Bayesian neural networks (BNNs) which exploits a local approximation of the curvature of the likelihood to estimate the ELBO without the need for stochastic sampling of the neural-network weights. The Variational Laplace objective is simple to evaluate, as it is (in essence) the log-likelihood, plus weight-decay, plus a squared-gradient regularizer. Variational Laplace gave better test performance and expected calibration errors than maximum a-posteriori inference and standard sampling-based variational inference, despite using the same variational approximate posterior. Finally, we emphasise care needed in benchmarking standard VI as there is a risk of stopping before the variance parameters have converged. We show that early-stopping can be avoided by increasing the learning rate for the variance parameters.
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