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CosmoBench: A Multiscale, Multiview, Multitask Cosmology Benchmark for Geometric Deep Learning
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Introduces CosmoBench, a multiscale, multiview, multitask benchmark of point clouds and merger trees from cosmological simulations, with baselines (2PCF-MLP, linear least squares, GNNs, linear theory, DeepSets, kNN, EPS) showing simple least-squares models often match or beat GNNs.
Problem
Cosmological simulations produce point clouds of halos/galaxies and directed merger trees, but there is no unified large-scale benchmark that formalizes cosmology tasks for geometric deep learning.
Approach
Curate three point-cloud suites (Quijote, CAMELS-SAM, CAMELS) and a merger-tree dataset (CS-Trees) into one benchmark with parameter regression, velocity prediction (including redshift-space variant), and merger-node classification/tree super-resolution tasks, and benchmark classical cosmology statistics against GNNs and simple symmetry-constrained linear models.
Key results
- On Quijote, LLS achieves R^2 0.83 for Omega_m and 0.80 for sigma_8, competitive with the 2PCF-MLP (0.85/0.84) and GNN (0.80/0.77) while using 49 parameters versus 671K for the GNN.
- For velocity prediction on Quijote, LLS reaches R^2 0.4347 versus 0.4100 for a GNN with 126k parameters and 0.3769 for the linear theory oracle.
- On merger-node classification, a 1-hop kNN reaches 0.72 accuracy using scale factor, comparable to a 4-hop GNN (0.70), exceeding EPS (0.53).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use LLS pairwise-distance statistics instead of GNN | Point-cloud velocity prediction · Quijote | R² velocity: 0.4100 -> 0.4347 | Helped |
| Use GNN instead of LLS | Point-cloud velocity prediction · CAMELS-SAM | R² velocity: 0.2107 -> 0.2865 | Helped |
| Use linear theory oracle instead of GNN | Point-cloud velocity prediction · CAMELS | R² velocity: 0.2527 -> 0.2970* | Helped |
| Modify the LLS baseline for redshift-space positions | Velocity prediction from redshift positions · CAMELS-SAM | R² velocity: 0.1172 -> 0.2116 | Helped |
| Modify the LLS baseline for redshift-space positions | Velocity prediction from redshift positions · CAMELS | R² velocity: 0.0801 -> 0.2185 | Helped |
| Remove edge-edge message passing (ablation) | Point-cloud GNN · Quijote cosmology prediction, Ωm | R²: 0.80 ± 0.004 -> 0.80 ± 0.004 | No clear effect |
| Use logarithmic rather than linear bins (25 bins) (ablation) | 2PCF cosmology predictor · Quijote, σ8 | R²: 0.74 ± 0.006 -> 0.84 ± 0.004 | Helped |
| Use 250 rather than 25 logarithmic bins (ablation) | 2PCF cosmology predictor · Quijote, Ωm | R²: 0.84 ± 0.004 -> 0.83 ± 0.004 | No clear effect |
| Use a 4× larger maximum bin radius than the base range (ablation) | 2PCF cosmology predictor · Quijote, σ8 | R²: 0.83 ± 0.004 -> 0.84 ± 0.004 | Helped |
| Use a 4× smaller minimum bin radius than the base range (ablation) | 2PCF cosmology predictor · CAMELS-SAM, Ωm | R²: 0.64 ± 0.03 -> 0.73 ± 0.03 | Helped |
| Use GNN rather than DeepSet to exploit merger-tree topology | Merger-tree cosmological parameter prediction · CS-Trees, Ωm (concentration-only features) | R²: 0.68 ± 0.008 -> 0.84 ± 0.004 | Helped |
Surprising findings
- Least-squares fits with a handful of invariant features sometimes outperform GNNs with hundreds of thousands of parameters and much longer training.
- ML velocity predictors outperform the linear theory oracle even though they do not use true cosmological parameters.
Limitations
- Several datasets are small (CAMELS with about 1,000 point clouds; 200 trees for node classification), limiting data-driven approaches.
- Redshift-space velocity baselines degrade substantially at small scales, and the paper uses a simplified line-of-sight setup.
- Some comparisons to prior Fisher-based cosmology results are not apples-to-apples.
Experimental setup
Datasets: Quijote CAMELS-SAM CAMELS CS-Trees
Benchmarks: CosmoBench
Metrics: R^2 accuracy bootstrap std
Baselines: 2PCF-MLP linear least squares (LLS) GNN linear theory oracle 1-nearest neighbor DeepSets k-nearest neighbor Extended Press-Schechter
Builds on: message passing neural network DeepSets Extended Press-Schechter
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