# Hybrid Neural Representations for Spherical Data

arXiv: https://arxiv.org/abs/2402.05965 · HTML: https://mlsanity.com/paper/2402.05965/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 47 references that are in the map.
- First posted on arXiv 5 Feb 2024.

## Builds on (most cited first, 27 of 27)

- [Instant Neural Graphics Primitives with a Multiresolution Hash Encoding](https://mlsanity.com/paper/2201.05989/) (2022)
- [DeepSDF: Learning Continuous Signed Distance Functions for Shape Representation](https://mlsanity.com/paper/1901.05103/) (2019)
- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Implicit Neural Representations with Periodic Activation Functions](https://mlsanity.com/paper/2006.09661/) (2020)
- [Fourier Features Let Networks Learn High Frequency Functions in Low Dimensional Domains](https://mlsanity.com/paper/2006.10739/) (2020)
- [On the Spectral Bias of Neural Networks](https://mlsanity.com/paper/1806.08734/) (2018)
- [Neural Sparse Voxel Fields](https://mlsanity.com/paper/2007.11571/) (2020)
- [Neural Body: Implicit Neural Representations with Structured Latent Codes for Novel View Synthesis of Dynamic Humans](https://mlsanity.com/paper/2012.15838/) (2020)
- [Learning Continuous Image Representation with Local Implicit Image Function](https://mlsanity.com/paper/2012.09161/) (2020)
- [Neural Fields in Visual Computing and Beyond](https://mlsanity.com/paper/2111.11426/) (2021)
- [Spherical CNNs](https://mlsanity.com/paper/1801.10130/) (2018)
- [Deep Local Shapes: Learning Local SDF Priors for Detailed 3D Reconstruction](https://mlsanity.com/paper/2003.10983/) (2020)
- [GraphCast: Learning skillful medium-range global weather forecasting](https://mlsanity.com/paper/2212.12794/) (2022)
- [Spherical Fourier Neural Operators: Learning Stable Dynamics on the Sphere](https://mlsanity.com/paper/2306.03838/) (2023)
- [WIRE: Wavelet Implicit Neural Representations](https://mlsanity.com/paper/2301.05187/) (2023)
- [Pangu-Weather: A 3D High-Resolution Model for Fast and Accurate Global Weather Forecast](https://mlsanity.com/paper/2211.02556/) (2022)
- [COIN++: Neural Compression Across Modalities](https://mlsanity.com/paper/2201.12904/) (2022)
- [DeepSphere: a graph-based spherical CNN](https://mlsanity.com/paper/2012.15000/) (2020)
- [C3: High-performance and low-complexity neural compression from a single image or video](https://mlsanity.com/paper/2312.02753/) (2023)
- [COOL-CHIC: Coordinate-based Low Complexity Hierarchical Image Codec](https://mlsanity.com/paper/2212.05458/) (2022)
- [SZ3: A Modular Framework for Composing Prediction-Based Error-Bounded Lossy Compressors](https://mlsanity.com/paper/2111.02925/) (2021)
- [Generalised Implicit Neural Representations](https://mlsanity.com/paper/2205.15674/) (2022)
- [Compressing multidimensional weather and climate data into neural networks](https://mlsanity.com/paper/2210.12538/) (2022)
- [Modality-Agnostic Variational Compression of Implicit Neural Representations](https://mlsanity.com/paper/2301.09479/) (2023)
- [Intrinsic Neural Fields: Learning Functions on Manifolds](https://mlsanity.com/paper/2203.07967/) (2022)
- [Fast and accurate learned multiresolution dynamical downscaling for precipitation](https://mlsanity.com/paper/2101.06813/) (2021)
- [DeepCMB: Lensing Reconstruction of the Cosmic Microwave Background with Deep Neural Networks](https://mlsanity.com/paper/1810.01483/) (2018)

## Built on by (most cited first, 3 of 3)

- [Fast Training of Sinusoidal Neural Fields via Scaling Initialization](https://mlsanity.com/paper/2410.04779/) (2024)
- [MeshFeat: Multi-Resolution Features for Neural Fields on Meshes](https://mlsanity.com/paper/2407.13592/) (2024)
- [Hybrid Spatial Representations for Species Distribution Modeling](https://mlsanity.com/paper/2410.10937/) (2024)

## Abstract (arXiv)

In this paper, we study hybrid neural representations for spherical data, a domain of increasing relevance in scientific research. In particular, our work focuses on weather and climate data as well as comic microwave background (CMB) data. Although previous studies have delved into coordinate-based neural representations for spherical signals, they often fail to capture the intricate details of highly nonlinear signals. To address this limitation, we introduce a novel approach named Hybrid Neural Representations for Spherical data (HNeR-S). Our main idea is to use spherical feature-grids to obtain positional features which are combined with a multilayer perception to predict the target signal. We consider feature-grids with equirectangular and hierarchical equal area isolatitude pixelization structures that align with weather data and CMB data, respectively. We extensively verify the effectiveness of our HNeR-S for regression, super-resolution, temporal interpolation, and compression tasks.