DeepSphere: Efficient spherical Convolutional Neural Network with HEALPix sampling for cosmological applications

By Nathanael Perraudin, Michaël Defferrard, Tomasz Kacprzak, Raphaël Sgier. 2018

197 citations recorded by the source corpus.

Convolutional Neural Networks (CNNs) are a cornerstone of the Deep Learning toolbox and have led to many breakthroughs in Artificial Intelligence. These networks have mostly been developed for regular Euclidean domains such as those supporting images, audio, or video. Because of their success, CNN-based methods are becoming increasingly popular in Cosmology. Cosmological data often comes as spherical maps, which make the use of the traditional CNNs more complicated. The commonly used pixelization scheme for spherical maps is the Hierarchical Equal Area isoLatitude Pixelisation (HEALPix). We present a spherical CNN for analysis of full and partial HEALPix maps, which we call DeepSphere. The spherical CNN is constructed by representing the sphere as a graph. Graphs are versatile data structures that can act as a discrete representation of a continuous manifold. Using the graph-based representation, we define many of the standard CNN operations, such as convolution and pooling. With filters restricted to being radial, our convolutions are equivariant to rotation on the sphere, and DeepSphere can be made invariant or equivariant to rotation. This way, DeepSphere is a special case of a graph CNN, tailored to the HEALPix sampling of the sphere. This approach is computationally more efficient than using spherical harmonics to perform convolutions. We demonstrate the method on a classification problem of weak lensing mass maps from two cosmological models and compare the performance of the CNN with that of two baseline classifiers. The results show that the performance of DeepSphere is always superior or equal to both of these baselines. For high noise levels and for data covering only a smaller fraction of the sphere, DeepSphere achieves typically 10% better classification accuracy than those baselines. Finally, we show how learned filters can be visualized to introspect the neural network.

Subfields: Artificial Intelligence, Astronomy and Astrophysics

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

In Astronomy and Astrophysics

Citations in the corpus

General E(2)-Equivariant Steerable CNNs (2019, background): “spherical CNNs [19, 5, 20, 21, 22, 23] or more general models of geometric deep learning [24, 25, 26, 27].”
Gauge Equivariant Convolutional Networks and the Icosahedral CNN (2019, methodology): “Spherical CNNs Besides the general theoretical framework of gauge equivariant convolution, we present in this paper a speciﬁc model (the Icosahedral CNN), which can be viewed as a fast and simple alternative to Spherical CNNs (Cohen et al., 2018b; Esteves et al., 2018; Boomsma & Frellsen, 2017; Su &”
Geometric Deep Learning for Volumetric Computational Fluid Dynamics (2019, methodology): “Even though this method was not what we were searching, it has been successful in other applications [30] [29].”
DeepCMB: Lensing Reconstruction of the Cosmic Microwave Background with Deep Neural Networks (2018, background): “During the revision stages of this manuscript, other architectures have been proposed to address this issue (Perraudin et al., 2019; Krachmalnicoff and Tomasi, 2019).”
WeatherBench: A Benchmark Data Set for Data‐Driven Weather Forecasting (2020, background): “A possible solution in the horizontal could be to use spherical convolutions (Cohen et al., 2018; Perraudin et al., 2019; Jiang et al., 2019) or to feed in latitude information to the network.”