DeepSphere: Efficient spherical convolutional neural network with HEALPix sampling for cosmological applications
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MethodBatch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
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BackgroundAdvances In Deep Learning On Graphs (Gsp'18 Workshop)Preprint
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“As HEALPix [27] is our target application, we tailor the method to that particular sampling in the subsequent exposition.”
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MethodGeometric Deep Learning: Going beyond Euclidean data
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BackgroundStriving for Simplicity: The All Convolutional Net
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“Observables that cover large parts of the sky, such as the Cosmic Microwave Background (CMB) [1–3], neutral hydrogen [4, 5], galaxy clustering [6], gravitational lensing [7, 8], and others, have been used to constrain cosmological and astrophysical models.”
BackgroundConvolutional Networks on Graphs for Learning Molecular Fingerprints
Duvenaud, D., Maclaurin, D., Aguilera-Iparraguirre, J., Gómez-Bombarelli, R., Hirzel, T., Aspuru-Guzik, A., & Adams, R. P. (2015) · arXiv · doi:10.48550/arxiv.1509.09292 · Cited by 2,628 · cited 1× · see citing works
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MethodRepresentation Learning on Graphs: Methods and ApplicationsPreprint
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Geometric Deep Learning on Graphs and Manifolds Using Mixture Model CNNs
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“Localization is desired for the transformation to be stable to local deformation [57], and most interactions in the data are local anyway.”
BackgroundHI4PI: a full-sky H i survey based on EBHIS and GASS
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Structured Sequence Modeling with Graph Convolutional Recurrent Networks
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Self-citationKiDS-450: cosmological parameter constraints from tomographic weak gravitational lensing
Hildebrandt, H., Viola, M., Heymans, C., Joudaki, S., Kuijken, K., Blake, C., Erben, T., Joachimi, B., Klaes, D., Miller, L., et al. (2016) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stw2805 · Cited by 817 · cited 1× · see citing works
“Observables that cover large parts of the sky, such as the Cosmic Microwave Background (CMB) [1–3], neutral hydrogen [4, 5], galaxy clustering [6], gravitational lensing [7, 8], and others, have been used to constrain cosmological and astrophysical models.”
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BackgroundMethodGeodesic Convolutional Neural Networks on Riemannian Manifolds
Masci, J., Boscaini, D., Bronstein, M. M., & Vandergheynst, P. (2015) · 2015 IEEE International Conference on Computer Vision Workshop (ICCVW) · doi:10.1109/iccvw.2015.112 · Cited by 721 · cited 1× · see citing works
“This idea has been generalized to arbitrary 2D manifolds for shape alignment and retrieval [50–52].”
MethodKondor, R., & Trivedi, S. (2018) · International Conference on Machine Learning · doi:10.48550/arxiv.1802.03690 · Cited by 684 · cited 1× · see citing works
“See [56] for a rigorous treatment of convolution and equivariance in NNs.”
BackgroundGeometric Matrix Completion with Recurrent Multi-Graph Neural NetworksPreprint
Monti, F., Bronstein, M., & Bresson, X. (2017) · Neural Information Processing Systems · doi:10.48550/arxiv.1704.06803 · Cited by 558 · cited 1× · see citing works
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Learning shape correspondence with anisotropic convolutional neural networksPreprint
Boscaini, D., Masci, J., Rodolà, E., & Bronstein, M. (2016) · Neural Information Processing Systems · doi:10.48550/arxiv.1605.06437 · Cited by 540 · cited 1× · see citing works
“This idea has been generalized to arbitrary 2D manifolds for shape alignment and retrieval [50–52].”
Method3D Graph Neural Networks for RGBD Semantic Segmentation
Qi, X., Liao, R., Jia, J., Fidler, S., & Urtasun, R. (2017) · 2017 IEEE International Conference on Computer Vision (ICCV) · doi:10.1109/iccv.2017.556 · Cited by 482 · cited 1× · see citing works
“Thanks to their versatility, graph neural networks have been used in a variety of tasks, such as identifying diseases from brain connectivity networks [61] or population graphs [62], designing drugs using molecular graphs [63], segmenting 3D point clouds [64], optimizing shapes to be aerodynamic [65], and many more.”
MethodCoors, B., Condurache, A., & Geiger, A. (2018) · European Conference on Computer Vision · doi:10.1007/978-3-030-01240-3_32 · Cited by 457 · cited 4× · see citing works
“A first approach, explored by [20] for molecular modeling and [21, 22] for omnidirectional imaging, is to use a 2D CNN on a discretisation of the sphere that is a grid, such as the equirectangular projection (Figure 6, left panel), or a set of grids, such as the cubed-sphere defined by [47] (Figure…”
BackgroundMethodInfluentialRecognizing scene viewpoint using panoramic place representation
Xiao, J.-X., Ehinger, K. A., Oliva, A., & Torralba, A. (2012) · 2012 IEEE Conference on Computer Vision and Pattern Recognition · doi:10.1109/cvpr.2012.6247991 · Cited by 414 · cited 1× · see citing works
“This approach has been extensively used for cosmological maps [9, 11, 12, 23] and omnidirectional imaging [48, 49].”
MethodClebsch-Gordan Nets: a Fully Fourier Space Spherical Convolutional Neural Network
Kondor, R., Lin, Z., & Trivedi, S. (2018) · Neural Information Processing Systems · doi:10.48550/arxiv.1806.09231 · Cited by 395 · cited 1×
“…log N pix , plus N pix matrix multiplications of size N pix for a total cost of O N 3 / 2 pix operations. leveraged to avoid SHTs between layers (it does a non-linear transformation in the spectral domain), the transform itself costs O ( N 3 / 2 pix ), for no reduction of overall complexity [55].”
BackgroundMetric learning with spectral graph convolutions on brain connectivity networks
Ktena, S. I., Parisot, S., Ferrante, E., Rajchl, M., Lee, M., Glocker, B., & Rueckert, D. (2017) · NeuroImage · doi:10.1016/j.neuroimage.2017.12.052 · Cited by 382 · cited 1× · see citing works
“…to their versatility, graph neural networks have been used in a variety of tasks, such as identifying diseases from brain connectivity networks [61] or population graphs [62], designing drugs using molecular graphs [63], segmenting 3D point clouds [64], optimizing shapes to be aerodynamic…”
MethodRonchi, C., Iacono, R., & Paolucci, P. (1996) · Journal of Computational Physics · doi:10.1006/jcph.1996.0047 · Cited by 381 · cited 2× · see citing works
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MethodBartelmann, M. (2010) · Classical and Quantum Gravity · doi:10.1088/0264-9381/27/23/233001 · Cited by 348 · see citing works
Convergence of Laplacian Eigenmaps
Belkin, M., & Niyogi, P. (2006) · Neural Information Processing Systems · doi:10.7551/mitpress/7503.003.0021 · Cited by 341 · cited 1× · see citing works
“Indeed, [34] showed that the graph Laplacian converges to the Laplace-Beltrami when the number of pixels goes to in-finity providing uniform sampling of the manifold and a fully connected graph built with exponentially decaying weights.”
BackgroundSpectral Graph Convolutions for Population-Based Disease Prediction
Parisot, S., Ktena, S. I., Ferrante, E., Lee, M., Moreno, R. G., Glocker, B., & Rueckert, D. (2017) · Lecture notes in computer science · doi:10.1007/978-3-319-66179-7_21 · Cited by 260 · cited 1× · see citing works
“…graph neural networks have been used in a variety of tasks, such as identifying diseases from brain connectivity networks [61] or population graphs [62], designing drugs using molecular graphs [63], segmenting 3D point clouds [64], optimizing shapes to be aerodynamic [65], and many more.”
MethodStationary Signal Processing on Graphs
Perraudin, N., & Vandergheynst, P. (2017) · IEEE Transactions on Signal Processing · doi:10.1109/tsp.2017.2690388 · Cited by 240 · cited 1× · see citing works
“We refer the reader to [37, Sec 2.2] for a detailed discussion of the connection between translation T i and localization T i .”
MethodInfluentialSelf-citationPanoContext: A Whole-Room 3D Context Model for Panoramic Scene Understanding
Zhang, Y., Song, S., Tan, P., & Xiao, J. (2014) · Lecture notes in computer science · doi:10.1007/978-3-319-10599-4_43 · Cited by 237 · cited 1× · see citing works
“This approach has been extensively used for cosmological maps [9, 11, 12, 23] and omnidirectional imaging [48, 49].”
MethodA fast transform for spherical harmonics
Mohlenkamp, M. J. (1997) · doi:10.1007/bf01261607 · Cited by 237 · cited 1×
“Accelerated schemes however exist for some sampling sets [see 39, 53, 54, for examples].”
BackgroundCosmology with a SKA HI intensity mapping survey
Santos, M. G., Bull, P., Alonso, D., Camera, S., Ferreira, P., Bernardi, G., Maartens, R., Viel, M., Villaescusa-Navarro, F., Abdalla, F., et al. (2015) · doi:10.22323/1.215.0019 · Cited by 172 · cited 1×
“Observables that cover large parts of the sky, such as the Cosmic Microwave Background (CMB) [1–3], neutral hydrogen [4, 5], galaxy clustering [6], gravitational lensing [7, 8], and others, have been used to constrain cosmological and astrophysical models.”
BackgroundFast Algorithms for Spherical Harmonic Expansions
Rokhlin, V., & Tygert, M. (2006) · SIAM Journal on Scientific Computing · doi:10.21236/ada461342 · Cited by 135 · cited 1×
“Accelerated schemes however exist for some sampling sets [see 39, 53, 54, for examples].”
BackgroundL-PICOLA: A parallel code for fast dark matter simulation
Howlett, C., Manera, M., & Percival, W. (2015) · Astronomy and Computing · doi:10.1016/j.ascom.2015.07.003 · Cited by 131 · cited 2× · see citing works
“L-PICOLA [72] is used for fast and approximate N-body simulations.”
MethodNon-Gaussian information from weak lensing data via deep learning
Gupta, A., Matilla, J. M. Z., Hsu, D., & Haiman, Z. (2018) · Physical Review D · doi:10.1103/physrevd.97.103515 · Cited by 128 · cited 4× · see citing works
“A typical global regression task is to infer the parameters of a cosmological model from maps [11, 23].”
BackgroundMethodInfluentialLearning Spherical Convolution for Fast Features from 360° ImageryPreprint
Su, Y.-C., & Grauman, K. L. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1708.00919 · Cited by 127 · cited 3× · see citing works
“One approach is to apply a standard 2D CNN to a grid discretisation of the sphere [20–22].”
BackgroundMethodLearning SO(3) Equivariant Representations with Spherical CNNs
Esteves, C., Allen-Blanchette, C., Makadia, A., & Daniilidis, K. (2019) · International Journal of Computer Vision · doi:10.1007/s11263-019-01220-1 · Cited by 119 · cited 3× · see citing works
“Ideally, we would compare DeepSphere to alternative spherical CNNs like [24] and [25].”
MethodInfluentialDeep learning from 21-cm tomography of the Cosmic Dawn and Reionization
Gillet, N., Mesinger, A., Greig, B., Liu, A., & Ucci, G. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz010 · Cited by 115 · see citing works
Geodesic Convolutional Shape OptimizationPreprint
Baqué, P., Remelli, E., Fleuret, F., & Fua, P. (2018) · International Conference on Machine Learning · doi:10.48550/arxiv.1802.04016 · Cited by 94 · cited 1× · see citing works
“Thanks to their versatility, graph neural networks have been used in a variety of tasks, such as identifying diseases from brain connectivity networks [61] or population graphs [62], designing drugs using molecular graphs [63], segmenting 3D point clouds [64], optimizing shapes to be aerodynamic [65], and many more.”
MethodEstimating Cosmological Parameters from the Dark Matter DistributionPreprint
Ravanbakhsh, S., Oliva, J. B., Fromenteau, S., Price, L. C., Ho, S., Schneider, J., & Póczos, B. (2016) · International Conference on Machine Learning · doi:10.48550/arxiv.1711.02033 · Cited by 90 · cited 1× · see citing works
“Convolutional Neural Networks (CNNs) have been proposed as an alternative analysis tool in cosmology thanks to their ability to automatically design relevant statistics to maximise the precision 1 of the parameter estimation [9–16], while maintaining robustness to noise.”
BackgroundCosmological constraints from noisy convergence maps through deep learning
Fluri, J., Kacprzak, T., Refregier, A., Amara, A., Lucchi, A., & Hofmann, T. (2018) · Physical Review D · doi:10.1103/physrevd.98.123518 · Cited by 83 · cited 4× · see citing works
“A typical global regression task is to infer the parameters of a cosmological model from maps [11, 23].”
BackgroundMethodInfluentialSelf-citationGraph-Based Classification of Omnidirectional Images
Pascal Frossard, B., & Khasanova, R. (2017) · IEEE International Conference on Computer Vision Workshops · doi:10.1109/iccvw.2017.106 · Cited by 76 · cited 2× · see citing works
“For example, [35] uses the inverse of the distance instead.”
MethodDark energy survey year 1 results: curved-sky weak lensing mass map
Chang, C., Pujol, A., Mawdsley, B., Bacon, D., Elvin-Poole, J., Melchior, P., Kovács, A., Jain, B., Leistedt, B., Giannantonio, T., et al. (2017) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stx3363 · Cited by 75 · see citing works
Self-citationLibsharp – spherical harmonic transforms revisited
Reinecke, M., & Seljebotn, D. S. (2013) · Astronomy and Astrophysics · doi:10.1051/0004-6361/201321494 · Cited by 75 · cited 3× · see citing works
“On a single core, a naive implementation of our method is ten to twenty times faster for N side = 2048, with K = 20 and K = 5, respectively, than using the spherical harmonic transform at (cid:96) max = 3 N side implemented by the highly optimized libsharp [39] library used by HEALPix.”
BackgroundMethodApproximate Fast Graph Fourier Transforms via Multilayer Sparse Approximations
Magoarou, L. L., Gribonval, R., & Tremblay, N. (2017) · IEEE Transactions on Signal and Information Processing over Networks · doi:10.1109/tsipn.2017.2710619 · Cited by 66 · cited 1× · see citing works
“As no efficient and general fast Fourier transform (FFT) exists for graphs [38], the execution of the Fourier transform by multiplication of the signal f by the dense matrix U costs O(N2 pix) operations.”
MethodGlobal and local uncertainty principles for signals on graphs
Perraudin, N., Ricaud, B., Shuman, D. I., & Vandergheynst, P. (2018) · APSIPA Transactions on Signal and Information Processing · doi:10.1017/atsip.2018.2 · Cited by 58 · see citing works
Self-citationDetecting cosmic strings in the CMB with the Canny algorithm
Amsel, S., Berger, J., & Brandenberger, R. (2007) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2008/04/015 · Cited by 58 · cited 1× · see citing works
“Segmentation and feature detection [41] are examples of dense classification tasks.”
BackgroundMachine learning cosmological structure formation
Lucie-Smith, L., Peiris, H., Pontzen, A., & Lochner, M. (2018) · Monthly notices of the Royal Astronomical Society · doi:10.1093/mnras/sty1719 · Cited by 56 · cited 1× · see citing works
“Convolutional Neural Networks (CNNs) have been proposed as an alternative analysis tool in cosmology thanks to their ability to automatically design relevant statistics to maximise the precision1 of the parameter estimation [9–16], while maintaining robustness to noise.”
BackgroundHop, P., Allgood, B., & Yu, J. (2018) · Molecular Pharmaceutics · doi:10.1021/acs.molpharmaceut.7b01144 · Cited by 53 · cited 1× · see citing works
“…graph neural networks have been used in a variety of tasks, such as identifying diseases from brain connectivity networks [61] or population graphs [62], designing drugs using molecular graphs [63], segmenting 3D point clouds [64], optimizing shapes to be aerodynamic [65], and many more.”
MethodKrachmalnicoff, N., & Tomasi, M. (2019) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201935211 · Cited by 47
Recent discoveries from the cosmic microwave background: a review of recent progress
Staggs, S. T., Dunkley, J., & Page, L. A. (2017) · Reports on Progress in Physics · doi:10.1088/1361-6633/aa94d5 · Cited by 45 · cited 1× · see citing works
“Observables that cover large parts of the sky, such as the Cosmic Microwave Background (CMB) [1–3], neutral hydrogen [4, 5], galaxy clustering [6], gravitational lensing [7, 8], and others, have been used to constrain cosmological and astrophysical models.”
BackgroundClassifying the large-scale structure of the universe with deep neural networks
Aragon-Calvo, M. (2018) · Monthly notices of the Royal Astronomical Society · doi:10.1093/mnras/stz393 · Cited by 42
Cosmological model discrimination with Deep LearningPreprint
Schmelzle, J., Lucchi, A., Kacprzak, T., Amara, A., Sgier, R., Réfrégier, A., & Hofmann, T. (2017) · arXiv (Cornell University) · doi:10.48550/arxiv.1707.05167 · Cited by 40 · cited 8× · see citing works
“This approach has been extensively used for cosmological maps [9, 11, 12, 23] and omnidirectional imaging [48, 49].”
BackgroundMethodInfluentialSelf-citationCosmological constraints from the convergence 1-point probability distribution
Patton, K., Blazek, J., Honscheid, K., Huff, E., Melchior, P., Ross, A., & Suchyta, E. (2016) · Monthly notices of the Royal Astronomical Society · doi:10.1093/mnras/stx1626 · Cited by 31 · cited 1×
“tures that are (i) the power spectral densities (PSD) of maps, and (ii) the histogram of pixels in the maps [72].”
BackgroundFast generation of covariance matrices for weak lensing
Sgier, R., Réfrégier, A., Amara, A., & Nicola, A. (2018) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2019/01/044 · Cited by 30 · cited 2× · see citing works
“The simulations are created using the fast lightcone method UFalcon described in [71].”
MethodSelf-citationA convolutional neural network for cosmic string detection in CMB temperature maps
Ciuca, R., Hern'andez, O. F., & Wolman, M. (2017) · Monthly notices of the Royal Astronomical Society · doi:10.1093/mnras/stz491 · Cited by 24 · see citing works
Harmonic inpainting of the cosmic microwave background sky: Formulation and error estimate
Inoue, K., Cabella, P., & Komatsu, E. (2008) · doi:10.1103/physrevd.77.123539 · Cited by 17 · cited 1×
“Some dense regression tasks are denoising, interpolation of missing values, or inpainting parts of a map [40].”
BackgroundPires, S., Starck, J., Leonard, A., & Refregier, A. R. (2012) · Chapman & Hall/CRC data mining and knowledge discovery series · doi:10.1201/b11822-19 · Cited by 16 · cited 1× · see citing works
“These kind of maps can be created using the gravitational lensing technique [see 29, for review].”
MethodReionization Models Classifier using 21cm Map Deep Learning
Hassan, S., Liu, A., Kohn, S., Aguirre, J., Plante, P. L., & Lidz, A. (2017) · Proceedings of the International Astronomical Union · doi:10.1017/s1743921317010833 · Cited by 4
Learning from deep learning: better cosmological parameter inference from weak lensing maps
Ribli, D., Pataki, B., & Csabai, I. (2018) · doi:10.48550/arxiv.1806.05995 · Cited by 3
(2018) · doi:10.4230/lipics.cp.2025.27 · cited 1×
“Another trend, parallel to the modeling of structured data, is the use of graph neural networks for relational reasoning [69].”
Background
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Deep learning modelling techniques: Current progress, applications, advantages, and challenges
Ahmed, S. F., Alam, M. S. B., Hassan, M., Rozbu, M. R., Ishtiak, T., Rafa, N., Mofijur, M., Shawkat Ali, A. B. M., & Gandomi, A. H. (2023) · Artificial Intelligence Review · doi:10.1007/s10462-023-10466-8 · Cited by 1,079 · see citing works
General E(2)-Equivariant Steerable CNNs
Weiler, M., & Cesa, G. (2019) · Neural Information Processing Systems · doi:10.48550/arxiv.1911.08251 · Cited by 755
“spherical CNNs [19, 5, 20, 21, 22, 23] or more general models of geometric deep learning [24, 25, 26, 27].”
BackgroundWeatherBench: A Benchmark Data Set for Data‐Driven Weather Forecasting
Rasp, S., Dueben, P. D., Scher, S., Weyn, J. A., Mouatadid, S., & Thuerey, N. (2020) · Journal of Advances in Modeling Earth Systems · doi:10.1029/2020ms002203 · Cited by 663 · see citing works
“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.”
BackgroundGauge Equivariant Convolutional Networks and the Icosahedral CNNPreprint
Cohen, T., Weiler, M., Kicanaoglu, B., & Welling, M. (2019) · arXiv (Cornell University) · doi:10.48550/arxiv.1902.04615 · Cited by 197 · see citing works
“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 & Grauman, 2017; Per…”
MethodInfluentialA General Theory of Equivariant CNNs on Homogeneous SpacesPreprint
Cohen, T., Geiger, M., & Weiler, M. (2018) · arXiv (Cornell University) · doi:10.48550/arxiv.1811.02017 · Cited by 70 · see citing works
Hyperbolic Deep Neural Networks: A Survey
Peng, W., Varanka, T., Mostafa, A., Shi, H., & Zhao, G. (2021) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2021.3136921 · Cited by 220 · see citing works
“Neural networks in the elliptic space [27], [28], [29], [30], using spherical harmonic transform or Laplacianbased graph convolution, have been successfully applied to”
MethodSpherical Message Passing for 3D Graph NetworksPreprint
Liu, Y., Wang, L., Liu, M., Zhang, X., Oztekin, B., & Ji, S. (2021) · arXiv (Cornell University) · doi:10.48550/arxiv.2102.05013 · Cited by 91 · see citing works
“Besides molecules, many other data objects are also represented as graphs, such as 3D point clouds (Guo et al., 2020; Simonovsky & Komodakis, 2017; Shen et al., 2018; Landrieu & Si-monovsky, 2018) and meshes (Bronstein et al., 2021; De Haan et al., 2020; Perraudin et al., 2019).”
BackgroundEbli, S., Defferrard, M., & Spreemann, G. (2020) · arXiv.org · doi:10.5281/zenodo.4309827 · Cited by 200
Self-citationLearning to predict the cosmological structure formation
He, S., Li, Y., Feng, Y., Ho, S., Ravanbakhsh, S., Chen, W., & Póczos, B. (2019) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1821458116 · Cited by 216 · see citing works
Gauge Equivariant Mesh CNNs: Anisotropic convolutions on geometric graphsPreprint
de Haan, P., Weiler, M., Cohen, T., & Welling, M. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2003.05425 · Cited by 63 · see citing works
“GCNs have been applied on spherical meshes (Perraudin et al., 2019) and cortical surfaces (Cucurull et al.”
MethodCosmological constraints with deep learning from KiDS-450 weak lensing maps
Fluri, J., Kacprzak, T., Lucchi, A., Refregier, A., Amara, A., Hofmann, T., & Schneider, A. (2019) · Physical Review D · doi:10.1103/physrevd.100.063514 · Cited by 151 · see citing works
Self-citationSurround-View Fisheye Camera Perception for Automated Driving: Overview, Survey & Challenges
Kumar, V. R., Eising, C., Witt, C., & Yogamani, S. K. (2023) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2023.3235057 · Cited by 121 · see citing works
“SphereNet [93] and its variants [94], [95], [96] formulate”
BackgroundGeometric deep learning and equivariant neural networks
Gerken, J. E., Aronsson, J., Carlsson, O., Linander, H., Ohlsson, F., Petersson, C., & Persson, D. (2023) · Artificial Intelligence Review · doi:10.1007/s10462-023-10502-7 · Cited by 69 · see citing works
“for fisheye cameras [3], cosmological data [6], weather data, molecular modeling [4] or diffusion MRI [5].”
BackgroundConditional Local Convolution for Spatio-Temporal Meteorological Forecasting
Lin, H., Gao, Z.-Y., Xu, Y., Wu, L.-R., Li, L., & Li, S. (2021) · AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i7.20711 · Cited by 127 · see citing works
“For the latter one, classical CNNs are usually used for intra-sequence temporal modeling.”
InfluentialDeepSphere: a graph-based spherical CNN
Defferrard, M., Milani, M., Gusset, F., & Perraudin, N. (2020) · International Conference on Learning Representations · doi:10.48550/arxiv.2012.15000 · Cited by 108
Self-citationThe Dawes Review 10: The impact of deep learning for the analysis of galaxy surveys
Huertas-Company, M., & Lanusse, F. (2023) · Publications of the Astronomical Society of Australia · doi:10.1017/pasa.2022.55 · Cited by 102 · see citing works
“More recently, (Wing Hei Yiu et al., 2021) extended that work to the sphere, using a DeepSphere (Perraudin et al., 2019b) graph convolutional architecture, to emulate the KiDS-1000 survey footprint as a function of (σ8,Ωm).”
BackgroundMethodInfluentialRashed, H., Mohamed, E., Sistu, G., Kumar, V., Eising, C., El-Sallab, A., & Yogamani, S. (2020) · IEEE Workshop/Winter Conference on Applications of Computer Vision · doi:10.1109/wacv48630.2021.00232 · Cited by 98 · see citing works
“SphereNet [3] and its variants [22, 27, 12] formulate CNNs on spherical surfaces.”
Applications and Techniques for Fast Machine Learning in Science
Deiana, A. M., Tran, N. V., Agar, J., Blott, M., Guglielmo, G. D., Duarte, J. M., Harris, P. C., Hauck, S., Liu, M., Neubauer, M. S., et al. (2022) · Frontiers in Big Data · doi:10.3389/fdata.2022.787421 · Cited by 81 · see citing works
Weak lensing cosmology with convolutional neural networks on noisy data
Ribli, D., Pataki, B., Matilla, J. M. Z., Hsu, D. J., Haiman, Z., & Csabai, I. (2019) · Monthly notices of the Royal Astronomical Society · doi:10.1093/mnras/stz2610 · Cited by 94 · see citing works
Large Scale Graph Learning from Smooth Signals
Kalofolias, V., & Perraudin, N. (2017) · International Conference on Learning Representations · doi:10.48550/arxiv.1710.05654 · Cited by 94
Self-citationLiDAR-Based Place Recognition For Autonomous Driving: A Survey
Zhang, Y.-J., Shi, P., & Li, J.-Y. (2023) · ACM Computing Surveys · doi:10.1145/3707446 · Cited by 86 · see citing works
Spin-Weighted Spherical CNNsPreprint
Esteves, C., Makadia, A., & Daniilidis, K. (2020) · Neural Information Processing Systems · doi:10.48550/arxiv.2006.10731 · Cited by 81 · see citing works
“Successful applications have been demonstrated in tasks such as 3D shape analysis [16, 18], medical imaging [42, 3], satellite/aerial imaging [13, 21], cosmology [13, 35], physics/chemistry [11, 26, 1].”
BackgroundMethodInfluentialDeepCMB: Lensing Reconstruction of the Cosmic Microwave Background with Deep Neural Networks
Caldeira, J., Wu, W., Nord, B., Avestruz, C., Trivedi, S., & Story, K. (2018) · Astronomy and Computing · doi:10.1016/j.ascom.2019.100307 · Cited by 76 · see citing works
“During the revision stages of this manuscript, other architectures have been proposed to address this issue (Perraudin et al., 2019; Krachmalnicoff and Tomasi, 2019).”
BackgroundMumuni, A., & Mumuni, F. (2021) · SN Computer Science · doi:10.1007/s42979-021-00735-0 · Cited by 71 · see citing works
Advancing Parsimonious Deep Learning Weather Prediction Using the HEALPix Mesh
Karlbauer, M., Cresswell-Clay, N., Durran, D., Moreno, R. A., Kurth, T., Bonev, B., Brenowitz, N. D., & Butz, M. V. (2023) · Journal of Advances in Modeling Earth Systems · doi:10.1029/2023ms004021 · Cited by 64 · see citing works
“Thus, Perraudin et al. (2019) explicitly define a graph from the HEALPix—by connecting adjacent neighbors with weighted edges—and perform a graph convolution to classify weak lensing maps from cosmology.”
Shi, N., Xu, J., Wurster, S. W., Guo, H.-Q., Woodring, J., van Roekel, L. V., & Shen, H. (2022) · IEEE Transactions on Visualization and Computer Graphics · doi:10.1109/tvcg.2022.3165345 · Cited by 61
“This weighting scheme performs well empirically, demonstrated in both DeepSphere [6] and our experiments.”
BackgroundMethodInfluentialVertex and energy reconstruction in JUNO with machine learning methods
Qian, Z., Belavin, V., Bokov, V., Brugnera, R., Compagnucci, A., Gavrikov, A., Garfagnini, A., Gonchar, M. O., Khatbullina, L., Li, Z., et al. (2021) · Nuclear Instruments and Methods in Physics Research Section A Accelerators Spectrometers Detectors and Associated Equipment · doi:10.1016/j.nima.2021.165527 · Cited by 51 · see citing works
“In this work, we adapt the DeepSphere model [46], previously used in cosmology, to the JUNO experiment.”
MethodClimate in a Bottle: Towards a Generative Foundation Model for the Kilometer-Scale Global Atmosphere
Brenowitz, N. D., Ge, T., Subramaniam, A., Manshausen, P., Gupta, A., Hall, D., Mardani, M., Vahdat, A., Kashinath, K., & Pritchard, M. S. (2025) · doi:10.48550/arxiv.2505.06474 · Cited by 56
“This structure is well-suited for deep-learning algorithms, especially for convolutional architectures and has been used in [31], [32] and [33]; the equal area property is also useful.”
de Haan, P., Cohen, T., & Welling, M. (2020) · Neural Information Processing Systems · doi:10.48550/arxiv.2007.08349 · Cited by 55
“We note that in addition to these methods, there are graph convolutional methods based on spectral rather than spatial techniques [Bruna et al., 2014, Defferrard et al., 2016, Perraudin et al., 2018].”
MethodSekkat, A. R., Dupuis, Y., Vasseur, P., & Honeiné, P. (2020) · Proceedings - IEEE International Conference on Robotics and Automation/Proceedings · doi:10.1109/icra40945.2020.9197144 · Cited by 45 · see citing works
“Much recent work, especially in deep learning applied on spherical images, have been confirming the need of omnidirectional image databases [16], [17], [18], [19], [20], [21], [22], [23].”
BackgroundA Hybrid Deep Learning Approach to Cosmological Constraints from Galaxy Redshift Surveys
Ntampaka, M., Eisenstein, D. J., Yuan, S., & Garrison, L. H. (2020) · The Astrophysical Journal · doi:10.3847/1538-4357/ab5f5e · Cited by 53 · see citing works
“However, the application of CNNs is not limited to flat Euclidean images (e.g., Perraudin et al. 2019), nor is it limited to two dimensions.”
BackgroundSpherical Sliced-WassersteinPreprint
Bonet, C., Berg, P., Courty, N., Septier, F., Drumetz, L., & Pham, M. (2022) · International Conference on Learning Representations · doi:10.48550/arxiv.2206.08780 · Cited by 48 · see citing works
“…learning solutions are being developed (Sra, 2018), but other applications concern for instance geophysical data (Di Marzio et al., 2014), meteorology (Besombes et al., 2021), cosmology (Perraudin et al., 2019) or extreme value theory for the estimation of spectral measures (Guillou et al., 2015).”
BackgroundKrachmalnicoff, N., & Tomasi, M. (2019) · Astronomy & Astrophysics · doi:10.1051/0004-6361/201935211 · Cited by 47
Efficient Generalized Spherical CNNs
Cobb, O., Wallis, C., Mavor-Parker, A. N., Marignier, A., Price, M. A., d'Avezac, M., & McEwen, J. (2020) · International Conference on Learning Representations · doi:10.48550/arxiv.2010.11661 · Cited by 45
“…on the sphere fall broadly into three categories: fully real (i.e. pixel) space approaches (e.g. Boomsma & Frellsen, 2017; Jiang et al., 2019; Perraudin et al., 2019; Cohen et al., 2019); combined real and harmonic space approaches (Cohen et al., 2018; Esteves et al., 2018; 2020); and fully…”
BackgroundA neural simulation-based inference approach for characterizing the Galactic Center γ-ray excess
Mishra-Sharma, S., & Cranmer, K. (2021) · Physical Review D · doi:10.1103/physrevd.105.063017 · Cited by 44 · see citing works
Guided Co-Modulated GAN for 360° Field of View Extrapolation
Dastjerdi, M. R. K., Hold-Geoffroy, Y., Eisenmann, J., Khodadadeh, S., & Lalonde, J.-F. (2022) · International Conference on 3D Vision · doi:10.1109/3dv57658.2022.00059 · Cited by 43 · see citing works
“It would be more natural to frame 360◦ FOV extrapolation using spherical representations [37, 46, 18], which presents another potential exciting direction for future work.”
BackgroundDecimated Framelet System on Graphs and Fast G-Framelet TransformsPreprint
Zheng, X., Zhong, B., Wang, Y. G., & Zhuang, X. (2020) · arXiv (Cornell University) · doi:10.48550/arxiv.2012.06922 · Cited by 25 · see citing works
“In physics, particles interact with each other following physics laws to form matters at different scales, such as atoms, molecules, planets, stars, solar systems, galaxies, and the whole universe Shlomi et al. (2020); Perraudin et al. (2019).”
BackgroundInfluentialRotation Equivariant Graph Convolutional Network for Spherical Image Classification
Yang, Q., Li, C.-L., Dai, W.-R., Zou, J.-N., Qi, G.-J., & Xiong, H. (2020) · Computer Vision and Pattern Recognition · doi:10.1109/cvpr42600.2020.00436 · Cited by 41 · see citing works
“[17] proposes a graph convolutional neural network for cosmological data that often come as spherical maps tailored by the Hierarchical Equal Area isoLatitude Pixelation (HEALPix).”
MethodHexagDLy - Processing hexagonally sampled data with CNNs in PyTorch
Steppa, C., & Holch, T. (2019) · SoftwareX · doi:10.1016/j.softx.2019.02.010 · Cited by 41 · see citing works
Direction of Arrival Estimation of Sound Sources Using Icosahedral CNNs
Díaz-Guerra, D., Miguel, A., & Beltrán, J. R. (2022) · IEEE/ACM Transactions on Audio Speech and Language Processing · doi:10.1109/taslp.2022.3224282 · Cited by 38 · see citing works
“Another approach is to analyze the spherical signal as a graph where each point is connected to its neighbors [32], [33], [34].”
BackgroundMethodFull-sky Cosmic Microwave Background Foreground Cleaning Using Machine Learning
Petroff, M., Addison, G., Bennett, C., & Weiland, J. (2020) · Astrophysical Journal · doi:10.3847/1538-4357/abb9a7 · Cited by 38 · see citing works
“However, this is not a complete solution, since the technique, as presented by Perraudin et al. (2019), only 1 The improved weighting scheme presented in Defferrard et al. (2020) was used. produces outputs suitable for regression or classification problems.”
BackgroundMethodDiffusion MRI with machine learning
Karimi, D., & Warfield, S. K. (2024) · Imaging Neuroscience · doi:10.1162/imag_a_00353 · Cited by 23 · see citing works
“Instead, they employ rotation-equivariant graph convolutions proposed in [210].”
Cosmological parameter estimation from large-scale structure deep learning
Pan, S., Liu, M.-X., Forero-Romero, J., Sabiu, C., Li, Z., Miao, H., & Li, X.-D. (2019) · Science China Physics Mechanics and Astronomy · doi:10.1007/s11433-020-1586-3 · Cited by 35 · see citing works
“…et al. 2019; Merten et al. 2019; Peel et al. 2019; Tewes et al. 2019), cosmic microwave background (Caldeira et al. 2018; Rodriguez et al. 2018; Perraudin et al. 2019; Mnchmeyer & Smith 2019; Mishra et al. 2019), cosmic large scale structure (Lucie-Smith et al. 2018; Modi et al. 2018; Berger &…”
BackgroundScalable and Equivariant Spherical CNNs by Discrete-Continuous (DISCO) Convolutions
Ocampo, J., Price, M. A., & McEwen, J. (2022) · International Conference on Learning Representations · doi:10.48550/arxiv.2209.13603 · Cited by 33
“Other approaches to spherical CNNs generally fall under the grid , graph or geodesic geometric deep learning categories yielding discrete approaches (Boomsma & Frellsen, 2017; Jiang et al., 2019; Zhang et al., 2019; Perraudin et al., 2019; Cohen et al., 2019).”
BackgroundFawaz, A., Williams, L., Alansary, A., Bass, C., Gopinath, K., da Silva, M., Dahan, S., Adamson, C., Alexander, B., Thompson, D. K., et al. (2021) · bioRxiv · doi:10.1101/2021.12.01.470730 · Cited by 33 · see citing works
“These include graphs e.g. patient relational data (Fang et al.,2021;Choi et al.,2020), chemical structures (Fout et al.,2017) and surfaces, both regular (Perraudin et al.,2019) and irregular (Gainza et al.,2020), with each motivating its own research directions.”
BackgroundScaling Spherical CNNsPreprint
Esteves, C., Slotine, J., & Makadia, A. (2023) · International Conference on Machine Learning · doi:10.48550/arxiv.2306.05420 · Cited by 32 · see citing works
“Perraudin et al. (2019) used a rotation equivariant graph CNN based on isotropic filters.”
MethodSPHARM-Net: Spherical Harmonics-Based Convolution for Cortical Parcellation
Ha, S.-Y., & Lyu, I. (2022) · IEEE Transactions on Medical Imaging · doi:10.1109/tmi.2022.3168670 · Cited by 32 · see citing works
“Some spherical CNNs [23], [24] can support rotation-equivariant convolution with a specific neighborhood definition, which might be promising to incorporate anatomical variability.”
BackgroundDeep learning in astronomy: a tutorial perspective
Meher, S., & Panda, G. (2021) · The European Physical Journal Special Topics · doi:10.1140/epjs/s11734-021-00207-9 · Cited by 32 · see citing works
Bidgoli, N. M., Azevedo, R. G. D. A., Maugey, T., Roumy, A., & Frossard, P. (2021) · IEEE Transactions on Image Processing · doi:10.1109/tip.2022.3202357 · Cited by 31 · see citing works
“Perraudin et al. [8] use Hierarchical Equal Area isoLatitude Pixelation (HEALPix) [29], and Yang et al. [28] use Geodesic ICOsahedral Pixelation (GICOPix).”
InfluentialHEAL-SWIN: A Vision Transformer on the Sphere
Carlsson, O., Gerken, J. E., Linander, H., Spiess, H., Ohlsson, F., Petersson, C., & Persson, D. (2023) · Computer Vision and Pattern Recognition · doi:10.1109/cvpr52733.2024.00580 · Cited by 30 · see citing works
“DeepSphere is a graph-based CNN which is rotationally equivariant for radial filters [11].”
PDO-eS2CNNs: Partial Differential Operator Based Equivariant Spherical CNNs
Shen, Z., Shen, T., Lin, Z.-C., & Ma, J.-W. (2021) · AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v35i11.17154 · Cited by 30 · see citing works
“For spherical data, some works (Bruna et al. 2014; Frossard and Khasanova 2017; Perraudin et al. 2019; Defferrard et al. 2020) represent the sampled sphere as a graph connecting pixels according to distance between them and utilize graph-based methods to process it.”
BackgroundMethodLabeling lateral prefrontal sulci using spherical data augmentation and context-aware training
Lyu, I., Bao, S., Hao, L., Yao, J. K., Miller, J. A., Voorhies, W. I., Taylor, W. D., Bunge, S. A., Weiner, K. S., & Landman, B. A. (2021) · NeuroImage · doi:10.1016/j.neuroimage.2021.117758 · Cited by 39 · see citing works
Scattering Networks on the Sphere for Scalable and Rotationally Equivariant Spherical CNNs
McEwen, J., Wallis, C., & Mavor-Parker, A. N. (2021) · International Conference on Learning Representations · doi:10.48550/arxiv.2102.02828 · Cited by 28
“, 2021); and (ii) those that are constructed on discretizations of the sphere and typically do not fully capture rotational equivariance (e.g. Boomsma & Frellsen, 2017; Jiang et al., 2019; Perraudin et al., 2019; Cohen et al., 2019).”
BackgroundDeepSphere: towards an equivariant graph-based spherical CNN
Defferrard, M., Perraudin, N., Kacprzak, T., & Sgier, R. (2019) · arXiv.org · doi:10.48550/arxiv.1904.05146 · Cited by 28
“DeepSphere is, however, easily used with other samplings as only two elements depend on it: (i) the choice of neighboring pixels when building the graph, and (ii) the choice of parent pixels when building the hierarchy.”
InfluentialSelf-citationElaldi, A., Dey, N., Kim, H., & Gerig, G. (2021) · Information Processing in Medical Imaging · doi:10.1007/978-3-030-78191-0_21 · Cited by 27 · see citing works
List, F., Rodd, N., Lewis, G., & Bhat, I. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.241102 · Cited by 27
Parameter estimation for the cosmic microwave background with Bayesian neural networks
Hortua, H. J., Volpi, R., Marinelli, D., & Malagò, L. (2020) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.102.103509 · Cited by 55 · see citing works
ST-GRF: Spatiotemporal graph neural networks for rainfall forecasting
Zhang, F., & Shao, Z. (2023) · Digit. Signal Process. · doi:10.1016/j.dsp.2023.103989 · Cited by 25
List, F., Rodd, N., & Lewis, G. (2021) · Physical Review D · doi:10.1103/physrevd.104.123022 · Cited by 25 · see citing works
Li, Q.-L., Zhang, C., Shangguan, W., Wei, Z.-W., Yuan, H., Zhu, J.-L., Li, X.-N., Li, L., Li, G., Liu, P., et al. (2023) · Expert systems with applications · doi:10.1016/j.eswa.2023.122917 · Cited by 24 · see citing works
Ćiprijanović, A., Kafkes, D., Snyder, G. F., Sánchez, J., Perdue, G., Pedro, K., Nord, B., Madireddy, S., & Wild, S. M. (2022) · Machine Learning Science and Technology · doi:10.1088/2632-2153/ac7f1a · Cited by 21 · see citing works
“, 2020), or cosmology via weak lensing (Perraudin et al., 2019).”
Spherical Image Generation from a Single Image by Considering Scene Symmetry
Hara, T., Mukuta, Y., & Harada, T. (2021) · AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v35i2.16242 · Cited by 24 · see citing works
“2018; Benjamin, Condurache, and Geiger 2018), and graph convolution on a sampled grid on a sphere (Khasanova and Frossard 2017; Perraudin et al. 2019; Yang et al. 2020), have also been proposed.”
BackgroundRibeiro, F. L., Bollmann, S., & Puckett, A. (2020) · bioRxiv · doi:10.1101/2020.02.11.934471 · Cited by 24 · see citing works
Survey on Fish-Eye Cameras and Their Applications in Intelligent Vehicles
Qian, Y., Yang, M. Z., & Dolan, J. M. (2022) · IEEE Transactions on Intelligent Transportation Systems · doi:10.1109/tits.2022.3210409 · Cited by 23 · see citing works
“In future work, various state-of-the-art deformable convolutional network structures [78], [79], [80], [81], [82], [83], [84] and domain adaptation methods should be developed in this field.”
BackgroundA generative model of galactic dust emission using variational autoencoders
Thorne, B., Knox, L., & Prabhu, K. (2021) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stab1011 · Cited by 23 · see citing works
Neural networks optimized by genetic algorithms in cosmology
Gómez-Vargas, I., Andrade, J. B., & Vazquez, J. (2022) · Physical Review D · doi:10.1103/physrevd.107.043509 · Cited by 22 · see citing works
“In cosmology, ANNs have recently been considered in several applications, such as, model-independent reconstructions (nonlinear regression) [2, 3, 4, 5, 6], to speed up numerical calculations [7, 8, 9, 10, 11] and on the classification of different objects [12, 13, 14, 11].”
MethodSpherical Multi-Modal Place Recognition for Heterogeneous Sensor Systems
Bernreiter, L., Ott, L., Nieto, J. I., Siegwart, R., & Cadena, C. (2021) · IEEE International Conference on Robotics and Automation · doi:10.1109/icra48506.2021.9561078 · Cited by 22
“Both modalities are projected onto the unit sphere and are given as an input to a spherical CNN [1]–[3].”
BackgroundMethodHexagonal Convolutional Neural Networks for Hexagonal Grids
Luo, J., Zhang, W., Su, J., & Xiang, F. (2019) · IEEE Access · doi:10.1109/access.2019.2944766 · Cited by 29 · see citing works
Classification of Protein-Binding Sites Using a Spherical Convolutional Neural Network
Scott, O. B., Gu, J., & Chan, A. W. E. (2022) · Journal of Chemical Information and Modeling · doi:10.1021/acs.jcim.2c00832 · Cited by 21 · see citing works
Machine Learning and CosmologyPreprint
Dvorkin, C., Mishra-Sharma, S., Nord, B., Villar, V., Avestruz, C., Bechtol, K., Ciprijanovic, A., Connolly, A. J., Garrison, L., Narayan, G., et al. (2022) · arXiv.org · doi:10.48550/arxiv.2203.08056 · Cited by 21 · see citing works
“Examples of these developments are custom spherical convolutional networks [112], efficient translation- and rotation-invariant normalizing flows [113], and fixed kernel-based”
BackgroundFluri, J., Kacprzak, T., Lucchi, A., Schneider, A., Réfrégier, A., & Hofmann, T. (2022) · Physical Review D · doi:10.1103/physrevd.105.083518 · Cited by 21 · see citing works
“The GCL of DeepSphere have the major advantage that they are approximately rotational equivariant.”
InfluentialSelf-citationBoosting deep neural networks with geometrical prior knowledge: a survey
Rath, M., & Condurache, A. (2020) · Artificial Intelligence Review · doi:10.1007/s10462-024-10722-5 · Cited by 21 · see citing works
“Perraudin et al. (2019) approximate the spherical convolution by treating the discrete sphere as a graph and applying a graph convolution.”
STHGCN: A spatiotemporal prediction framework based on higher-order graph convolution networks
Wang, J., Wang, W., Yu, W., Liu, X., Jia, K.-Y., Li, X., Zhong, M., Sun, Y.-H., & Xu, Y. (2022) · Knowledge-Based Systems · doi:10.1016/j.knosys.2022.109985 · Cited by 20 · see citing works
Equivariant Networks for Pixelized SpheresPreprint
Shakerinava, M., & Ravanbakhsh, S. (2021) · International Conference on Machine Learning · doi:10.48550/arxiv.2106.06662 · Cited by 19 · see citing works
“Some of the papers that more specifically consider the subgroups of the orthogonal group are (Cohen et al., 2018; Esteves et al., 2018; Perraudin et al., 2019; Anderson et al., 2019; Bogatskiy et al., 2020; Dym & Maron, 2020).”
BackgroundRecovering the CMB Signal with Machine Learning
Wang, G.-J., Shi, H., Yan, Y., Xia, J.-Q., Zhao, Y.-Y., Li, S.-Y., & Li, J.-F. (2022) · Astrophysical Journal Supplement Series · doi:10.3847/1538-4365/ac5f4a · Cited by 18 · see citing works
“In their analysis, a DeepSphere graph-based convolution (Perraudin et al. 2019) is adopted to the HEALPix sphere to extend traditional CNNs to the sphere, making this method suitable for full-sky CMB maps.”
MethodQuantum algorithms for group convolution, cross-correlation, and equivariant transformations
Castelazo, G., Nguyen, Q. T., Palma, G. D., Englund, D. R., Lloyd, S., & Kiani, B. T. (2022) · Physical Review A · doi:10.1103/physreva.106.032402 · Cited by 9 · see citing works
On the Predictability of Hrtfs from Ear Shapes Using Deep Networks
Zhou, Y., Jiang, H., & Ithapu, V. (2021) · IEEE International Conference on Acoustics, Speech, and Signal Processing · doi:10.1109/icassp39728.2021.9414042 · Cited by 17
“Existing works on classifying spherical inputs like [21, 22], although partly relevant, do not directly apply for our problem”
BackgroundEmulation of Cosmological Mass Maps with Conditional Generative Adversarial Networks
Perraudin, N., Marcon, S., Lucchi, A., & Kacprzak, T. (2020) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2021.673062 · Cited by 16 · see citing works
“Spherical convolutional neural networks architectures have been proposed (Perraudin et al., 2018; Krachmalnicoff and Tomasi, 2019; McEwen et al., 2021).”
BackgroundSelf-citationBister, T., Erdmann, M., Glombitza, J., Langner, N., Schulte, J., & Wirtz, M. (2020) · Astroparticle physics · doi:10.1016/j.astropartphys.2020.102527 · Cited by 16 · see citing works
Inferring dark matter substructure with astrometric lensing beyond the power spectrum
Mishra-Sharma, S. (2021) · Machine Learning: Science and Technology · doi:10.1088/2632-2153/ac494a · Cited by 15 · see citing works
HEAL-ViT: Vision Transformers on a spherical mesh for medium-range weather forecasting
Ramavajjala, V. (2024) · arXiv.org · doi:10.48550/arxiv.2403.17016 · Cited by 14
SphereGlue: Learning Keypoint Matching on High Resolution Spherical Images
Gava, C., Mukunda, V., Habtegebrial, T., Raue, F., Palacio, S. M., & Dengel, A. (2023) · 2023 IEEE/CVF Conference on Computer Vision and Pattern Recognition Workshops (CVPRW) · doi:10.1109/cvprw59228.2023.00653 · Cited by 14 · see citing works
“We adopt a spherical graph model [19–21, 47 ], where For simplicity, here A and B represent spherical images.”
BackgroundMethodInfluentialSpherical Image Generation From a Few Normal-Field-of-View Images by Considering Scene Symmetry
Hara, T., Mukuta, Y., & Harada, T. (2022) · IEEE Transactions on Pattern Analysis and Machine Intelligence · doi:10.1109/tpami.2022.3215933 · Cited by 14 · see citing works
“Other approaches that do not use 2D planar CNNs, such as generalized FFT-based CNNs on a sphere [48], [49], distortion-aware sampling [50], [51], and graph convolution on a sampled grid on a sphere [52], [53], [54], have also been proposed.”
BackgroundPseudocylindrical Convolutions for Learned Omnidirectional Image Compression
Li, M., Ma, K.-D., Li, J.-X., & Zhang, D. (2021) · IEEE transactions on circuits and systems for video technology (Print) · doi:10.1109/tcsvt.2025.3638018 · Cited by 14 · see citing works
“These methods are generally categorized by how they address sphere-to-plane distortions: 1) spatially adaptive convolutions [21], [22], 2) knowledge distillation [23], [24], and 3) reparameterization [25], [26], [27].”
Cosmological parameter estimation and inference using deep summaries
Fluri, J., Kacprzak, T., Réfrégier, A., Lucchi, A., & Hofmann, T. (2021) · Physical Review D · doi:10.1103/physrevd.104.123526 · Cited by 14 · see citing works
Self-citationAccelerating MCMC algorithms through Bayesian Deep Networks
Hort'ua, H. J., Volpi, R., Marinelli, D., & Malagò, L. (2020) · arXiv.org · doi:10.48550/arxiv.2011.14276 · Cited by 14
Mishra-Sharma, S., Tilburg, K. V., & Weiner, N. (2020) · doi:10.1103/physrevd.102.023026 · Cited by 14
Wang, M., Wang, J.-L., Yu, M., & Yang, F. (2024) · Scientific Reports · doi:10.1038/s41598-024-78303-8 · Cited by 13 · see citing works
GEORGIA: A Graph Neural Network Based EmulatOR for Glacial Isostatic Adjustment
Lin, Y.-C., Whitehouse, P., Valentine, A. P., & Woodroffe, S. (2023) · Geophysical Research Letters · doi:10.1029/2023gl103672 · Cited by 13 · see citing works
“For this study, we adopt the SCNN algorithms from the DeepSphere package (Defferrard et al., 2019, 2020), which has been successfully used in cosmological and weather prediction applications (Perraudin et al., 2019).”
BackgroundMethodGround state search by local and sequential updates of neural network quantum states
Zhang, W.-X., Xu, X., Wu, Z., Balachandran, V., & Poletti, D. (2023) · Physical review. B./Physical review. B · doi:10.1103/physrevb.107.165149 · Cited by 13 · see citing works
Cosmic Velocity Field Reconstruction Using AI
Wu, Z., Zhang, Z., Pan, S., Miao, H., Luo, X., Wang, X., Sabiu, C. G., Forero-Romero, J., Wang, Y., & Li, X.-D. (2021) · The Astrophysical Journal · doi:10.3847/1538-4357/abf3bb · Cited by 22 · see citing works
“…et al. 2020; Merten et al. 2019; Peel et al. 2019; Tewes et al. 2019), the cosmic microwave background (Caldeira et al. 2018; Rodriguez et al. 2018; Perraudin et al. 2019; Münchmeyer & Smith 2019; Mishra et al. 2019), the large-scale structure (Ravanbakhsh et al. 2017; Lucie-Smith et al. 2018;…”
BackgroundIdentifying nearby sources of ultra-high-energy cosmic rays with deep learning
Kalashev, O., Pshirkov, M., & Zotov, M. (2019) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2020/11/005 · Cited by 13
“A number of implementations for convolutional operations on the sphere were proposed recently [20–22].”
BackgroundScore‐Based Generative Emulation of Impact‐Relevant Earth System Model Outputs
Bouabid, S., Souza, A., & Ferrari, R. (2025) · Journal of Advances in Modeling Earth Systems · doi:10.1029/2025ms005558 · Cited by 12
Billings, G., & Johnson-Roberson, M. (2020) · IEEE Robotics and Automation Letters · doi:10.1109/lra.2020.2994036 · Cited by 12 · see citing works
“Beyond naively applying CNNs directly to a flattened equirectangular projection of an omni-directional image, which has been shown to suffer from the nonlinear distortions of the spherical mapping to the plane and attain sub-optimal performance [7], the methods of dealing with omni-directional distortions can be rough…”
MethodYang, Z.-K., Liu, J.-X., Duyang, H., Guo, W.-L., He, X.-H., Hu, Y.-X., Li, T., Liu, Z., Luo, W.-M., Luo, X.-J., et al. (2023) · Physical Review D · doi:10.1103/physrevd.109.052005 · Cited by 11
Yiu, T. W. H., Fluri, J., & Kacprzak, T. (2021) · Journal of Cosmology and Astroparticle Physics · doi:10.1088/1475-7516/2022/12/013 · Cited by 11 · see citing works
“The statistics of tomographic maps with z-bin 2 and 4 are excluded from the presented plots for the sake of clarity, as they look similar to (6)The 48 pixels at the vertices of the base dodecahedron have only 7 neighbouring pixels [51].”
BackgroundMethodInfluentialSelf-citationDeep learning the astrometric signature of dark matter substructure
Vattis, K., Toomey, M., & Koushiappas, S. (2020) · Physical Review D · doi:10.1103/physrevd.104.123541 · Cited by 11 · see citing works
Spherical Tree-Sliced Wasserstein Distance
Tran, H. V., Chu, T. T., Nguyen-Nhat, M.-K., Pham, H., Le, T., & Nguyen, T. (2025) · International Conference on Learning Representations · doi:10.48550/arxiv.2503.11249 · Cited by 10
“…2017; Pewsey & Garc ´ ıa-Portugu ´ es, 2021), geophysical data (Di Marzio et al., 2014), cosmology (Jupp, 1995; Cabella & Marinucci, 2009; Perraudin et al., 2019), texture mapping (Elad et al., 2005; Dominitz & Tannenbaum, 2009), magnetoencephalography imaging (Vrba & Robinson, 2001),…”
Cosmological particle production and pairwise hotspots on the CMB
Kim, J. H., Kumar, S., Martin, A., & Tsai, Y.-H. (2021) · Journal of High Energy Physics · doi:10.1007/jhep11(2021)158 · Cited by 10
Conditional Generative Modeling via Learning the Latent SpacePreprint
Ramasinghe, S., Ranasinghe, K., Khan, S. H., Barnes, N., & Gould, S. (2020) · International Conference on Learning Representations · doi:10.48550/arxiv.2010.03132 · Cited by 10 · see citing works
“Spherical harmonics and Zernike polynomials are orthogonal and complete functions in S2 and B3, respectively, hence, 3D point clouds can be represented by a set of coefficients corresponding to a linear combination of these functions Perraudin et al. (2019); Ramasinghe et al. (2019a;c).”
Background
- Authors
- Perraudin, N., Defferrard, M., Kacprzak, T., & Sgier, R.
- Affiliations
- Swiss Data Science Center (CH)
- École Polytechnique Fédérale de Lausanne (CH)
- ETH Zurich (CH)
- Corresponding author
- Perraudin, N.
- Venue
- Astronomy and Computing
- Publisher
- Elsevier BV
- Published
- 2019-04
- Volume
- 27
- Pages
- 130-146
- ISSN
- 2213-1337 (ISSN-L)
- OpenAlex
- W2898187790
- Cited by
- 184
- References
- 76
- Citations by year
- 2026: 9 · 2025: 24 · 2024: 22 · 2023: 23 · 2022: 29 · 2021: 33 · 2020: 28 · 2019: 14 · 2018: 1 · 2017: 1
- FWCI
- 13.88
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Astronomy and Computing (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- Infoscience (Ecole Polytechnique Fédérale de Lausanne) (submittedVersion, cc-by-nc-nd)
- arXiv (Cornell University)
- Funders
- Swiss Data Science Center (200021_169130)
- Topics
- Physical Sciences › Physics and Astronomy › Astronomy and Astrophysics › Cosmology and Gravitation Theories
- Physical Sciences › Computer Science › Computational Theory and Mathematics › Topological and Geometric Data Analysis
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Neural Network Applications
- Keywords
- spherical convolutional neural networks, HEALPix, graph convolutional networks, rotation equivariance, spherical maps
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Registry, retraction, Cites and statistics results are computed, not judged, with one exception: a printed reference that no index lists is read once by a model before it counts as a citation error. Claims are extracted by a model and kept only when their quote appears verbatim in the text; each cited source is then checked, with a model’s help, for whether it says what the claim relies on. Those verdicts can be wrong — read the claim’s quote and the cited source before relying on one.
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