Predicting Exoplanetary Features with a Residual Model for Uniform and Gaussian Distributions

TL;DR

This work addresses predicting posterior distributions for seven exoplanetary features from simulated spectra and auxiliary data in the Ariel Data Challenge. It introduces a two-model framework—an ensemble combining a Multivariate Gaussian head with a Gaussian posterior, and a Uniform Quantile head—that is trained in two phases with a shared residual CNN backbone and cross-validated ensembles. Results show the Uniform Quantile ensemble achieves strong posterior performance, and when combined with the Gaussian head, attains competitive final rankings, highlighting the value of ensembling diverse posterior representations for exoplanet atmospheric inference. The approach offers a scalable, efficient means to sample and evaluate exoplanet posteriors, with potential extensions in hyperparameter tuning, transfer learning, and mixture-of-experts integration to further improve accuracy and robustness.

Abstract

The advancement of technology has led to rampant growth in data collection across almost every field, including astrophysics, with researchers turning to machine learning to process and analyze this data. One prominent example of this data in astrophysics is the atmospheric retrievals of exoplanets. In order to help bridge the gap between machine learning and astrophysics domain experts, the 2023 Ariel Data Challenge was hosted to predict posterior distributions of 7 exoplanetary features. The procedure outlined in this paper leveraged a combination of two deep learning models to address this challenge: a Multivariate Gaussian model that generates the mean and covariance matrix of a multivariate Gaussian distribution, and a Uniform Quantile model that predicts quantiles for use as the upper and lower bounds of a uniform distribution. Training of the Multivariate Gaussian model was found to be unstable, while training of the Uniform Quantile model was stable. An ensemble of uniform distributions was found to have competitive results during testing (posterior score of 696.43), and when combined with a multivariate Gaussian distribution achieved a final rank of third in the 2023 Ariel Data Challenge (final score of 681.57).

Figures (7)

• Figure 1: Weighted histograms of the trace data for one planet. The dashed cyan lines represent the 16th, 50th and 84th percentiles, and the dashed-dotted deep pink lines represent the forward model parameters. This illustrates the varied distribution shapes of the target values, and the forward model parameters not necessarily lining up with the 50th percentile.
• Figure 2: Resnet block with a skip connection shown in orange. The output of the two blue nodes is added in the final node, resulting in the residual skip connection.
• Figure 3: Training loss. The solid lines represent the validation loss, which controlled the early stopping during training. The lighter dashed line represent the loss on the training set.
• Figure 4: Pretraining model.
• Figure 5: Multivariate Gaussian model. Note that the final two dense layers were concatenated for convenience when calculating the loss.