4th Place Solution: Explicit Simulation of Limb Darkening

We present the 4th place solution of the NeurIPS - Ariel Data Challenge 2025. At its core the solution is based on explicitly modeling a planet passing in front of a star, where the light intensity decreases toward the rim of the star (limb darkening). The simulation is used to generate high quality features as inputs for linear regression models for estimating the squared radius of the planet relative to the star, and neural networks for estimating the uncertainty of the outputs from linear regression. The main challenges of the solution were optimizing the bespoke limb darkening model without ending up in an undesirable local optimum, and training the neural networks with very little data without overfitting. A Kalman smoother was used to generate the starting point for training the limb darkening model, and principal component analysis was used to further improve the final features.