# Augmenting astrophysical scaling relations with machine learning: application to reducing the Sunyaev-Zeldovich flux-mass scatter

arXiv: https://arxiv.org/abs/2201.01305 · HTML: https://mlsanity.com/paper/2201.01305/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 28 of its 191 references that are in the map.
- First posted on arXiv 4 Jan 2022.

## Builds on (most cited first, 28 of 28)

- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Universal Differential Equations for Scientific Machine Learning](https://mlsanity.com/paper/2001.04385/) (2020)
- [Discovering Symbolic Models from Deep Learning with Inductive Biases](https://mlsanity.com/paper/2006.11287/) (2020)
- [Grammar Variational Autoencoder](https://mlsanity.com/paper/1703.01925/) (2017)
- [Learning Equations for Extrapolation and Control](https://mlsanity.com/paper/1806.07259/) (2018)
- [Chaos as an interpretable benchmark for forecasting and data-driven modelling](https://mlsanity.com/paper/2110.05266/) (2021)
- [AI Poincar'e: Machine Learning Conservation Laws from Trajectories](https://mlsanity.com/paper/2011.04698/) (2020)
- [DeepMoD: Deep learning for Model Discovery in noisy data](https://mlsanity.com/paper/1904.09406/) (2019)
- [A Bayesian machine scientist to aid in the solution of challenging scientific problems](https://mlsanity.com/paper/2004.12157/) (2020)
- [Learning Symbolic Physics with Graph Networks](https://mlsanity.com/paper/1909.05862/) (2019)
- [From Fourier to Koopman: Spectral Methods for Long-term Time Series Prediction](https://mlsanity.com/paper/2004.00574/) (2020)
- [Learning to Predict the Cosmological Structure Formation](https://mlsanity.com/paper/1811.06533/) (2018)
- [The CAMELS Multifield Dataset: Learning the Universe's Fundamental Parameters with Artificial Intelligence](https://mlsanity.com/paper/2109.10915/) (2021)
- [AI-assisted super-resolution cosmological simulations](https://mlsanity.com/paper/2010.06608/) (2020)
- [Inferring halo masses with Graph Neural Networks](https://mlsanity.com/paper/2111.08683/) (2021)
- [Disentangling a Deep Learned Volume Formula](https://mlsanity.com/paper/2012.03955/) (2020)
- [Symbolic regression outperforms other models for small data sets](https://mlsanity.com/paper/2103.15147/) (2021)
- [Multifield Cosmology with Artificial Intelligence](https://mlsanity.com/paper/2109.09747/) (2021)
- [A volumetric deep Convolutional Neural Network for simulation of mock dark matter halo catalogues](https://mlsanity.com/paper/1805.04537/) (2018)
- [Painting with baryons: augmenting N-body simulations with gas using deep generative models](https://mlsanity.com/paper/1903.12173/) (2019)
- [Mass Estimation of Galaxy Clusters with Deep Learning I: Sunyaev-Zel'dovich Effect](https://mlsanity.com/paper/2003.06135/) (2020)
- [Robust marginalization of baryonic effects for cosmological inference at the field level](https://mlsanity.com/paper/2109.10360/) (2021)
- [AI-assisted super-resolution cosmological simulations II: Halo substructures, velocities and higher order statistics](https://mlsanity.com/paper/2105.01016/) (2021)
- [From Dark Matter to Galaxies with Convolutional Networks](https://mlsanity.com/paper/1902.05965/) (2019)
- [Learning neutrino effects in Cosmology with Convolutional Neural Networks](https://mlsanity.com/paper/1910.04255/) (2019)
- [From Dark Matter to Galaxies with Convolutional Neural Networks](https://mlsanity.com/paper/1910.07813/) (2019)
- [HIGAN: Cosmic Neutral Hydrogen with Generative Adversarial Networks](https://mlsanity.com/paper/1904.12846/) (2019)
- [A machine learning approach to galaxy properties: joint redshift-stellar mass probability distributions with Random Forest](https://mlsanity.com/paper/2012.05928/) (2020)

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

- [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)
- [SymbolNet: Neural Symbolic Regression with Adaptive Dynamic Pruning for Compression](https://mlsanity.com/paper/2401.09949/) (2024)
- [The SZ flux-mass (Y-M) relation at low halo masses: improvements with symbolic regression and strong constraints on baryonic feedback](https://mlsanity.com/paper/2209.02075/) (2022)
- [Interactive Symbolic Regression through Offline Reinforcement Learning: A Co-Design Framework](https://mlsanity.com/paper/2402.05306/) (2024)
- [Data-driven Progressive Discovery of Physical Laws](https://mlsanity.com/paper/2603.13727/) (2026)

## Abstract (arXiv)

Complex astrophysical systems often exhibit low-scatter relations between observable properties (e.g., luminosity, velocity dispersion, oscillation period). These scaling relations illuminate the underlying physics, and can provide observational tools for estimating masses and distances. Machine learning can provide a fast and systematic way to search for new scaling relations (or for simple extensions to existing relations) in abstract high-dimensional parameter spaces. We use a machine learning tool called symbolic regression (SR), which models patterns in a dataset in the form of analytic equations. We focus on the Sunyaev-Zeldovich flux-cluster mass relation (YSZ-M), the scatter in which affects inference of cosmological parameters from cluster abundance data. Using SR on the data from the IllustrisTNG hydrodynamical simulation, we find a new proxy for cluster mass which combines YSZ and concentration of ionized gas (cgas): M propto Yconc3/5 equiv YSZ3/5 (1-A, cgas). Yconc reduces the scatter in the predicted M by ~ 20-30% for large clusters (Mgtrsim 1014, h-1 , M_odot), as compared to using just YSZ. We show that the dependence on cgas is linked to cores of clusters exhibiting larger scatter than their outskirts. Finally, we test Yconc on clusters from CAMELS simulations and show that Yconc is robust against variations in cosmology, subgrid physics, and cosmic variance. Our results and methodology can be useful for accurate multiwavelength cluster mass estimation from upcoming CMB and X-ray surveys like ACT, SO, eROSITA and CMB-S4.