# Symbolic Regression and Differentiable Fits in Beyond the Standard Model Physics

arXiv: https://arxiv.org/abs/2510.20453 · HTML: https://mlsanity.com/paper/2510.20453/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 44 references that are in the map.
- First posted on arXiv 23 Oct 2025.

## Builds on (most cited first, 15 of 15)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Optuna: A Next-generation Hyperparameter Optimization Framework](https://mlsanity.com/paper/1907.10902/) (2019)
- [AI Feynman: a Physics-Inspired Method for Symbolic Regression](https://mlsanity.com/paper/1905.11481/) (2019)
- [Pyro: Deep Universal Probabilistic Programming](https://mlsanity.com/paper/1810.09538/) (2018)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Contemporary Symbolic Regression Methods and their Relative Performance](https://mlsanity.com/paper/2107.14351/) (2021)
- [Composable Effects for Flexible and Accelerated Probabilistic Programming in NumPyro](https://mlsanity.com/paper/1912.11554/) (2019)
- [Interpretable Machine Learning for Science with PySR and SymbolicRegression.jl](https://mlsanity.com/paper/2305.01582/) (2023)
- [Learning Symbolic Physics with Graph Networks](https://mlsanity.com/paper/1909.05862/) (2019)
- [Exhaustive Symbolic Regression](https://mlsanity.com/paper/2211.11461/) (2022)
- [Symbolic Regression on FPGAs for Fast Machine Learning Inference](https://mlsanity.com/paper/2305.04099/) (2023)
- [Interpretable Symbolic Regression for Data Science: Analysis of the 2022 Competition](https://mlsanity.com/paper/2304.01117/) (2023)
- [Optimal Inflationary Potentials](https://mlsanity.com/paper/2310.16786/) (2023)
- [Symbolic Regression for Beyond the Standard Model Physics](https://mlsanity.com/paper/2405.18471/) (2024)
- [Exploration of Parameter Spaces Assisted by Machine Learning](https://mlsanity.com/paper/2207.09959/) (2022)

## Built on by (most cited first, 1 of 1)

- [Symbolic Classification-Enabled LHC Limits for BSM Global Fits](https://mlsanity.com/paper/2605.22330/) (2026)

## Abstract (arXiv)

We demonstrate the efficacy of symbolic regression (SR) to probe models of particle physics Beyond the Standard Model (BSM), by considering the so-called Constrained Minimal Supersymmetric Standard Model (CMSSM). Like many incarnations of BSM physics this model has a number (four) of arbitrary parameters, which determine the experimental signals, and cosmological observables such as the dark matter relic density. We show that analysis of the phenomenology can be greatly accelerated by using symbolic expressions derived for the observables in terms of the input parameters. Here we focus on the Higgs mass, the cold dark matter relic density, and the contribution to the anomalous magnetic moment of the muon. We find that SR can produce remarkably accurate expressions. Using them we make global fits to derive the posterior probability densities of the CMSSM input parameters which are in good agreement with those performed using conventional methods. Moreover, we demonstrate a major advantage of SR which is the ability to make fits using differentiable methods rather than sampling methods. We also compare the method with neural network (NN) regression. SR produces more globally robust results, while NNs require data that is focussed on the promising regions in order to be equally performant.