Research map / Label-efficient and robust learning / Recognition and long-tail
Hybrid Neural Representations for Spherical Data
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes HNeR-S, a hybrid neural representation for spherical data that pairs hierarchical equirectangular and HEALPix spherical feature-grids with an MLP, evaluated on weather/climate (ERA5) and CMB (Planck PR1) tasks.
Problem
Coordinate-based MLP neural representations struggle to capture highly nonlinear spherical signals such as weather/climate fields and CMB maps, and existing Euclidean hybrid grid methods do not directly apply to the sphere.
Approach
Replace Euclidean grids with spherical feature-grids (equirectangular for weather, HEALPix for CMB) organized hierarchically, using bilinear spherical interpolation in latitude and longitude to produce multi-resolution positional features fed to an MLP.
Key results
- Regression on temperature: HNeR-S achieves 63.45 weighted PSNR vs. 59.81 for the second-best baseline (WIRE).
- Temporal interpolation: HNeR-S achieves best weekly results (23.97 geopotential, 24.50 temperature), and best daily temperature (27.55).
- Compression at 0.114 BPP: HNeR-S achieves WRMSE 124.0 vs. 688.7 for WIRE and 616.0 for SIREN among spatial compression methods.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use HNeR-S instead of WIRE | ERA5 geopotential regression · ERA5 geopotential regression | weighted PSNR: 65.93 -> 66.17 | Helped |
| use HNeR-S instead of WIRE | ERA5 temperature regression · ERA5 temperature regression | weighted PSNR: 59.81 -> 63.45 | Helped |
| use HNeR-S instead of SIREN | ERA5 geopotential daily temporal interpolation · ERA5 geopotential daily temporal interpolation | PSNR: 28.80 -> 28.79 | Hurt |
| use HNeR-S instead of FFN | ERA5 geopotential weekly temporal interpolation · ERA5 geopotential weekly temporal interpolation | PSNR: 23.54 -> 23.97 | Helped |
| use HNeR-S instead of SHINR | ERA5 temperature daily temporal interpolation · ERA5 temperature daily temporal interpolation | PSNR: 27.27 -> 27.55 | Helped |
| use HNeR-S instead of FFN | ERA5 temperature weekly temporal interpolation · ERA5 temperature weekly temporal interpolation | PSNR: 23.73 -> 24.50 | Helped |
| use HNeR-S instead of SIREN | ERA5 spatial compression · ERA5 compression, 0.031 ≤ BPP ≤ 0.080 | WRMSE: 669.5 -> 144.8 | Helped |
| use HNeR-S instead of SIREN | ERA5 spatial compression · ERA5 compression, 0.031 ≤ BPP ≤ 0.080 | WMAE: 462.1 -> 99.4 | Helped |
| use HNeR-S instead of SIREN | ERA5 spatial compression · ERA5 compression, 0.099 ≤ BPP ≤ 0.119 | WRMSE: 616.0 -> 124.0 | Helped |
| use HNeR-S instead of SIREN | ERA5 spatial compression · ERA5 compression, 0.099 ≤ BPP ≤ 0.119 | WMAE: 404.8 -> 50.3 | Helped |
| replace spatial HNeR-S compression with FFN-T spatiotemporal compression | ERA5 compression · ERA5 compression, 0.031 ≤ BPP ≤ 0.080 | WRMSE: 144.8 vs 143.1 | Mixed |
| replace spatial HNeR-S compression with FFN-T spatiotemporal compression | ERA5 compression · ERA5 compression, 0.099 ≤ BPP ≤ 0.119 | WRMSE: 124.0 vs 73.6 | Helped |
Surprising findings
- On daily geopotential temporal interpolation SIREN (28.80) slightly outperforms HNeR-S (28.79).
Limitations
- Interpolation is bilinear in latitude/longitude and not geodesic-aware, which the authors note as future work.
- Compression comparison with FFN-T is not direct since FFN-T is spatiotemporal while HNeR-S is spatial-only.
- Code promised only upon acceptance; not released in the paper.
Experimental setup
Datasets: ERA5 Planck PR1 CMB temperature maps
Benchmarks: ERA5 weather and climate regression ERA5 super-resolution ERA5 temporal interpolation ERA5 compression Planck PR1 CMB super-resolution and regression
Metrics: weighted PSNR weighted RMSE weighted MAE bits per pixel
Baselines: ReLU+P.E. SIREN SHINR WIRE FFN SZ3 FFN-T
Builds on: Instant-NGP WIRE SIREN Fourier feature networks
Closest papers by meaning
- Geographic Location Encoding with Spherical Harmonics and Sinusoidal Representation Networks (ICLR 2024 · similarity 0.85)
- No Location Left Behind: Measuring and Improving the Fairness of Implicit Representations for Earth Data (ICLR 2025 · similarity 0.82)
- Neural Processing of Tri-Plane Hybrid Neural Fields (ICLR 2024 · similarity 0.82)
- Gridded Transformer Neural Processes for Spatio-Temporal Data (ICML 2025 · similarity 0.82)
- Continuous Field Reconstruction from Sparse Observations with Implicit Neural Networks (ICLR 2024 · similarity 0.82)
- Attention on the Sphere (NeurIPS 2025 · similarity 0.81)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.