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Learning the Universe with the 2nd Generation of CAMELS: Varying 35 parameters of the IllustrisTNG model in (50Mpc/h)^3 boxes

This paper presents the second generation of the CAMELS project, featuring 1,192 cosmological simulations with eight times larger volumes than its predecessor to explore a 35-parameter space, demonstrating that while these larger volumes improve neural network-based parameter inference, the gains are sub-linear due to mode coupling and parameter degeneracies.

Original authors: Shy Genel, Yongseok Jo, Boon Kiat Oh, Megan Taylor Tillman, Max E. Lee, Jun-Young Lee, Elena Hernández-Martínez, Christopher C. Lovell, Xavier Sims, Blakesley Burkhart, Kentaro Nagamine, Daniel Anglés

Published 2026-06-10✓ Author reviewed ⓘ

📖 6 min read🧠 Deep dive

CC BY 4.0

Original authors: Shy Genel, Yongseok Jo, Boon Kiat Oh, Megan Taylor Tillman, Max E. Lee, Jun-Young Lee, Elena Hernández-Martínez, Christopher C. Lovell, Xavier Sims, Blakesley Burkhart, Kentaro Nagamine, Daniel Anglés-Alcázar, Francisco Villaescusa-Navarro

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

Imagine you are trying to understand how a giant, complex machine works—like a universe—by watching it run. Scientists have been building digital models of the universe for decades, but they've faced a tricky problem: the universe is huge, and the physics inside it (how stars form, how gas heats up, how black holes grow) is incredibly complicated.

This paper introduces a new, massive upgrade to a project called CAMELS (Cosmology and Astrophysics with MachinE Learning Simulations). Think of CAMELS as a giant training gym for artificial intelligence (AI). The goal is to teach the AI to look at a picture of the universe and guess the "settings" or "knobs" that were used to create it.

Here is a breakdown of what they did and what they found, using simple analogies:

1. The Upgrade: From a Small Room to a Whole City

In the past, the CAMELS project ran simulations in boxes that were 25 units wide (imagine a small room). In this new paper, they built boxes that are 50 units wide (a whole city block).

Why does size matter? In a small room, you might only see a few people and a few trees. You miss the big picture. In the larger city-sized box, the AI can see massive galaxy clusters, huge empty spaces (voids), and rare events that simply don't exist in the smaller boxes.
The Result: The new simulations are 8 times larger in volume than the old ones. This gives the AI much more data to learn from, reducing the "noise" or randomness that comes from looking at a small sample.

2. The Control Panel: 35 Knobs to Turn

The universe isn't just about gravity; it's about gas, stars, black holes, and radiation. The old simulations tweaked about 28 "knobs" (parameters) on the control panel.

The New Feature: This new version adds 7 more knobs, bringing the total to 35.
What's new? They specifically added controls for the background radiation (the UV and X-ray light that fills the universe). Think of this as adding a dimmer switch for the sun and a timer for when it turns on. This helps the AI understand how this radiation heats up the gas between galaxies, which is crucial for understanding the early universe.

3. The Experiment: Teaching the AI to Guess

The researchers created 1,192 different "universes," each with a unique combination of these 35 knobs turned to different settings. They then fed data from these universes into different types of AI to see how well the AI could guess the settings back.

They tested four different ways of looking at the data:

The "Power Spectrum" (The Sound Wave): Looking at the overall patterns of matter like a sound wave.
The "Maps" (The Photographs): Looking at 2D slices of the universe, like looking at a map of a city.
The "Graphs" (The Social Network): Looking at how galaxies are connected to each other, like a social network graph.
The "Halo Profiles" (The X-Ray): Looking inside massive galaxy clusters to see their temperature and density.

4. The Surprising Results: Bigger Isn't Always That Much Better

The team expected that because the new boxes were 8 times bigger, the AI's accuracy would improve by a factor of roughly 2.8 (the square root of 8). This is the "naive" expectation: more data = better results.

However, the results were more subtle:

The "Mode Coupling" Effect: Imagine you are listening to a choir. In a small room, the sound waves bounce off the walls and mix up (couple) in a simple way. In a huge cathedral, the sound waves interact in incredibly complex ways. The paper found that in these larger, more realistic universes, the different parts of the data become so tightly linked (coupled) that adding more volume doesn't give you as much new information as you'd hope. It's like trying to hear a whisper in a noisy room; making the room bigger doesn't always make the whisper clearer if the noise is also getting louder and more complex.
The "Knob" Confusion: Some of the knobs "confused" the AI: the AI couldn't always tell if a change in the data was caused by a cosmological setting (like the density of the universe) or an astrophysical setting (like the timing of radiation). This created "degeneracies," where different settings produced similar-looking results.

5. What Worked Best?

The Maps Won: Looking at the actual 2D "photographs" of the universe (the density maps) gave the best results. It was much better than just looking at the "sound waves" (power spectrum).
The "Monopole" Trick: When they let the AI see the total amount of mass in the map (the "monopole"), it got very good at guessing the density of the universe ( $\Omega_m$ ). It's like if you could weigh the whole city at once; you'd instantly know how many people live there.
The Graphs Struggled: Looking at galaxy connections (graphs) was harder. This is because galaxies are formed by messy, complex physics (subgrid physics). The AI had a hard time separating the "cosmology" settings from the "galaxy formation" settings.

6. The Takeaway

This paper is a major step forward. It proves that we can simulate the universe on a larger scale with more complex physics.

The Good News: The new, larger simulations allow us to study massive galaxy clusters and rare environments that were impossible to see before. The AI can now learn from a more diverse set of universes.
The Reality Check: Simply making the simulation bigger doesn't automatically make the AI's predictions perfect. The universe is so complex that the "noise" (cosmic variance) and the "coupling" of different physical effects limit how much extra information we get from just adding more space.

In short: They built a bigger, more detailed digital universe with more control knobs. They taught an AI to read it. The AI got better, but not as much better as they hoped, because the universe is a messy, interconnected place where everything affects everything else. This new dataset is now public, allowing other scientists to try to crack the code of the universe with their own AI tools.

Technical Summary: Learning the Universe with the 2nd Generation of CAMELS

Problem Statement
The standard cosmological model ( $\Lambda$ CDM) has been successful on large scales, but extracting precise constraints on cosmological and astrophysical parameters from small-scale, non-linear structures requires robust theoretical predictions that account for complex baryonic physics. Previous simulation-based inference efforts, specifically the first generation of the CAMELS (Cosmology and Astrophysics with MachinE Learning Simulations) project, utilized $(25 h^{-1}\text{Mpc})^3$ boxes. While effective for training machine learning models, these volumes suffered from significant limitations: they lacked rare, massive objects (e.g., massive clusters), missed long-wavelength density modes, and exhibited substantial sample variance. Furthermore, the first generation varied a limited set of parameters (up to 28), leaving uncertainties in the ionizing background radiation and other astrophysical processes unexplored. These constraints hindered the ability to marginalize over baryonic effects and accurately infer fundamental parameters from small-scale observables.

Methodology
This paper introduces the second generation of CAMELS simulations, specifically the SB35 suite, which addresses the volume and parameter limitations of previous iterations.

Simulation Setup: The new suite consists of 1,024 hydrodynamical simulations using the IllustrisTNG model implemented in the Arepo code. The simulation volume is increased to $(50 h^{-1}\text{Mpc})^3$ , eight times larger than the previous $(25 h^{-1}\text{Mpc})^3$ boxes, while maintaining the same mass resolution ( $512^3$ dark matter particles and gas cells).
Parameter Space: The simulations vary 35 parameters in total. This includes the original 28 parameters (5 cosmological, 23 astrophysical) from the SB28 suite, plus 7 new parameters. The new parameters specifically target the ionizing background radiation (amplitude and timing of H and He reionization: $\beta_H, \Delta z_H, \beta_{He}, \Delta z_{He}$ ) and numerical parameters like gravitational softening ( $\epsilon$ ).
Simulation Sets: The suite includes:
- SB35: 1,024 simulations sampling the 35-dimensional space via a Sobol sequence.
- 1P: 141 simulations varying one parameter at a time to isolate effects.
- CV50: 27 simulations with fiducial parameters but different initial conditions to quantify cosmic variance.
Inference Techniques: The authors employ various machine learning architectures to infer parameters from different data products:
- Multilayer Perceptrons (MLPs) for matter power spectra.
- Convolutional Neural Networks (CNNs) for projected 2D matter density maps.
- Graph Neural Networks (GNNs) for galaxy spatial distributions.
- Gaussian Processes (GPs) for emulating thermodynamical properties of massive halos.
- Comparisons are systematically made against the previous SB28 ( $(25 h^{-1}\text{Mpc})^3$ , 28 parameters) and LH (6 parameters) suites.

Key Contributions

Expanded Volume and Resolution: The provision of $(50 h^{-1}\text{Mpc})^3$ boxes allows for the study of more massive halos and a broader range of environments, reducing sample variance and capturing long-wavelength modes previously inaccessible.
Extended Parameter Space: The inclusion of 7 new parameters, particularly those governing the ionizing background, enables the assessment of how reionization uncertainties propagate to observables like the Intergalactic Medium (IGM) thermal state and neutral hydrogen distribution.
Systematic Benchmarking: The paper provides a rigorous "apples-to-apples" comparison between the new larger volumes and previous smaller ones, isolating the effects of volume size versus parameter space complexity on inference performance.
Public Release: The simulation outputs and ancillary data are made publicly available to facilitate further development of simulation-based inference methods.

Results

Global Properties: The SB35 suite extends coverage to larger scales and more massive halos compared to SB28. While SB35 and SB28 agree in overlapping ranges, the SB35 results show enhanced mode coupling and higher physical fidelity. The 6-parameter LH set shows systematic offsets, highlighting the limitations of restricted parameter spaces.
IGM Response: Varying the ionizing background parameters ( $\beta_H, \Delta z_H, \beta_{He}, \Delta z_{He}$ ) produces measurable changes in the IGM temperature-density relation ( $T_0$ and $\gamma$ ), particularly around the epochs of H and He reionization.
Parameter Inference Performance:
- Matter Power Spectra: Constraints on $\Omega_m$ barely improve (RMSE $\approx$ 0.09 to 0.088), and $\sigma_8$ improves by only a factor of $\approx 1.3$ (RMSE 0.091 to 0.073). This is far below the naive $\sqrt{8} \approx 2.8$ scaling expected from volume increase. The authors attribute this to strong mode coupling in non-linear evolution, which reduces the effective number of independent modes, and the fact that cosmic variance in the power spectrum ratio only decreases by $\approx 15\%$ between volumes.
- Projected Maps (CNNs): Field-level inference from 2D density maps yields tighter constraints than power spectra. Improvements from SB28 to SB35 are factors of $\approx 1.3$ (no-monopole) to $\approx 1.5$ (with monopole). Unnormalized maps (retaining total mass) are particularly powerful for $\Omega_m$ .
- Galaxy Graphs (GNNs): Inference from galaxy graphs shows modest improvements (factors of 1.4 for $\Omega_m$ , 1.2 for $\sigma_8$ ). The scaling is weaker than for matter-based inputs, likely due to degeneracies between cosmological and astrophysical parameters affecting galaxy populations, and potential optimization challenges with larger graphs.
- Massive Halos (GPs): Emulators trained on SB35 halos accurately recover the Sunyaev-Zeldovich $Y-M$ relation, outperforming SB28 emulators, particularly at the high-mass end where SB28 suffers from poor sampling. Inference from thermodynamical profiles confirms that while inner regions ( $<0.9 R_{200c}$ ) hold the most information, outer regions ( $0.9-2.5 R_{200c}$ ) still contain significant constraining power for parameters like $\Omega_m$ , $H_0$ , and wind speeds.

Significance and Claims
The paper claims that the second-generation CAMELS simulations provide a more robust foundation for simulation-based inference in cosmology. By increasing the volume, the authors demonstrate that while larger boxes reduce sample variance and improve the sampling of massive halos, the gains in parameter constraints are sub-linear relative to the volume increase. This is interpreted as a consequence of mode coupling (information loss due to non-linear correlations) and parameter degeneracies in high-dimensional spaces.

The authors emphasize that the new suite is not merely a volume expansion but a necessary step to:

Access the full diversity of cosmic environments and massive halos.
Explicitly model uncertainties in the ionizing background and reionization history.
Train flexible models (neural networks, GPs) that can be applied to real observational data, moving beyond simplified analytic models to capture complex, high-order patterns in structure formation.

The work serves as a public resource for the community to develop algorithms that connect observations to simulation parameters in the presence of complex astrophysical effects, supporting the broader "Learning the Universe" collaboration's goal of inferring the fundamental parameters of the Universe.