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DeepSphere: Efficient spherical convolutional neural network with HEALPix sampling for cosmological applications
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Gradient-based learning applied to document recognition
Lecun, Y., Bottou, L., Bengio, Y., & Haffner, P. (1998) · Proceedings of the IEEE · doi:10.1109/5.726791 · Cited by 58,805 · cited 1×
“A CNN is composed of the following main building blocks [32]: (i) a convolution, (ii) a non-linearity, and, optionally, (iii) a down-sampling operation, (iv) a pooling operation, and (v) a normalization.”
BackgroundFully convolutional networks for semantic segmentation
Long, J., Shelhamer, E., & Darrell, T. (2015) · 2015 IEEE Conference on Computer Vision and Pattern Recognition (CVPR) · doi:10.1109/cvpr.2015.7298965 · Cited by 38,834 · cited 1×
“Fully convolutional networks (FCNs) have been introduced by [42] and are mostly used for the semantic segmentation of images, a dense classification task.”
MethodBatch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift
Ioffe, S., & Szegedy, C. (2015) · arXiv · doi:10.48550/arxiv.1502.03167 · Cited by 27,818 · cited 2×
“The batch normalization layer [33] computes Y = BN(X) such as”
BackgroundSEVEN-YEAR WILKINSON MICROWAVE ANISOTROPY PROBE(WMAP) OBSERVATIONS: COSMOLOGICAL INTERPRETATION
Komatsu, E., Smith, K. M., Dunkley, J., Bennett, C. L., Gold, B., Hinshaw, G., Jarosik, N., Larson, D., Nolta, M. R., Page, L., et al. (2011) · The Astrophysical Journal Supplement Series · doi:10.1088/0067-0049/192/2/18 · Cited by 8,802 · 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.”
BackgroundAdvances In Deep Learning On Graphs (Gsp'18 Workshop)Preprint
Defferrard, M., Bresson, X., & Vandergheynst, P. (2016) · arXiv (Cornell University) · doi:10.48550/arxiv.1606.09375 · Cited by 7,021 · cited 3×
“We use the graph CNN formulation introduced in [26], and a pooling strategy that exploits a hierarchical pixelisation of the sphere to analyse the data at multiple scales.”
MethodSelf-citationGórski, K., Hivon, E., Banday, A., Wandelt, B. D., Hansen, F., Reinecke, M., & Bartelmann, M. (2004) · The Astrophysical Journal · doi:10.1086/427976 · Cited by 5,217 · cited 3×
“As HEALPix [27] is our target application, we tailor the method to that particular sampling in the subsequent exposition.”
MethodPlanck 2015 results. II. Low Frequency Instrument data processings
Ade, P., Aghanim, N., Ashdown, M., Aumont, J., Baccigalupi, C., Ballardini, M., Banday, A., Barreiro, R., Bartolo, N., Basak, S., et al. (2013) · doi:10.1051/0004-6361/201525818 · Cited by 4,758
Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., & Vandergheynst, P. (2013) · IEEE Signal Processing Magazine · doi:10.1109/msp.2012.2235192 · Cited by 4,421 · cited 2×
“For this contribution, we chose the formulation of [26] as its root on strong graph signal processing theory makes the concept of convolutions and filters explicit [36].”
BackgroundMethodGeometric Deep Learning: Going beyond Euclidean data
Bronstein, M. M., Bruna, J., LeCun, Y., Szlam, A., & Vandergheynst, P. (2017) · IEEE Signal Processing Magazine · doi:10.1109/msp.2017.2693418 · Cited by 3,661 · cited 1×
“Many formulations of graph neural networks, reviewed by [59] and [60], have been proposed.”
BackgroundA Convolutional Neural Network for Modelling Sentences
Kalchbrenner, N., Grefenstette, E., & Blunsom, P. (2014) · Proceedings of the 52nd Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers) · doi:10.3115/v1/p14-1062 · Cited by 3,601 · cited 1×
“Second, they did not take 11 Heisenberg’s uncertainty principle states that a filter cannot be arbitrarily concentrated in one domain without being de-concentrated in the other. advantage of a hierarchical pixelization of the sphere and resorted to dynamic pooling [58].”
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- 2016, Planck 2015 results. xiii. cosmological parameters, Astron. Astrophys., 594, A13, 10.1051/0004-6361/201525830 · DOI
- Cohen, T.S., Geiger, M., Koehler, J., Welling, M., 2018. Spherical CNNs arXiv:1801.10130. · arXiv
- 2018. The Dark Energy Survey Data Release 1 arxiv:1801.03181. · arXiv
- Glorot, X., Bengio, Y., 2010. Understanding the difficulty of training deep feedforward neural networks, in: Proceedings of the Thirteenth International Conference on Artificial Intelligence and Statistics, pp. 249–256.
- Kingma, D.P., Ba, J., 2014. Adam: A method for stochastic optimization, arXiv:1412.6980. · arXiv
- Lin, M., Chen, Q., Yan, S., 2013. Network in network arXiv:1312.4400. · arXiv
- Troxel, M.A., MacCrann, N., Zuntz, J., Eifler, T.F., Krause, E., Dodelson, S., Gruen, D., Blazek, J., Friedrich, O., Samuroff, S., Prat, J., Secco, L.F., Davis, C., Ferté, A., DeRose, J., Alarcon, A., Amara, A., Baxter, E., Becker, M.R., Bernstein, G.M., Bridle, S.L., Cawthon, R., Chang, C., Choi, A., De Vicente, J., Drlica-Wagner, A., Elvin-Poole, J., Frieman, J., Gatti, M., Hartley, W.G., Honscheid, K., Hoyle, B., Huff, E.M., Huterer, D., Jain, B., Jarvis, M., Kacprzak, T., Kirk, D., Kokron, N., Krawiec, C., Lahav, O., Liddle, A.R., Peacock, J., Rau, M.M., Refregier, A., Rollins, R.P., Rozo, E., Rykoff, E.S., Sánchez, C., Sevilla-Noarbe, I., Sheldon, E., Stebbins, A., Varga, T.N., Vielzeuf, P., Wang, M., Wechsler, R.H., Yanny, B., Abbott, T.M.C., Abdalla, F.B., Allam, S., Annis, J., Bechtol, K., Benoit-Lévy, A., Bertin, E., Brooks, D., Buckley-Geer, E., Burke, D.L., Carnero Rosell, A., Carrasco Kind, M., Carretero, J., Castander, F.J., Crocce, M., Cunha, C.E., D’Andrea, C.B., da Costa, L.N., DePoy, D.L., Desai, S., Diehl, H.T., Dietrich, J.P., Doel, P., Fernandez, E., Flaugher, B., Fosalba, P., García-Bellido, J., Gaztanaga, E., Gerdes, D.W., Giannantonio, T., Goldstein, D.A., Gruendl, R.A., Gschwend, J., Gutierrez, G., James, D.J., Jeltema, T., Johnson, M.W.G., Johnson, M.D., Kent, S., Kuehn, K., Kuhlmann, S., Kuropatkin, N., Li, T.S., Lima, M., Lin, H., Maia, M.A.G., March, M., Marshall, J.L., Martini, P., Melchior, P., Menanteau, F., Miquel, R., Mohr, J.J., Neilsen, E., Nichol, R.C., Nord, B., Petravick, D., Plazas, A.A., Romer, A.K., Roodman, A., Sako, M., Sanchez, E., Scarpine, V., Schindler, R., Schubnell, M., Smith, M., Smith, R.C., Soares-Santos, M., Sobreira, F., Suchyta, E., Swanson, M.E.C., Tarle, G., Thomas, D., Tucker, D.L., Vikram, V., Walker, A.R., Weller, J., Zhang, Y., 2017. Dark energy survey year 1 results: Cosmological constraints from cosmic shear, arxiv:1708.01538. · DOI
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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
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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
“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
“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
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 250
“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
“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 238
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
“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
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 132
“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
“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., Xu, Y., Wu, L., Li, L., & Li, S. Z. (2022) · Proceedings of the AAAI Conference on Artificial Intelligence · doi:10.1609/aaai.v36i7.20711 · Cited by 108
“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
“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. R., Eising, C., El-Sallab, A., & Yogamani, S. K. (2021) · IEEE Winter Conference on Applications of Computer Vision · doi:10.1109/wacv48630.2021.00232 · Cited by 104
“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 104
Weak lensing cosmology with convolutional neural networks on noisy data
Ribli, D., Pataki, B., Matilla, J. M. Z., Hsu, D., Haiman, Z., & Csabai, I. (2019) · Monthly Notices of the Royal Astronomical Society · doi:10.1093/mnras/stz2610 · Cited by 120
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
Spin-Weighted Spherical CNNsPreprint
Esteves, C., Makadia, A., & Daniilidis, K. (2020) · Neural Information Processing Systems · doi:10.48550/arxiv.2006.10731 · Cited by 81
“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. L. K., Nord, B., Avestruz, C., Trivedi, S., & Story, K. T. (2019) · Astronomy and Computing · doi:10.1016/j.ascom.2019.100307 · Cited by 99
“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 74
Advancing Parsimonious Deep Learning Weather Prediction Using the HEALPix Mesh
Karlbauer, M., Cresswell‐Clay, N., Durran, D. R., Moreno, R. A., Kurth, T., Bonev, B., Brenowitz, N., & Butz, M. V. (2024) · Journal of Advances in Modeling Earth Systems · doi:10.1029/2023ms004021 · Cited by 58
“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., 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 59
“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 AtmospherePreprint
Brenowitz, N., Ge, T., Subramaniam, A., Manshausen, P., Gupta, A., Hall, D. M., Mardani, M., Vahdat, A., Kashinath, K., & Pritchard, M. S. (2025) · arXiv (Cornell University) · doi:10.48550/arxiv.2505.06474 · Cited by 54
“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
“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
“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
“…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
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
“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
“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
“[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. L. (2019) · SoftwareX · doi:10.1016/j.softx.2019.02.010 · Cited by 48
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
“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
“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
“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
“…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. Z. J., Alansary, A., Bass, C., Gopinath, K. K., da Silva, M., Dahan, S., Adamson, C. L., Alexander, B., Thompson, D. K., et al. (2021) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2021.12.01.470730 · Cited by 29
“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.-J. E., & Makadia, A. (2023) · arXiv (Cornell University) · doi:10.48550/arxiv.2306.05420 · Cited by 24
“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
“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. K., & Panda, G. (2021) · The European Physical Journal Special Topics · doi:10.1140/epjs/s11734-021-00207-9 · Cited by 37
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
“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. (2024) · IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings - IEEE Computer Society Conference on Computer Vision and Pattern Recognition/Proceedings · doi:10.1109/cvpr52733.2024.00580 · Cited by 16
“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
“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
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
List, F., Rodd, N. L., Lewis, G. F., & Bhat, I. (2020) · Physical Review Letters · doi:10.1103/physrevlett.125.241102 · Cited by 55
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
ST-GRF: Spatiotemporal graph neural networks for rainfall forecasting
Zhang, F.-H., & Shao, Z.-G. (2023) · Digital Signal Processing · doi:10.1016/j.dsp.2023.103989 · Cited by 23
Extracting the Galactic Center excess’ source-count distribution with neural nets
List, F., Rodd, N. L., & Lewis, G. F. (2021) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.104.123022 · Cited by 43
Li, Q., Zhang, C., Shangguan, W., Wei, Z., Yuan, H., Zhu, J., Li, X., Li, L., Li, G., Liu, P., et al. (2023) · Expert Systems with Applications · doi:10.1016/j.eswa.2023.122917 · Cited by 29
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 24
“, 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
“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. M. (2020) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/2020.02.11.934471 · Cited by 4
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
“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
Neural networks optimized by genetic algorithms in cosmology
Gómez-Vargas, I., Andrade, J. B., & Vazquez, J. A. (2023) · Physical review. D/Physical review. D. · doi:10.1103/physrevd.107.043509 · Cited by 26
“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
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
Machine Learning and CosmologyPreprint
Dvorkin, C., Mishra-Sharma, S., Nord, B., Villar, V. A., Avestruz, C., Bechtol, K., Ćiprijanović, A., Connolly, A. J., Garrison, L. H., Narayan, G., et al. (2022) · arXiv (Cornell University) · doi:10.48550/arxiv.2203.08056 · Cited by 52
“Examples of these developments are custom spherical convolutional networks [112], efficient translation- and rotation-invariant normalizing flows [113], and fixed kernel-based”
BackgroundFull wCDM analysis of KiDS-1000 weak lensing maps using deep learning
Fluri, J., Kacprzak, T., Lucchi, A., Schneider, A., Réfrégier, A., & Hofmann, T. (2022) · Physical Review D · doi:10.1103/physrevd.105.083518 · Cited by 21
“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. P. (2024) · Artificial Intelligence Review · doi:10.1007/s10462-024-10722-5 · Cited by 19
“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., Li, X., Zhong, M., Sun, Y., & Xu, Y. (2022) · Knowledge-Based Systems · doi:10.1016/j.knosys.2022.109985 · Cited by 20
Equivariant Networks for Pixelized SpheresPreprint
Shakerinava, M., & Ravanbakhsh, S. (2021) · International Conference on Machine Learning · doi:10.48550/arxiv.2106.06662 · Cited by 19
“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
“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
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. (2021) · Frontiers in Artificial Intelligence · doi:10.3389/frai.2021.673062 · Cited by 26
“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
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
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
“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
“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
“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
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., Yu, M., & Yang, F. (2024) · Scientific Reports · doi:10.1038/s41598-024-78303-8 · Cited by 8
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
“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 15
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
“…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
“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
“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
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
“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
Metadata
- 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
- 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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