# Optimal Inflationary Potentials

arXiv: https://arxiv.org/abs/2310.16786 · HTML: https://mlsanity.com/paper/2310.16786/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 40 references that are in the map.
- First posted on arXiv 25 Oct 2023.

## Builds on (most cited first, 5 of 5)

- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Rediscovering orbital mechanics with machine learning](https://mlsanity.com/paper/2202.02306/) (2022)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Deep symbolic regression for physics guided by units constraints: toward the automated discovery of physical laws](https://mlsanity.com/paper/2303.03192/) (2023)
- [Priors for symbolic regression](https://mlsanity.com/paper/2304.06333/) (2023)

## Built on by (most cited first, 6 of 6)

- [Symbolic Regression for Beyond the Standard Model Physics](https://mlsanity.com/paper/2405.18471/) (2024)
- [Statistical Patterns in the Equations of Physics and the Emergence of a Meta-Law of Nature](https://mlsanity.com/paper/2408.11065/) (2024)
- [(Exhaustive) Symbolic Regression and model selection by minimum description length](https://mlsanity.com/paper/2507.13033/) (2025)
- [Symbolic Regression and Differentiable Fits in Beyond the Standard Model Physics](https://mlsanity.com/paper/2510.20453/) (2025)
- [Constraining dark matter halo profiles with symbolic regression](https://mlsanity.com/paper/2511.23073/) (2025)
- [Symbolic Classification-Enabled LHC Limits for BSM Global Fits](https://mlsanity.com/paper/2605.22330/) (2026)

## Abstract (arXiv)

Inflation is a highly favoured theory for the early Universe. It is compatible with current observations of the cosmic microwave background and large scale structure and is a driver in the quest to detect primordial gravitational waves. It is also, given the current quality of the data, highly under-determined with a large number of candidate implementations. We use a new method in symbolic regression to generate all possible simple scalar field potentials for one of two possible basis sets of operators. Treating these as single-field, slow-roll inflationary models we then score them with an information-theoretic metric ("minimum description length") that quantifies their efficiency in compressing the information in current data. We explore two possible priors on the parameter space of potentials, one related to the functions' structural complexity and one that uses a Katz back-off language model to prefer functions that may be theoretically motivated. This enables us to identify the inflaton potentials that optimally balance simplicity with accuracy at explaining current data, which may subsequently find theoretical motivation. Our exploratory study opens the door to extraction of fundamental physics directly from data, and may be augmented with more refined theoretical priors in the quest for a complete understanding of the early Universe.