# Analytical Modelling of Exoplanet Transit Specroscopy with Dimensional Analysis and Symbolic Regression

arXiv: https://arxiv.org/abs/2112.11600 · HTML: https://mlsanity.com/paper/2112.11600/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 47 references that are in the map.
- First posted on arXiv 22 Dec 2021.

## Builds on (most cited first, 4 of 4)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [An Ensemble of Bayesian Neural Networks for Exoplanetary Atmospheric Retrieval](https://mlsanity.com/paper/1905.10659/) (2019)
- [Peeking inside the Black Box: Interpreting Deep Learning Models for Exoplanet Atmospheric Retrievals](https://mlsanity.com/paper/2011.11284/) (2020)
- [Accelerating Understanding of Scientific Experiments with End to End Symbolic Regression](https://mlsanity.com/paper/2112.04023/) (2021)

## Built on by (most cited first, 18 of 18)

- [SymFormer: End-to-end symbolic regression using transformer-based architecture](https://mlsanity.com/paper/2205.15764/) (2022)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [Deep Learning Symmetries and Their Lie Groups, Algebras, and Subalgebras from First Principles](https://mlsanity.com/paper/2301.05638/) (2023)
- [Is the Machine Smarter than the Theorist: Deriving Formulas for Particle Kinematics with Symbolic Regression](https://mlsanity.com/paper/2211.08420/) (2022)
- [Oracle-Preserving Latent Flows](https://mlsanity.com/paper/2302.00806/) (2023)
- [Exploring the Truth and Beauty of Theory Landscapes with Machine Learning](https://mlsanity.com/paper/2401.11513/) (2024)
- [Unsupervised Machine Learning for Exploratory Data Analysis of Exoplanet Transmission Spectra](https://mlsanity.com/paper/2201.02696/) (2022)
- [Searching for Novel Chemistry in Exoplanetary Atmospheres using Machine Learning for Anomaly Detection](https://mlsanity.com/paper/2308.07604/) (2023)
- [Reproducing Bayesian Posterior Distributions for Exoplanet Atmospheric Parameter Retrievals with a Machine Learning Surrogate Model](https://mlsanity.com/paper/2310.10521/) (2023)
- [Intercomparison of Brown Dwarf Model Grids and Atmospheric Retrieval Using Machine Learning](https://mlsanity.com/paper/2305.07719/) (2023)
- [Seeking Truth and Beauty in Flavor Physics with Machine Learning](https://mlsanity.com/paper/2311.00087/) (2023)
- [Physical Symbolic Optimization](https://mlsanity.com/paper/2312.03612/) (2023)
- [Discovering Nuclear Models from Symbolic Machine Learning](https://mlsanity.com/paper/2404.11477/) (2024)
- [Discovery and inversion of the viscoelastic wave equation in inhomogeneous media](https://mlsanity.com/paper/2409.18370/) (2024)
- [Reinforced Symbolic Learning with Logical Constraints for Predicting Turbine Blade Fatigue Life](https://mlsanity.com/paper/2412.03580/) (2024)
- [Hunting for "Oddballs" with Machine Learning: Detecting Anomalous Exoplanets Using a Deep-Learned Low-Dimensional Representation of Transit Spectra with Autoencoders](https://mlsanity.com/paper/2601.02324/) (2026)
- [Symbolic Regression for Shared Expressions: Introducing Partial Parameter Sharing](https://mlsanity.com/paper/2601.04051/) (2026)

## Abstract (arXiv)

The physical characteristics and atmospheric chemical composition of newly discovered exoplanets are often inferred from their transit spectra which are obtained from complex numerical models of radiative transfer. Alternatively, simple analytical expressions provide insightful physical intuition into the relevant atmospheric processes. The deep learning revolution has opened the door for deriving such analytical results directly with a computer algorithm fitting to the data. As a proof of concept, we successfully demonstrate the use of symbolic regression on synthetic data for the transit radii of generic hot Jupiter exoplanets to derive a corresponding analytical formula. As a preprocessing step, we use dimensional analysis to identify the relevant dimensionless combinations of variables and reduce the number of independent inputs, which improves the performance of the symbolic regression. The dimensional analysis also allowed us to mathematically derive and properly parametrize the most general family of degeneracies among the input atmospheric parameters which affect the characterization of an exoplanet atmosphere through transit spectroscopy.