Hybrid Neural Representations for Spherical Data

TL;DR

This paper tackles the challenge of representing highly nonlinear spherical signals, such as weather, climate, and cosmic microwave background data. It presents Hybrid Neural Representations for Spherical data (HNeR-S), a hybrid approach that combines hierarchical spherical feature-grids with an MLP to produce positional encodings via bilinear spherical interpolation: $\hat{y}=f_\theta(\mathbf{x}_{\text{in}})=\mathrm{MLP}(\mathbf{Z}(\mathbf{x}_{\text{in}}))$. Two grid variants—an equirectangular grid for weather/climate and a HEALPix grid for CMB—are trained end-to-end on the respective datasets and evaluated on regression, super-resolution, temporal interpolation, and compression, where HNeR-S consistently outperforms five INR baselines. The results suggest that spherical-hybrid representations enable high-fidelity reconstruction and scalable processing of global data, with potential future directions including adaptive grids and geodesic-aware interpolation.

Abstract

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.

Figures (10)

• Figure 1: Overview of hybrid neural representation for spherical data (HNeR-S). HNeR-S considers an input point as the spherical coordinate $\mathbf{x}_{\text{in}}=(\psi, \phi)$, a pair of latitude $\psi \in [-\frac{1}{2}\pi, \frac{1}{2}\pi]$ and longitude $\phi \in [0, 2\pi)$. Then the model interpolates the neighborhood feature-grid parameters and constructs the positional features $\mathbf{Z}(\mathbf{x}_{\text{in}})$. The MLP predicts the target signal values from the positional features.
• Figure 2: Overview of equirectangular and HEALPix grid. Note that the uniformity of feature-grid refers to the consistency in the area covered by each unit cell within the grid.
• Figure 3: Neighborhood structure of the equirectangular grid. The yellow point indicates the input point $\mathbf{x}_{\text{in}}$ and green points indicate the neighborhood grid points $\mathcal{N}^{(\ell)}(\mathbf{x}_{\text{in}})$.
• Figure 3: Results of super-resolution on weather and climate data. The evaluation metric is weighted PSNR and the best metric is highlighted in bold.
• Figure 4: Pole singularity and periodicity of equirectangular grid. Different spherical coordinates can indicate the same point on a sphere, i.e., points at the North pole $(\psi=-\frac{\pi}{2})$, South pole $(\psi=\frac{\pi}{2})$, and the prime meridian ($\phi=0$ and $\phi=2\pi$). Our HNeR-S avoided assigning different parameters for such spherical coordinates. Points with the same marker and color share the associated parameters.