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Revealing the 3D Cosmic Web through Gravitationally Constrained Neural Fields
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Reconstructs a 3D dark matter overdensity field from weak lensing shear via a gravitationally constrained coordinate MLP (neural field) ensemble fit through a differentiable lensing forward model.
Problem
3D dark matter mass mapping from single-viewpoint weak lensing shear measurements, which is ill-posed and dominated by intrinsic shape noise; prior methods rely on strong Gaussian or sparsity priors.
Approach
Model the continuous 3D overdensity field with a positionally encoded MLP optimized through a differentiable forward model (convergence and shear operators) fit to galaxy ellipticities, with a lens-plane power spectrum regularizer and a median over a 100-member deep ensemble, instead of a Gaussian (Wiener) prior.
Key results
- Kinematic WL: CC 0.60 vs Wiener 0.39; blurred CC 0.80 vs 0.70.
- Traditional WL: CC 0.52 vs Wiener 0.34; blurred CC 0.77 vs 0.61.
- MNIST non-Gaussian toy: CC 0.61 vs Wiener 0.52; blurred CC 0.86 vs 0.68.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use the neural-field method instead of the Wiener filter | 3D mass mapping · Kinematic WL | CC: 0.39 -> 0.60 | Helped |
| Use the neural-field method instead of the Wiener filter | 3D mass mapping · Kinematic WL | CC (Blur): 0.70 -> 0.80 | Helped |
| Use the neural-field method instead of the Wiener filter | 3D mass mapping · Traditional WL | CC: 0.34 -> 0.52 | Helped |
| Use the neural-field method instead of the Wiener filter | 3D mass mapping · Traditional WL | CC (Blur): 0.61 -> 0.77 | Helped |
| Use the neural-field method instead of the Wiener filter | 3D mass mapping · MNIST Reconstruction | CC: 0.52 -> 0.61 | Helped |
| Use the neural-field method instead of the Wiener filter | 3D mass mapping · MNIST Reconstruction | CC (Blur): 0.68 -> 0.86 | Helped |
Surprising findings
- The Wiener filter produces heavy artifacts and misplaced digit traces on non-Gaussian MNIST lens planes, which the neural field avoids.
Limitations
- Relies on simulated, low-resolution N-body data (75x75 pixels, 5 degree field) rather than realistic survey data.
- Ensemble members do not correspond to Bayesian posterior samples; uncertainty is only empirically calibrated.
- Radial SNR decreases with distance so only z<=1 is reconstructed.
Experimental setup
Datasets: JaxPM N-body simulations MNIST
Benchmarks: simulated kinematic weak lensing simulated traditional weak lensing MNIST lens-plane toy reconstruction
Metrics: normalized cross-correlation normalized cross-correlation after optimal Gaussian blur optimal radial blur
Baselines: Wiener filter voxel grid neural field (prior work)
Builds on: Wiener filter mass mapping positional encoding / Fourier features Adam JaxPM
Closest papers by meaning
- Single View Refractive Index Tomography with Neural Fields (CVPR 2024 · similarity 0.86)
- CosmoBench: A Multiscale, Multiview, Multitask Cosmology Benchmark for Geometric Deep Learning (NeurIPS 2025 · similarity 0.82)
- Unified Framework for Diffusion Generative Models in SO(3): Applications in Computer Vision and Astrophysics (AAAI 2024 · similarity 0.81)
- Galaxy Walker: Geometry-aware VLMs For Galaxy-scale Understanding (CVPR 2025 · similarity 0.80)
- TIDMAD: Time Series Dataset for Discovering Dark Matter with AI Denoising (NeurIPS 2025 · similarity 0.80)
- A Data-Driven Prism: Multi-View Source Separation with Diffusion Model Priors (NeurIPS 2025 · similarity 0.79)
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