Emulators are Machine Learning models that map cosmological (and nuisance) parameters to cosmological data vectors, just like many numerical packages for corresponding observables. The advantage of emulators is the fast evaluation time. As cosmology moves into an era in which increasingly precise and high-resolution experiments require more and more computational resources, many traditional numerical packages become too slow in terms of evaluation time. Emulators are developed to overcome this issue and can widely replace many numerical packages in MCMCs.
In this repository, we provide emulators for various data vectors and in different architectures. The architectures include Residual Multi-Layer Perceptron, Transformer, Convolutional Neural Network, and Gaussian processing models.
Cosmic Microwave Background (CMB) emulators are trained to emulate TT (temperature auto spectrum), TE (temperature-polarization cross spectrum), and EE (polarization auto spectrum) power spectra output calculated by the CAMB Boltzmann code.
We provide a few architecture options; for instance, the users can select modeltype to be either TRF (standing for Transformer) or CNN (standing for Convolutional Neural Network).
Users then need to specify the corresponding emulator, which corresponds to a specific cosmological model, as well as a particular CAMB version and accuracy settings. This specification is done as follows.
Step 1️⃣: Select the 'ordering' list, which needs to be the exact sequence of parameters input to the emulator.,
Step 2️⃣: Select the emulator information files as shown below
#Switch the prefix xy for (tt, te, ee)
'xyfilename': emulator model parameters and
'xyextraname': normalization factors, .
Step 3️⃣: Specify ellmax, which is the largest ell mode that the emulator is trained to evaluate.
Step 4️⃣: If users want to sample the parameter theta_* (recommended) instead of H_0, specify the following parameters
'thetaordering': # exact sequence of parameters input to the Gaussian Processing emulator.
'GPfilename': # Gaussian Processing for the mapping between theta_* and thetaordering params to H_0.
'GPextraname': # Gaussian Processing for the mapping between theta_* and thetaordering params to H_0.
For Supernovae luminosity distances and BAO observable emulators, we adopt ResMLP for luminosity distance and Hubble parameter. On top of that, we have a Gaussian processing emulator for
Step 1️⃣: Select the 'ordering' list, which needs to be the exact sequence of parameters input to the emulator.,
Step 2️⃣: Select the Hubbe Parameter emulator information files as shown below
'filename': emulator model parameters and
'extraname': normalization factors, .
Step 3️⃣: Specify z arrays for both H and distance, which are the redshift arrays on which the emulator will compute the data vector. Internally, we then save an interpolator to output values of H and distance at any redshift within the range.
Step 4️⃣: Internally integrate to get the supernovae distance based on the output of Hubble emulator
Step 5️⃣: Similarly specify the 'filename' and 'extraname' for the GP for
This repo exists only because of the hard work of the Ph.D. students Victoria Lloyd, Evan Saraivanov, and Yijie Zhu, and was developed after the science of emulators was painstakingly tested in the following papers.
@article{Zhu:2025jim,
author = "Zhu, Yijie and Saraivanov, Evan and Kable, Joshua A. and Giannakopoulou, Artemis Sofia and Nijjar, Amritpal and Miranda, Vivian and Bonici, Marco and Eifler, Tim and Krause, Elisabeth",
title = "{Attention-based Neural Network Emulators for Multi-Probe Data Vectors Part III: Modeling The Next Generation Surveys}",
eprint = "2505.22574",
archivePrefix = "arXiv",
primaryClass = "astro-ph.CO",
month = "5",
year = "2025"
}
@article{Saraivanov:2024soy,
author = "Saraivanov, Evan and Zhong, Kunhao and Miranda, Vivian and Boruah, Supranta S. and Eifler, Tim and Krause, Elisabeth",
title = "{Attention-based neural network emulators for multiprobe data vectors. II. Assessing tension metrics}",
eprint = "2403.12337",
archivePrefix = "arXiv",
primaryClass = "astro-ph.CO",
doi = "10.1103/PhysRevD.111.123520",
journal = "Phys. Rev. D",
volume = "111",
number = "12",
pages = "123520",
year = "2025"
}
@article{Zhong:2024xuk,
author = "Zhong, Kunhao and Saraivanov, Evan and Caputi, James and Miranda, Vivian and Boruah, Supranta S. and Eifler, Tim and Krause, Elisabeth",
title = "{Attention-based neural network emulators for multiprobe data vectors. I. Forecasting the growth-geometry split}",
eprint = "2402.17716",
archivePrefix = "arXiv",
primaryClass = "astro-ph.CO",
doi = "10.1103/PhysRevD.111.123519",
journal = "Phys. Rev. D",
volume = "111",
number = "12",
pages = "123519",
year = "2025"
}
The original code we used in these three papers has only partial integration to Cocoa and was based on an underlying infrastructure developed by Supranta S. Boruah for the paper (please cite it as well)
@article{Boruah:2022uac,
author = "Boruah, Supranta S. and Eifler, Tim and Miranda, Vivian and M, Sai Krishanth P.",
title = "{Accelerating cosmological inference with Gaussian processes and neural networks {\textendash} an application to LSST Y1 weak lensing and galaxy clustering}",
eprint = "2203.06124",
archivePrefix = "arXiv",
primaryClass = "astro-ph.CO",
doi = "10.1093/mnras/stac3417",
journal = "Mon. Not. Roy. Astron. Soc.",
volume = "518",
number = "4",
pages = "4818--4831",
year = "2022"
}
Our Matter Power Spectrum emulator also depends on a modified version of symbolic_pk. We basically use the EH code with modifications we are implementing to make it faster. So please also cite
@article{Bartlett:2023cyr,
author = "Bartlett, Deaglan J. and Kammerer, Lukas and Kronberger, Gabriel and Desmond, Harry and Ferreira, Pedro G. and Wandelt, Benjamin D. and Burlacu, Bogdan and Alonso, David and Zennaro, Matteo",
title = "{A precise symbolic emulator of the linear matter power spectrum}",
eprint = "2311.15865",
archivePrefix = "arXiv",
primaryClass = "astro-ph.CO",
doi = "10.1051/0004-6361/202348811",
journal = "Astron. Astrophys.",
volume = "686",
pages = "A209",
year = "2024"
}