Daily Papers

Fourier Neural Operators (FNOs) have proven to be an efficient and effective method for resolution-independent operator learning in a broad variety of application areas across scientific machine learning. A key reason for their success is their ability to accurately model long-range dependencies in spatio-temporal data by learning global convolutions in a computationally efficient manner. To this end, FNOs rely on the discrete Fourier transform (DFT), however, DFTs cause visual and spectral artifacts as well as pronounced dissipation when learning operators in spherical coordinates since they incorrectly assume a flat geometry. To overcome this limitation, we generalize FNOs on the sphere, introducing Spherical FNOs (SFNOs) for learning operators on spherical geometries. We apply SFNOs to forecasting atmospheric dynamics, and demonstrate stable auto\-regressive rollouts for a year of simulated time (1,460 steps), while retaining physically plausible dynamics. The SFNO has important implications for machine learning-based simulation of climate dynamics that could eventually help accelerate our response to climate change.

Neural operators learn mappings between function spaces, which is practical for learning solution operators of PDEs and other scientific modeling applications. Among them, the Fourier neural operator (FNO) is a popular architecture that performs global convolutions in the Fourier space. However, such global operations are often prone to over-smoothing and may fail to capture local details. In contrast, convolutional neural networks (CNN) can capture local features but are limited to training and inference at a single resolution. In this work, we present a principled approach to operator learning that can capture local features under two frameworks by learning differential operators and integral operators with locally supported kernels. Specifically, inspired by stencil methods, we prove that we obtain differential operators under an appropriate scaling of the kernel values of CNNs. To obtain local integral operators, we utilize suitable basis representations for the kernels based on discrete-continuous convolutions. Both these approaches preserve the properties of operator learning and, hence, the ability to predict at any resolution. Adding our layers to FNOs significantly improves their performance, reducing the relative L2-error by 34-72% in our experiments, which include a turbulent 2D Navier-Stokes and the spherical shallow water equations.

Spherical CNNs generalize CNNs to functions on the sphere, by using spherical convolutions as the main linear operation. The most accurate and efficient way to compute spherical convolutions is in the spectral domain (via the convolution theorem), which is still costlier than the usual planar convolutions. For this reason, applications of spherical CNNs have so far been limited to small problems that can be approached with low model capacity. In this work, we show how spherical CNNs can be scaled for much larger problems. To achieve this, we make critical improvements including novel variants of common model components, an implementation of core operations to exploit hardware accelerator characteristics, and application-specific input representations that exploit the properties of our model. Experiments show our larger spherical CNNs reach state-of-the-art on several targets of the QM9 molecular benchmark, which was previously dominated by equivariant graph neural networks, and achieve competitive performance on multiple weather forecasting tasks. Our code is available at https://github.com/google-research/spherical-cnn.

Rotation estimation of high precision from an RGB-D object observation is a huge challenge in 6D object pose estimation, due to the difficulty of learning in the non-linear space of SO(3). In this paper, we propose a novel rotation estimation network, termed as VI-Net, to make the task easier by decoupling the rotation as the combination of a viewpoint rotation and an in-plane rotation. More specifically, VI-Net bases the feature learning on the sphere with two individual branches for the estimates of two factorized rotations, where a V-Branch is employed to learn the viewpoint rotation via binary classification on the spherical signals, while another I-Branch is used to estimate the in-plane rotation by transforming the signals to view from the zenith direction. To process the spherical signals, a Spherical Feature Pyramid Network is constructed based on a novel design of SPAtial Spherical Convolution (SPA-SConv), which settles the boundary problem of spherical signals via feature padding and realizesviewpoint-equivariant feature extraction by symmetric convolutional operations. We apply the proposed VI-Net to the challenging task of category-level 6D object pose estimation for predicting the poses of unknown objects without available CAD models; experiments on the benchmarking datasets confirm the efficacy of our method, which outperforms the existing ones with a large margin in the regime of high precision.

We describe a novel method for the application of Convolutional Neural Networks (CNNs) to fields defined on the sphere, using the HEALPix tessellation scheme. Specifically, We have developed a pixel-based approach to implement convolutional layers on the spherical surface, similarly to what is commonly done for CNNs in Euclidian space. The algorithm is fully integrable with existing libraries for NNs (e.g., PyTorch or TensorFlow). We present two applications: (i) recognition of handwritten digits projected on the sphere; (ii) estimation of cosmological parameter from Cosmic Microwave Background (CMB) simulated maps. We have built a simple NN architecture, consisting in four convolutional+pooling layers, and have used it for all the applications explored herein. For what concerns the handwritten digits, our CNN reaches an accuracy of about 95%, comparable with other existing spherical CNNs. For CMB applications, we have tested the CNN on the estimation of a "mock" parameter, defining the angular scale at which the power spectrum of a Gaussian field projected on the sphere peaks. We have estimated this parameter directly from maps, in several cases: temperature and polarization, presence of noise and partial sky coverage. In all the cases, the NN performances are comparable with those from standard spectrum-based bayesian methods. We demonstrate, for the first time, the capability of CNNs to extract information from polarization fields and to distinguish between E and B-modes. Lastly, we have applied our CNN to the estimation of the Thomson scattering optical depth at reionization (tau) from simulated CMB maps. Even without any specific optimization of the NN architecture, we reach an accuracy comparable with standard bayesian methods. This work represents a first step towards the exploitation of NNs in CMB parameter estimation and demonstrates the feasibility of our approach.

Spherical equivariant graph neural networks (EGNNs) provide a principled framework for learning on three-dimensional molecular and biomolecular systems, where predictions must respect the rotational symmetries inherent in physics. These models extend traditional message-passing GNNs and Transformers by representing node and edge features as spherical tensors that transform under irreducible representations of the rotation group SO(3), ensuring that predictions change in physically meaningful ways under rotations of the input. This guide develops a complete, intuitive foundation for spherical equivariant modeling - from group representations and spherical harmonics, to tensor products, Clebsch-Gordan decomposition, and the construction of SO(3)-equivariant kernels. Building on this foundation, we construct the Tensor Field Network and SE(3)-Transformer architectures and explain how they perform equivariant message-passing and attention on geometric graphs. Through clear mathematical derivations and annotated code excerpts, this guide serves as a self-contained introduction for researchers and learners seeking to understand or implement spherical EGNNs for applications in chemistry, molecular property prediction, protein structure modeling, and generative modeling.

Learning feature representations of geographical space is vital for any machine learning model that integrates geolocated data, spanning application domains such as remote sensing, ecology, or epidemiology. Recent work mostly embeds coordinates using sine and cosine projections based on Double Fourier Sphere (DFS) features -- these embeddings assume a rectangular data domain even on global data, which can lead to artifacts, especially at the poles. At the same time, relatively little attention has been paid to the exact design of the neural network architectures these functional embeddings are combined with. This work proposes a novel location encoder for globally distributed geographic data that combines spherical harmonic basis functions, natively defined on spherical surfaces, with sinusoidal representation networks (SirenNets) that can be interpreted as learned Double Fourier Sphere embedding. We systematically evaluate the cross-product of positional embeddings and neural network architectures across various classification and regression benchmarks and synthetic evaluation datasets. In contrast to previous approaches that require the combination of both positional encoding and neural networks to learn meaningful representations, we show that both spherical harmonics and sinusoidal representation networks are competitive on their own but set state-of-the-art performances across tasks when combined. We provide source code at www.github.com/marccoru/locationencoder

Panorama has a full FoV (360^circtimes180^circ), offering a more complete visual description than perspective images. Thanks to this characteristic, panoramic depth estimation is gaining increasing traction in 3D vision. However, due to the scarcity of panoramic data, previous methods are often restricted to in-domain settings, leading to poor zero-shot generalization. Furthermore, due to the spherical distortions inherent in panoramas, many approaches rely on perspective splitting (e.g., cubemaps), which leads to suboptimal efficiency. To address these challenges, we propose DA^{2}: Depth Anything in Any Direction, an accurate, zero-shot generalizable, and fully end-to-end panoramic depth estimator. Specifically, for scaling up panoramic data, we introduce a data curation engine for generating high-quality panoramic depth data from perspective, and create sim543K panoramic RGB-depth pairs, bringing the total to sim607K. To further mitigate the spherical distortions, we present SphereViT, which explicitly leverages spherical coordinates to enforce the spherical geometric consistency in panoramic image features, yielding improved performance. A comprehensive benchmark on multiple datasets clearly demonstrates DA^{2}'s SoTA performance, with an average 38% improvement on AbsRel over the strongest zero-shot baseline. Surprisingly, DA^{2} even outperforms prior in-domain methods, highlighting its superior zero-shot generalization. Moreover, as an end-to-end solution, DA^{2} exhibits much higher efficiency over fusion-based approaches. Both the code and the curated panoramic data will be released. Project page: https://depth-any-in-any-dir.github.io/.

We present a new and general framework for convolutional neural network operations on spherical (or omnidirectional) images. Our approach represents the surface as a graph of connected points that doesn't rely on a particular sampling strategy. Additionally, by using an interpolated version of SelectionConv, we can operate on the sphere while using existing 2D CNNs and their weights. Since our method leverages existing graph implementations, it is also fast and can be fine-tuned efficiently. Our method is also general enough to be applied to any surface type, even those that are topologically non-simple. We demonstrate the effectiveness of our technique on the tasks of style transfer and segmentation for spheres as well as stylization for 3D meshes. We provide a thorough ablation study of the performance of various spherical sampling strategies.

Studying low-likelihood high-impact extreme weather events in a warming world is a significant and challenging task for current ensemble forecasting systems. While these systems presently use up to 100 members, larger ensembles could enrich the sampling of internal variability. They may capture the long tails associated with climate hazards better than traditional ensemble sizes. Due to computational constraints, it is infeasible to generate huge ensembles (comprised of 1,000-10,000 members) with traditional, physics-based numerical models. In this two-part paper, we replace traditional numerical simulations with machine learning (ML) to generate hindcasts of huge ensembles. In Part I, we construct an ensemble weather forecasting system based on Spherical Fourier Neural Operators (SFNO), and we discuss important design decisions for constructing such an ensemble. The ensemble represents model uncertainty through perturbed-parameter techniques, and it represents initial condition uncertainty through bred vectors, which sample the fastest growing modes of the forecast. Using the European Centre for Medium-Range Weather Forecasts Integrated Forecasting System (IFS) as a baseline, we develop an evaluation pipeline composed of mean, spectral, and extreme diagnostics. Using large-scale, distributed SFNOs with 1.1 billion learned parameters, we achieve calibrated probabilistic forecasts. As the trajectories of the individual members diverge, the ML ensemble mean spectra degrade with lead time, consistent with physical expectations. However, the individual ensemble members' spectra stay constant with lead time. Therefore, these members simulate realistic weather states, and the ML ensemble thus passes a crucial spectral test in the literature. The IFS and ML ensembles have similar Extreme Forecast Indices, and we show that the ML extreme weather forecasts are reliable and discriminating.

Singular regular points often arise in differential equations describing physical phenomena such as fluid dynamics, electromagnetism, and gravitation. Traditional numerical techniques often fail or become unstable near these points, requiring the use of semi-analytical tools, such as series expansions and perturbative methods, in combination with numerical algorithms; or to invoke more sophisticated methods. In this work, we take an alternative route and leverage the power of machine learning to exploit Physics Informed Neural Networks (PINNs) as a modern approach to solving ordinary differential equations with singular points. PINNs utilize deep learning architectures to approximate solutions by embedding the differential equations into the loss function of the neural network. We discuss the advantages of PINNs in handling singularities, particularly their ability to bypass traditional grid-based methods and provide smooth approximations across irregular regions. Techniques for enhancing the accuracy of PINNs near singular points, such as adaptive loss weighting, are used in order to achieve high efficiency in the training of the network. We exemplify our results by studying four differential equations of interest in mathematics and gravitation -- the Legendre equation, the hypergeometric equation, the solution for black hole space-times in theories of Lorentz violating gravity, and the spherical accretion of a perfect fluid in a Schwarzschild geometry.

Omnidirectional images (ODIs) have become increasingly popular, as their large field-of-view (FoV) can offer viewers the chance to freely choose the view directions in immersive environments such as virtual reality. The M\"obius transformation is typically employed to further provide the opportunity for movement and zoom on ODIs, but applying it to the image level often results in blurry effect and aliasing problem. In this paper, we propose a novel deep learning-based approach, called OmniZoomer, to incorporate the M\"obius transformation into the network for movement and zoom on ODIs. By learning various transformed feature maps under different conditions, the network is enhanced to handle the increasing edge curvatures, which alleviates the blurry effect. Moreover, to address the aliasing problem, we propose two key components. Firstly, to compensate for the lack of pixels for describing curves, we enhance the feature maps in the high-resolution (HR) space and calculate the transformed index map with a spatial index generation module. Secondly, considering that ODIs are inherently represented in the spherical space, we propose a spherical resampling module that combines the index map and HR feature maps to transform the feature maps for better spherical correlation. The transformed feature maps are decoded to output a zoomed ODI. Experiments show that our method can produce HR and high-quality ODIs with the flexibility to move and zoom in to the object of interest. Project page is available at http://vlislab22.github.io/OmniZoomer/.

Processing information on 3D objects requires methods stable to rigid-body transformations, in particular rotations, of the input data. In image processing tasks, convolutional neural networks achieve this property using rotation-equivariant operations. However, contrary to images, graphs generally have irregular topology. This makes it challenging to define a rotation-equivariant convolution operation on these structures. In this work, we propose Spherical Graph Convolutional Network (S-GCN) that processes 3D models of proteins represented as molecular graphs. In a protein molecule, individual amino acids have common topological elements. This allows us to unambiguously associate each amino acid with a local coordinate system and construct rotation-equivariant spherical filters that operate on angular information between graph nodes. Within the framework of the protein model quality assessment problem, we demonstrate that the proposed spherical convolution method significantly improves the quality of model assessment compared to the standard message-passing approach. It is also comparable to state-of-the-art methods, as we demonstrate on Critical Assessment of Structure Prediction (CASP) benchmarks. The proposed technique operates only on geometric features of protein 3D models. This makes it universal and applicable to any other geometric-learning task where the graph structure allows constructing local coordinate systems.

Recent advances in deep generative models have led to immense progress in 3D shape synthesis. While existing models are able to synthesize shapes represented as voxels, point-clouds, or implicit functions, these methods only indirectly enforce the plausibility of the final 3D shape surface. Here we present a 3D shape synthesis framework (SurfGen) that directly applies adversarial training to the object surface. Our approach uses a differentiable spherical projection layer to capture and represent the explicit zero isosurface of an implicit 3D generator as functions defined on the unit sphere. By processing the spherical representation of 3D object surfaces with a spherical CNN in an adversarial setting, our generator can better learn the statistics of natural shape surfaces. We evaluate our model on large-scale shape datasets, and demonstrate that the end-to-end trained model is capable of generating high fidelity 3D shapes with diverse topology.

We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and robotics, where preserving spherical symmetries and topology is essential for physical accuracy. By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant, providing strong inductive biases and leading to better performance than Cartesian approaches. To further enhance both scalability and model performance, we propose neighborhood attention on the sphere, which confines interactions to geodesic neighborhoods. This approach reduces computational complexity and introduces the additional inductive bias for locality, while retaining the symmetry properties of our method. We provide optimized CUDA kernels and memory-efficient implementations to ensure practical applicability. The method is validated on three diverse tasks: simulating shallow water equations on the rotating sphere, spherical image segmentation, and spherical depth estimation. Across all tasks, our spherical Transformers consistently outperform their planar counterparts, highlighting the advantage of geometric priors for learning on spherical domains.

Guided depth map super-resolution (GDSR), as a hot topic in multi-modal image processing, aims to upsample low-resolution (LR) depth maps with additional information involved in high-resolution (HR) RGB images from the same scene. The critical step of this task is to effectively extract domain-shared and domain-private RGB/depth features. In addition, three detailed issues, namely blurry edges, noisy surfaces, and over-transferred RGB texture, need to be addressed. In this paper, we propose the Spherical Space feature Decomposition Network (SSDNet) to solve the above issues. To better model cross-modality features, Restormer block-based RGB/depth encoders are employed for extracting local-global features. Then, the extracted features are mapped to the spherical space to complete the separation of private features and the alignment of shared features. Shared features of RGB are fused with the depth features to complete the GDSR task. Subsequently, a spherical contrast refinement (SCR) module is proposed to further address the detail issues. Patches that are classified according to imperfect categories are input into the SCR module, where the patch features are pulled closer to the ground truth and pushed away from the corresponding imperfect samples in the spherical feature space via contrastive learning. Extensive experiments demonstrate that our method can achieve state-of-the-art results on four test datasets, as well as successfully generalize to real-world scenes. The code is available at https://github.com/Zhaozixiang1228/GDSR-SSDNet.

Modeling the energy and forces of atomic systems is a fundamental problem in computational chemistry with the potential to help address many of the world's most pressing problems, including those related to energy scarcity and climate change. These calculations are traditionally performed using Density Functional Theory, which is computationally very expensive. Machine learning has the potential to dramatically improve the efficiency of these calculations from days or hours to seconds. We propose the Spherical Channel Network (SCN) to model atomic energies and forces. The SCN is a graph neural network where nodes represent atoms and edges their neighboring atoms. The atom embeddings are a set of spherical functions, called spherical channels, represented using spherical harmonics. We demonstrate, that by rotating the embeddings based on the 3D edge orientation, more information may be utilized while maintaining the rotational equivariance of the messages. While equivariance is a desirable property, we find that by relaxing this constraint in both message passing and aggregation, improved accuracy may be achieved. We demonstrate state-of-the-art results on the large-scale Open Catalyst dataset in both energy and force prediction for numerous tasks and metrics.

We present the first simulations of core-collapse supernovae in axial symmetry with feedback from fast neutrino flavor conversion (FFC). Our schematic treatment of FFCs assumes instantaneous flavor equilibration under the constraint of lepton-number conservation individually for each flavor. Systematically varying the spatial domain where FFCs are assumed to occur, we find that they facilitate SN explosions in low-mass (9-12 solar masses) progenitors that otherwise explode with longer time delays, whereas FFCs weaken the tendency to explode of higher-mass (around 20 solar masses) progenitors.

In this paper, we present GALEX-SDSS-WISE Legacy Catalog (GSWLC), a catalog of physical properties (stellar masses, dust attenuations and star formation rates (SFRs)) of ~700,000 galaxies with SDSS redshifts below 0.3. GSWLC contains galaxies within the GALEX footprint, regardless of a UV detection, covering 90% of SDSS. The physical properties were obtained from UV/optical SED fitting following Bayesian methodology of Salim et al. (2007), with improvements such as blending corrections for low-resolution UV photometry, flexible dust attenuation laws, and emission line corrections. GSWLC includes mid-IR SFRs derived from IR templates based upon 22 micron WISE observations. These estimates are independent of UV/optical SED fitting, in order to separate possible systematics. The paper argues that the comparison of specific SFRs (SSFRs) is more informative and physically motivated than the comparison of SFRs. SSFRs resulting from the UV/optical SED fitting are compared to the mid-IR SSFRs, and to SSFRs from three published catalogs. For "main sequence" galaxies with no AGN contribution all SSFRs are in very good agreement (within 0.1 dex on average). In particular, the widely-used aperture-corrected SFRs from MPA/JHU catalog show no systematic offsets, in contrast to some integral-field spectroscopy results. For galaxies below the main sequence (log SSFR<-11), mid-IR (S)SFRs based on fixed luminosity-SFR conversion are severely biased (up to 2 dex) because the dust is primarily heated by old stars. Furthermore, mid-IR (S)SFRs are overestimated by up to 0.6 dex for galaxies with AGN, presumably due to non-stellar dust heating. UV/optical (S)SFRs are thus preferred to IR-based (S)SFRs for quenched galaxies and those which host AGN.

As the most common representation for 3D shapes, mesh is often stored discretely with arrays of vertices and faces. However, 3D shapes in the real world are presented continuously. In this paper, we propose to learn a continuous representation for meshes with fixed topology, a common and practical setting in many faces-, hand-, and body-related applications. First, we split the template into multiple closed manifold genus-0 meshes so that each genus-0 mesh can be parameterized onto the unit sphere. Then we learn spherical implicit surface (SIS), which takes a spherical coordinate and a global feature or a set of local features around the coordinate as inputs, predicting the vertex corresponding to the coordinate as an output. Since the spherical coordinates are continuous, SIS can depict a mesh in an arbitrary resolution. SIS representation builds a bridge between discrete and continuous representation in 3D shapes. Specifically, we train SIS networks in a self-supervised manner for two tasks: a reconstruction task and a super-resolution task. Experiments show that our SIS representation is comparable with state-of-the-art methods that are specifically designed for meshes with a fixed resolution and significantly outperforms methods that work in arbitrary resolutions.

Graph neural networks that model 3D data, such as point clouds or atoms, are typically desired to be SO(3) equivariant, i.e., equivariant to 3D rotations. Unfortunately equivariant convolutions, which are a fundamental operation for equivariant networks, increase significantly in computational complexity as higher-order tensors are used. In this paper, we address this issue by reducing the SO(3) convolutions or tensor products to mathematically equivalent convolutions in SO(2) . This is accomplished by aligning the node embeddings' primary axis with the edge vectors, which sparsifies the tensor product and reduces the computational complexity from O(L^6) to O(L^3), where L is the degree of the representation. We demonstrate the potential implications of this improvement by proposing the Equivariant Spherical Channel Network (eSCN), a graph neural network utilizing our novel approach to equivariant convolutions, which achieves state-of-the-art results on the large-scale OC-20 and OC-22 datasets.

Deep face recognition has achieved great success due to large-scale training databases and rapidly developing loss functions. The existing algorithms devote to realizing an ideal idea: minimizing the intra-class distance and maximizing the inter-class distance. However, they may neglect that there are also low quality training images which should not be optimized in this strict way. Considering the imperfection of training databases, we propose that intra-class and inter-class objectives can be optimized in a moderate way to mitigate overfitting problem, and further propose a novel loss function, named sigmoid-constrained hypersphere loss (SFace). Specifically, SFace imposes intra-class and inter-class constraints on a hypersphere manifold, which are controlled by two sigmoid gradient re-scale functions respectively. The sigmoid curves precisely re-scale the intra-class and inter-class gradients so that training samples can be optimized to some degree. Therefore, SFace can make a better balance between decreasing the intra-class distances for clean examples and preventing overfitting to the label noise, and contributes more robust deep face recognition models. Extensive experiments of models trained on CASIA-WebFace, VGGFace2, and MS-Celeb-1M databases, and evaluated on several face recognition benchmarks, such as LFW, MegaFace and IJB-C databases, have demonstrated the superiority of SFace.

Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available at https://github.com/pavlo-melnyk/steerable-3d-neurons.

Panoramic imagery offers a full 360° field of view and is increasingly common in consumer devices. However, it introduces non-pinhole distortions that challenge joint pose estimation and 3D reconstruction. Existing feed-forward models, built for perspective cameras, generalize poorly to this setting. We propose PanoVGGT, a permutation-equivariant Transformer framework that jointly predicts camera poses, depth maps, and 3D point clouds from one or multiple panoramas in a single forward pass. The model incorporates spherical-aware positional embeddings and a panorama-specific three-axis SO(3) rotation augmentation, enabling effective geometric reasoning in the spherical domain. To resolve inherent global-frame ambiguity, we further introduce a stochastic anchoring strategy during training. In addition, we contribute PanoCity, a large-scale outdoor panoramic dataset with dense depth and 6-DoF pose annotations. Extensive experiments on PanoCity and standard benchmarks demonstrate that PanoVGGT achieves competitive accuracy, strong robustness, and improved cross-domain generalization. Code and dataset will be released.

Deep learning surrogate models have shown promise in solving partial differential equations (PDEs). Among them, the Fourier neural operator (FNO) achieves good accuracy, and is significantly faster compared to numerical solvers, on a variety of PDEs, such as fluid flows. However, the FNO uses the Fast Fourier transform (FFT), which is limited to rectangular domains with uniform grids. In this work, we propose a new framework, viz., geo-FNO, to solve PDEs on arbitrary geometries. Geo-FNO learns to deform the input (physical) domain, which may be irregular, into a latent space with a uniform grid. The FNO model with the FFT is applied in the latent space. The resulting geo-FNO model has both the computation efficiency of FFT and the flexibility of handling arbitrary geometries. Our geo-FNO is also flexible in terms of its input formats, viz., point clouds, meshes, and design parameters are all valid inputs. We consider a variety of PDEs such as the Elasticity, Plasticity, Euler's, and Navier-Stokes equations, and both forward modeling and inverse design problems. Geo-FNO is 10^5 times faster than the standard numerical solvers and twice more accurate compared to direct interpolation on existing ML-based PDE solvers such as the standard FNO.

The recent advancements in 3D Gaussian splatting (3D-GS) have not only facilitated real-time rendering through modern GPU rasterization pipelines but have also attained state-of-the-art rendering quality. Nevertheless, despite its exceptional rendering quality and performance on standard datasets, 3D-GS frequently encounters difficulties in accurately modeling specular and anisotropic components. This issue stems from the limited ability of spherical harmonics (SH) to represent high-frequency information. To overcome this challenge, we introduce Spec-Gaussian, an approach that utilizes an anisotropic spherical Gaussian (ASG) appearance field instead of SH for modeling the view-dependent appearance of each 3D Gaussian. Additionally, we have developed a coarse-to-fine training strategy to improve learning efficiency and eliminate floaters caused by overfitting in real-world scenes. Our experimental results demonstrate that our method surpasses existing approaches in terms of rendering quality. Thanks to ASG, we have significantly improved the ability of 3D-GS to model scenes with specular and anisotropic components without increasing the number of 3D Gaussians. This improvement extends the applicability of 3D GS to handle intricate scenarios with specular and anisotropic surfaces.

Data-driven deep learning models are transforming global weather forecasting. It is an open question if this success can extend to climate modeling, where the complexity of the data and long inference rollouts pose significant challenges. Here, we present the first conditional generative model that produces accurate and physically consistent global climate ensemble simulations by emulating a coarse version of the United States' primary operational global forecast model, FV3GFS. Our model integrates the dynamics-informed diffusion framework (DYffusion) with the Spherical Fourier Neural Operator (SFNO) architecture, enabling stable 100-year simulations at 6-hourly timesteps while maintaining low computational overhead compared to single-step deterministic baselines. The model achieves near gold-standard performance for climate model emulation, outperforming existing approaches and demonstrating promising ensemble skill. This work represents a significant advance towards efficient, data-driven climate simulations that can enhance our understanding of the climate system and inform adaptation strategies.

The increasing demand for AR/VR applications has highlighted the need for high-quality 360-degree panoramic content. However, generating high-quality 360-degree panoramic images and videos remains a challenging task due to the severe distortions introduced by equirectangular projection (ERP). Existing approaches either fine-tune pretrained diffusion models on limited ERP datasets or attempt tuning-free methods that still rely on ERP latent representations, leading to discontinuities near the poles. In this paper, we introduce SphereDiff, a novel approach for seamless 360-degree panoramic image and video generation using state-of-the-art diffusion models without additional tuning. We define a spherical latent representation that ensures uniform distribution across all perspectives, mitigating the distortions inherent in ERP. We extend MultiDiffusion to spherical latent space and propose a spherical latent sampling method to enable direct use of pretrained diffusion models. Moreover, we introduce distortion-aware weighted averaging to further improve the generation quality in the projection process. Our method outperforms existing approaches in generating 360-degree panoramic content while maintaining high fidelity, making it a robust solution for immersive AR/VR applications. The code is available here. https://github.com/pmh9960/SphereDiff

Scientific machine learning and the advent of the Physics-Informed Neural Network (PINN) show considerable potential in their capacity to identify solutions to complex differential equations. Over the past two years, much work has gone into the development of PINNs capable of solving the gravity field modeling problem -- i.e.\ learning a differentiable form of the gravitational potential from position and acceleration estimates. While the past PINN gravity models (PINN-GMs) have demonstrated advantages in model compactness, robustness to noise, and sample efficiency; there remain key modeling challenges which this paper aims to address. Specifically, this paper introduces the third generation of the Physics-Informed Neural Network Gravity Model (PINN-GM-III) which solves the problems of extrapolation error, bias towards low-altitude samples, numerical instability at high-altitudes, and compliant boundary conditions through numerous modifications to the model's design. The PINN-GM-III is tested by modeling a known heterogeneous density asteroid, and its performance is evaluated using seven core metrics which showcases its strengths against its predecessors and other analytic and numerical gravity models.

Cross-view geo-localization (CVGL) aims to establish spatial correspondences between images captured from significantly different viewpoints and constitutes a fundamental technique for visual localization in GNSS-denied environments. Nevertheless, CVGL remains challenging due to severe geometric asymmetry, texture inconsistency across imaging domains, and the progressive degradation of discriminative local information. Existing methods predominantly rely on spatial domain feature alignment, which is inherently sensitive to large scale viewpoint variations and local disturbances. To alleviate these limitations, this paper proposes the Spatial and Frequency Domain Enhancement Network (SFDE), which leverages complementary representations from spatial and frequency domains. SFDE adopts a three branch parallel architecture to model global semantic context, local geometric structure, and statistical stability in the frequency domain, respectively, thereby characterizing consistency across domains from the perspectives of scene topology, multiscale structural patterns, and frequency invariance. The resulting complementary features are jointly optimized in a unified embedding space via progressive enhancement and coupled constraints, enabling the learning of cross-view representations with consistency across multiple granularities. Comprehensive experiments show that SFDE achieves competitive performance and in many cases even surpasses state-of-the-art methods, while maintaining a lightweight and computationally efficient design. {Our code is available at https://github.com/Mashuaishuai669/SFDE

We propose a new method to determine the shape of the gravitational potential of the dark matter (DM) halo of the Milky Way (MW) with the galactocentric tangential velocities of a sample of hypervelocity stars (HVSs). We compute the trajectories of different samples of HVSs in a MW where the baryon distribution is axisymmetric and the DM potential either is spherical or is spheroidal or triaxial with radial-dependent axis ratios. We determine the shape of the DM potential with the distribution of the latitudinal velocity |v_{vartheta}| in axisymmetric Galactic potentials, or with the distribution of |v_{vartheta}| and of a function bar v_{varphi} of the azimuthal velocity in non-axisymmetric Galactic potentials. We recover the correct shape of the DM potential by comparing the distribution of |v_{vartheta}| and bar v_{varphi} against the corresponding distributions of mock samples of HVSs that traveled in DM halos of different shapes. We use the largest possible sample of sim 800 HVSs of 4~M_odot ejected with the Hills mechanism at a rate sim 10^{-4} yr^{-1}, currently outgoing, and located at more than 10 kpc from the Galactic center. In our ideal case of galactocentric velocities with null uncertainties and no observational limitations, our method recovers the correct shape of the DM potential with a success rate Sgtrsim 89% in axisymmetric Galactic potentials, and S > 96% in the explored non-axisymmetric cases. The unsuccessful cases yield axis ratios of the DM potential that are off by pm 0.1. The success rate decreases with decreasing sample size: for example, for a spherical DM halo, S drops from sim 98% to sim 38% when the sample size decreases from sim 800 to sim 40 HVSs. A robust determination of the shape of the DM potential thus requires the measure of the galactocentric velocity of a few hundred genuine HVSs.

We present a parsimonious deep learning weather prediction model to forecast seven atmospheric variables with 3-h time resolution for up to one-year lead times on a 110-km global mesh using the Hierarchical Equal Area isoLatitude Pixelization (HEALPix). In comparison to state-of-the-art (SOTA) machine learning (ML) weather forecast models, such as Pangu-Weather and GraphCast, our DLWP-HPX model uses coarser resolution and far fewer prognostic variables. Yet, at one-week lead times, its skill is only about one day behind both SOTA ML forecast models and the SOTA numerical weather prediction model from the European Centre for Medium-Range Weather Forecasts. We report several improvements in model design, including switching from the cubed sphere to the HEALPix mesh, inverting the channel depth of the U-Net, and introducing gated recurrent units (GRU) on each level of the U-Net hierarchy. The consistent east-west orientation of all cells on the HEALPix mesh facilitates the development of location-invariant convolution kernels that successfully propagate weather patterns across the globe without requiring separate kernels for the polar and equatorial faces of the cube sphere. Without any loss of spectral power after the first two days, the model can be unrolled autoregressively for hundreds of steps into the future to generate realistic states of the atmosphere that respect seasonal trends, as showcased in one-year simulations.

The increasing availability of large-scale global datasets has generated a demand for scalable spatial prediction methods defined on spherical domains. Classical spatial models that rely on Euclidean distance representations are inappropriate for spherical data because planar projections distort geodesic distances and spatial neighborhood structures, while traditional kriging-based prediction methods are often computationally prohibitive for massive datasets. To address these challenges, we propose a Spherical DeepKriging framework for spatial prediction on S^2. The proposed approach constructs a flexible prediction model by integrating thin-plate spline (TPS) basis functions defined intrinsically on the sphere. Simulation studies and real data analyses are presented to demonstrate the superior predictive performance of the proposed method.

Scaling large models requires optimization strategies that ensure rapid convergence grounded in stability. Maximal Update Parametrization (boldsymbolμP) provides a theoretical safeguard for width-invariant Θ(1) activation control, whereas emerging optimizers like Muon are only ``half-aligned'' with these constraints: they control updates but allow weights to drift. To address this limitation, we introduce the Spectral Sphere Optimizer (SSO), which enforces strict module-wise spectral constraints on both weights and their updates. By deriving the steepest descent direction on the spectral sphere, SSO realizes a fully boldsymbolμP-aligned optimization process. To enable large-scale training, we implement SSO as an efficient parallel algorithm within Megatron. Through extensive pretraining on diverse architectures, including Dense 1.7B, MoE 8B-A1B, and 200-layer DeepNet models, SSO consistently outperforms AdamW and Muon. Furthermore, we observe significant practical stability benefits, including improved MoE router load balancing, suppressed outliers, and strictly bounded activations.

We present SF3D, a novel method for rapid and high-quality textured object mesh reconstruction from a single image in just 0.5 seconds. Unlike most existing approaches, SF3D is explicitly trained for mesh generation, incorporating a fast UV unwrapping technique that enables swift texture generation rather than relying on vertex colors. The method also learns to predict material parameters and normal maps to enhance the visual quality of the reconstructed 3D meshes. Furthermore, SF3D integrates a delighting step to effectively remove low-frequency illumination effects, ensuring that the reconstructed meshes can be easily used in novel illumination conditions. Experiments demonstrate the superior performance of SF3D over the existing techniques. Project page: https://stable-fast-3d.github.io

360-degree images offer a significantly wider field of view compared to traditional pinhole cameras, enabling sparse sampling and dense 3D reconstruction in low-texture environments. This makes them crucial for applications in VR, AR, and related fields. However, the inherent distortion caused by the wide field of view affects feature extraction and matching, leading to geometric consistency issues in subsequent multi-view reconstruction. In this work, we propose 360Recon, an innovative MVS algorithm for ERP images. The proposed spherical feature extraction module effectively mitigates distortion effects, and by combining the constructed 3D cost volume with multi-scale enhanced features from ERP images, our approach achieves high-precision scene reconstruction while preserving local geometric consistency. Experimental results demonstrate that 360Recon achieves state-of-the-art performance and high efficiency in depth estimation and 3D reconstruction on existing public panoramic reconstruction datasets.

Do contemporary diffusion models preserve the class geometry of hyperspherical data? Standard diffusion models rely on isotropic Gaussian noise in the forward process, inherently favoring Euclidean spaces. However, many real-world problems involve non-Euclidean distributions, such as hyperspherical manifolds, where class-specific patterns are governed by angular geometry within hypercones. When modeled in Euclidean space, these angular subtleties are lost, leading to suboptimal generative performance. To address this limitation, we introduce HyperSphereDiff to align hyperspherical structures with directional noise, preserving class geometry and effectively capturing angular uncertainty. We demonstrate both theoretically and empirically that this approach aligns the generative process with the intrinsic geometry of hyperspherical data, resulting in more accurate and geometry-aware generative models. We evaluate our framework on four object datasets and two face datasets, showing that incorporating angular uncertainty better preserves the underlying hyperspherical manifold. Resources are available at: {https://github.com/IAB-IITJ/Harmonizing-Geometry-and-Uncertainty-Diffusion-with-Hyperspheres/}

We present Hubble Space Telescope (HST) imaging of Pegasus V and Pisces VII, along with a re-analysis of the archival imaging of Pegasus W, and Jansky Very Large Array (VLA) neutral gas (HI) observations of all three. These three ultra-faint dwarfs (UFDs) are all within the Local Group in the approximate direction of M31. The VLA observations place stringent upper limits on their HI content, with all having M_HI < 10^4;M_odot. As the red giant branches of these UFDs are sparsely populated, we determined distances from the HST photometry of horizontal branch (HB) stars in comparison to a fiducial HB population (from M92), with all three falling in the range 0.7-1 Mpc. Using a new Python-based star formation history (SFH) fitting code (based on StarFISH), we derive SFHs of all three UFDs. As found previously, the best fit SFH for Pegasus W includes significant star formation well beyond the end of reionization, while the SFHs calculated for Pegasus V and Pisces VII are consistent with them having quenched shortly after reionization. These findings for the latter two objects indicate that, like those in the vicinity of the Milky Way, lower mass UFDs in the vicinity of M31 likely quenched at early times.

Novel view synthesis (NVS) enables to generate new images of a scene or convert a set of 2D images into a comprehensive 3D model. In the context of Space Domain Awareness, since space is becoming increasingly congested, NVS can accurately map space objects and debris, improving the safety and efficiency of space operations. Similarly, in Rendezvous and Proximity Operations missions, 3D models can provide details about a target object's shape, size, and orientation, allowing for better planning and prediction of the target's behavior. In this work, we explore the generalization abilities of these reconstruction techniques, aiming to avoid the necessity of retraining for each new scene, by presenting a novel approach to 3D spacecraft reconstruction from single-view images, DreamSat, by fine-tuning the Zero123 XL, a state-of-the-art single-view reconstruction model, on a high-quality dataset of 190 high-quality spacecraft models and integrating it into the DreamGaussian framework. We demonstrate consistent improvements in reconstruction quality across multiple metrics, including Contrastive Language-Image Pretraining (CLIP) score (+0.33%), Peak Signal-to-Noise Ratio (PSNR) (+2.53%), Structural Similarity Index (SSIM) (+2.38%), and Learned Perceptual Image Patch Similarity (LPIPS) (+0.16%) on a test set of 30 previously unseen spacecraft images. Our method addresses the lack of domain-specific 3D reconstruction tools in the space industry by leveraging state-of-the-art diffusion models and 3D Gaussian splatting techniques. This approach maintains the efficiency of the DreamGaussian framework while enhancing the accuracy and detail of spacecraft reconstructions. The code for this work can be accessed on GitHub (https://github.com/ARCLab-MIT/space-nvs).

Developing equivariant neural networks for the E(3) group plays an important role in modeling 3D data across real-world applications. Enforcing this equivariance primarily involves the tensor products of irreducible representations (irreps). However, the computational complexity of such operations increases significantly as higher-order tensors are used. In this work, we propose a systematic approach to substantially accelerate the computation of the tensor products of irreps. We mathematically connect the commonly used Clebsch-Gordan coefficients to the Gaunt coefficients, which are integrals of products of three spherical harmonics. Through Gaunt coefficients, the tensor product of irreps becomes equivalent to the multiplication between spherical functions represented by spherical harmonics. This perspective further allows us to change the basis for the equivariant operations from spherical harmonics to a 2D Fourier basis. Consequently, the multiplication between spherical functions represented by a 2D Fourier basis can be efficiently computed via the convolution theorem and Fast Fourier Transforms. This transformation reduces the complexity of full tensor products of irreps from O(L^6) to O(L^3), where L is the max degree of irreps. Leveraging this approach, we introduce the Gaunt Tensor Product, which serves as a new method to construct efficient equivariant operations across different model architectures. Our experiments on the Open Catalyst Project and 3BPA datasets demonstrate both the increased efficiency and improved performance of our approach.

We consider Proca field perturbations in a five-dimensional Schwarzschild-anti-de Sitter (Schwarzschild-AdS_{5}) black hole geometry. Using the vector spherical harmonic (VSH) method, we show that the Proca field decomposes into scalar-type and vector-type components according to their tensorial behavior on the three-sphere. Two degrees of freedom of the field are described by scalar-type components, which are coupled due to the mass term, while the remaining two degrees of freedom are described by a vector-type component, which decouples completely. Motivated by the Frolov-Krtouš-Kubizňák-Santos (FKKS) ansatz in the limit of zero spin, we use a field transformation to decouple the scalar-type components at the expense of introducing a complex separation parameter β. This parameter can be determined analytically, and its values correspond to two distinct polarizations of the scalar-type sector: "electromagnetic" and "non-electromagnetic", denoted by β_{+} and β_{-}, respectively. In the scalar-type sector, the radial differential equation for each polarization is a Fuchsian differential equation with five singularities, whereas in the vector-type sector, the radial equation has four singularities. By means of the isomonodromy method, we reformulate the boundary value problem in terms of the initial conditions of the Painlevé VI τ function and, using a series expansion of the τ function, we compute the scalar-type and vector-type quasinormal modes (QNMs) in the small horizon limit. Our results are in overall very good agreement with those obtained via the numerical integration method. This shows that the isomonodromy method is a reliable method to compute quasinormal modes in the small horizon limit with high accuracy.

We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for nearest neighbors queries. In this first installment we provide three types of queries: bubble, shell and the nth-nearest; as well as three different metrics of interest in astronomy: the euclidean and two distance functions in spherical coordinates of varying precision, haversine and Vincenty; and the possibility of providing a custom distance function. This package results particularly useful for large datasets where a brute-force search turns impractical.

FourCastNet 3 advances global weather modeling by implementing a scalable, geometric machine learning (ML) approach to probabilistic ensemble forecasting. The approach is designed to respect spherical geometry and to accurately model the spatially correlated probabilistic nature of the problem, resulting in stable spectra and realistic dynamics across multiple scales. FourCastNet 3 delivers forecasting accuracy that surpasses leading conventional ensemble models and rivals the best diffusion-based methods, while producing forecasts 8 to 60 times faster than these approaches. In contrast to other ML approaches, FourCastNet 3 demonstrates excellent probabilistic calibration and retains realistic spectra, even at extended lead times of up to 60 days. All of these advances are realized using a purely convolutional neural network architecture tailored for spherical geometry. Scalable and efficient large-scale training on 1024 GPUs and more is enabled by a novel training paradigm for combined model- and data-parallelism, inspired by domain decomposition methods in classical numerical models. Additionally, FourCastNet 3 enables rapid inference on a single GPU, producing a 60-day global forecast at 0.25{\deg}, 6-hourly resolution in under 4 minutes. Its computational efficiency, medium-range probabilistic skill, spectral fidelity, and rollout stability at subseasonal timescales make it a strong candidate for improving meteorological forecasting and early warning systems through large ensemble predictions.

Learning 3D representations that generalize well to arbitrarily oriented inputs is a challenge of practical importance in applications varying from computer vision to physics and chemistry. We propose a novel multi-resolution convolutional architecture for learning over concentric spherical feature maps, of which the single sphere representation is a special case. Our hierarchical architecture is based on alternatively learning to incorporate both intra-sphere and inter-sphere information. We show the applicability of our method for two different types of 3D inputs, mesh objects, which can be regularly sampled, and point clouds, which are irregularly distributed. We also propose an efficient mapping of point clouds to concentric spherical images, thereby bridging spherical convolutions on grids with general point clouds. We demonstrate the effectiveness of our approach in improving state-of-the-art performance on 3D classification tasks with rotated data.

An accurate solar wind speed model is important for space weather predictions, catastrophic event warnings, and other issues concerning solar wind - magnetosphere interaction. In this work, we construct a model based on convolutional neural network (CNN) and Potential Field Source Surface (PFSS) magnetograms, considering a solar wind source surface of R_{rm SS}=2.5R_odot, aiming to predict the solar wind speed at the Lagrange 1 (L1) point of the Sun-Earth system. The input of our model consists of four Potential Field Source Surface (PFSS) magnetograms at R_{rm SS}, which are 7, 6, 5, and 4 days before the target epoch. Reduced magnetograms are used to promote the model's efficiency. We use the Global Oscillation Network Group (GONG) photospheric magnetograms and the potential field extrapolation model to generate PFSS magnetograms at the source surface. The model provides predictions of the continuous test dataset with an averaged correlation coefficient (CC) of 0.52 and a root mean square error (RMSE) of 80.8 km/s in an eight-fold validation training scheme with the time resolution of the data as small as one hour. The model also has the potential to forecast high speed streams of the solar wind, which can be quantified with a general threat score of 0.39.

Existing benchmarks for Earth science multimodal learning exhibit critical limitations in systematic coverage of geosystem components and cross-sphere interactions, often constrained to isolated subsystems (only in Human-activities sphere or atmosphere) with limited evaluation dimensions (less than 16 tasks). To address these gaps, we introduce OmniEarth-Bench, the first comprehensive multimodal benchmark spanning all six Earth science spheres (atmosphere, lithosphere, Oceansphere, cryosphere, biosphere and Human-activities sphere) and cross-spheres with one hundred expert-curated evaluation dimensions. Leveraging observational data from satellite sensors and in-situ measurements, OmniEarth-Bench integrates 29,779 annotations across four tiers: perception, general reasoning, scientific knowledge reasoning and chain-of-thought (CoT) reasoning. This involves the efforts of 2-5 experts per sphere to establish authoritative evaluation dimensions and curate relevant observational datasets, 40 crowd-sourcing annotators to assist experts for annotations, and finally, OmniEarth-Bench is validated via hybrid expert-crowd workflows to reduce label ambiguity. Experiments on 9 state-of-the-art MLLMs reveal that even the most advanced models struggle with our benchmarks, where none of them reach 35\% accuracy. Especially, in some cross-spheres tasks, the performance of leading models like GPT-4o drops to 0.0\%. OmniEarth-Bench sets a new standard for geosystem-aware AI, advancing both scientific discovery and practical applications in environmental monitoring and disaster prediction. The dataset, source code, and trained models were released.

Fast moving celestial objects are characterized by velocities across the celestial sphere that significantly differ from the motions of background stars. In observational images, these objects exhibit distinct shapes, contrasting with the typical appearances of stars. Depending on the observational method employed, these celestial entities may be designated as near-Earth objects or asteroids. Historically, fast moving celestial objects have been observed using ground-based telescopes, where the relative stability of stars and Earth facilitated effective image differencing techniques alongside traditional fast moving celestial object detection and classification algorithms. However, the growing prevalence of space-based telescopes, along with their diverse observational modes, produces images with different properties, rendering conventional methods less effective. This paper presents a novel algorithm for detecting fast moving celestial objects within star fields. Our approach enhances state-of-the-art fast moving celestial object detection neural networks by transforming them into physical-inspired neural networks. These neural networks leverage the point spread function of the telescope and the specific observational mode as prior information; they can directly identify moving fast moving celestial objects within star fields without requiring additional training, thereby addressing the limitations of traditional techniques. Additionally, all neural networks are integrated using the mixture of experts technique, forming a comprehensive fast moving celestial object detection algorithm. We have evaluated our algorithm using simulated observational data that mimics various observations carried out by space based telescope scenarios and real observation images. Results demonstrate that our method effectively detects fast moving celestial objects across different observational modes.

Geospatial Foundation Models (GFMs) have emerged as powerful tools for extracting representations from Earth observation data, but their evaluation remains inconsistent and narrow. Existing works often evaluate on suboptimal downstream datasets and tasks, that are often too easy or too narrow, limiting the usefulness of the evaluations to assess the real-world applicability of GFMs. Additionally, there is a distinct lack of diversity in current evaluation protocols, which fail to account for the multiplicity of image resolutions, sensor types, and temporalities, which further complicates the assessment of GFM performance. In particular, most existing benchmarks are geographically biased towards North America and Europe, questioning the global applicability of GFMs. To overcome these challenges, we introduce PANGAEA, a standardized evaluation protocol that covers a diverse set of datasets, tasks, resolutions, sensor modalities, and temporalities. It establishes a robust and widely applicable benchmark for GFMs. We evaluate the most popular GFMs openly available on this benchmark and analyze their performance across several domains. In particular, we compare these models to supervised baselines (e.g. UNet and vanilla ViT), and assess their effectiveness when faced with limited labeled data. Our findings highlight the limitations of GFMs, under different scenarios, showing that they do not consistently outperform supervised models. PANGAEA is designed to be highly extensible, allowing for the seamless inclusion of new datasets, models, and tasks in future research. By releasing the evaluation code and benchmark, we aim to enable other researchers to replicate our experiments and build upon our work, fostering a more principled evaluation protocol for large pre-trained geospatial models. The code is available at https://github.com/VMarsocci/pangaea-bench.

This paper presents a novel preconditioning strategy for the classic 8-point algorithm (8-PA) for estimating an essential matrix from 360-FoV images (i.e., equirectangular images) in spherical projection. To alleviate the effect of uneven key-feature distributions and outlier correspondences, which can potentially decrease the accuracy of an essential matrix, our method optimizes a non-rigid transformation to deform a spherical camera into a new spatial domain, defining a new constraint and a more robust and accurate solution for an essential matrix. Through several experiments using random synthetic points, 360-FoV, and fish-eye images, we demonstrate that our normalization can increase the camera pose accuracy by about 20% without significantly overhead the computation time. In addition, we present further benefits of our method through both a constant weighted least-square optimization that improves further the well known Gold Standard Method (GSM) (i.e., the non-linear optimization by using epipolar errors); and a relaxation of the number of RANSAC iterations, both showing that our normalization outcomes a more reliable, robust, and accurate solution.

The stellar initial mass function is of great significance for the study of star formation and galactic structure. Observations indicate that the IMF follows a power-law form. This work derived that when the expected number of stars formed from a spherical molecular cloud is much greater than 1, there is a relationship between the slope alpha of the IMF and r^n in the radius-density relation of spherically symmetric gas clouds, given by alpha = 3/(n+3) (Gamma_{IMF} = n/(n+3)). This conclusion is close to the results of numerical simulations and observations, but it is derived from a pure probabilistic model, which may have underlying reasons worth pondering.

Latent flow matching for image generation usually transports Gaussian noise to variational autoencoder latents along linear paths. Both endpoints, however, concentrate in thin spherical shells, and a Euclidean chord leaves those shells even when preprocessing aligns their radii. By decomposing each latent token into radial and angular components, we show through component-swap probes that decoded perceptual and semantic content is carried predominantly by direction, with radius contributing much less. We therefore project data latents onto a fixed token radius, use the radial projection of Gaussian noise as the spherical prior, finetune the decoder with the encoder frozen, and replace linear interpolation with spherical linear interpolation. The resulting geodesic paths stay on the sphere at every timestep, and their velocity targets are purely angular by construction. Under matched training, the method consistently improves class-conditional ImageNet-256 FID across different image tokenizers, leaves the diffusion architecture unchanged, and requires no auxiliary encoder or representation-alignment objective.

Geo-Foundation Models (GFMs) have been evaluated across diverse Earth observation task including multiple domains and have demonstrated strong potential of producing reliable maps even with sparse labels. However, benchmarking GFMs for Cryosphere applications has remained limited, primarily due to the lack of suitable evaluation datasets. To address this gap, we introduce Cryo-Bench, a benchmark compiled to evaluate GFM performance across key Cryospheric components. Cryo-Bench includes debris-covered glaciers, glacial lakes, sea ice, and calving fronts, spanning multiple sensors and broad geographic regions. We evaluate 14 GFMs alongside UNet and ViT baselines to assess their advantages, limitations, and optimal usage strategies. With a frozen encoder, UNet achieves the highest average mIoU of 66.38, followed by TerraMind at 64.02 across five evluation dataset included in Cryo-Bench. In the few-shot setting (10\% input data), GFMs such as DOFA and TerraMind outperform UNet, achieving mIoU scores of 59.53, 56.62, and 56.60, respectively, comapred to U-Net's 56.60. When fully finetuning GFMs, we observe inconsistent performance across datasets and models. However, tuning learning rate along with finetuning substantially improves GFM performance. For example, evaluation on two representative datasets (GLID and CaFFe) shows an average relative improvement of 12.77\%. Despite having minimal Cryosphere representation in their pretraining data, GFMs exhibit notable domain adaptation capabilities and produce meaningful results across tasks. Based on our findings, We recommend encoder fine-tuning with hyperparameter optimization optimization to achieve the best possible performance, while using frozen encoders when users need quick results without extensive experimentation.(https://github.com/Sk-2103/Cryo-Bench{GitHub}).

3D Gaussian Splatting (3D-GS) has recently attracted great attention with real-time and photo-realistic renderings. This technique typically takes perspective images as input and optimizes a set of 3D elliptical Gaussians by splatting them onto the image planes, resulting in 2D Gaussians. However, applying 3D-GS to panoramic inputs presents challenges in effectively modeling the projection onto the spherical surface of {360^circ} images using 2D Gaussians. In practical applications, input panoramas are often sparse, leading to unreliable initialization of 3D Gaussians and subsequent degradation of 3D-GS quality. In addition, due to the under-constrained geometry of texture-less planes (e.g., walls and floors), 3D-GS struggles to model these flat regions with elliptical Gaussians, resulting in significant floaters in novel views. To address these issues, we propose 360-GS, a novel 360^{circ} Gaussian splatting for a limited set of panoramic inputs. Instead of splatting 3D Gaussians directly onto the spherical surface, 360-GS projects them onto the tangent plane of the unit sphere and then maps them to the spherical projections. This adaptation enables the representation of the projection using Gaussians. We guide the optimization of 360-GS by exploiting layout priors within panoramas, which are simple to obtain and contain strong structural information about the indoor scene. Our experimental results demonstrate that 360-GS allows panoramic rendering and outperforms state-of-the-art methods with fewer artifacts in novel view synthesis, thus providing immersive roaming in indoor scenarios.

In solving partial differential equations (PDEs), Fourier Neural Operators (FNOs) have exhibited notable effectiveness compared to Convolutional Neural Networks (CNNs). This paper presents clear empirical evidence through spectral analysis to elucidate the superiority of FNO over CNNs: FNO is significantly more capable of learning low-frequencies. This empirical evidence also unveils FNO's distinct low-frequency bias, which limits FNO's effectiveness in learning high-frequency information from PDE data. To tackle this challenge, we introduce SpecBoost, an ensemble learning framework that employs multiple FNOs to better capture high-frequency information. Specifically, a secondary FNO is utilized to learn the overlooked high-frequency information from the prediction residual of the initial FNO. Experiments demonstrate that SpecBoost noticeably enhances FNO's prediction accuracy on diverse PDE applications, achieving an up to 71% improvement.

We introduce the Sphere Encoder, an efficient generative framework capable of producing images in a single forward pass and competing with many-step diffusion models using fewer than five steps. Our approach works by learning an encoder that maps natural images uniformly onto a spherical latent space, and a decoder that maps random latent vectors back to the image space. Trained solely through image reconstruction losses, the model generates an image by simply decoding a random point on the sphere. Our architecture naturally supports conditional generation, and looping the encoder/decoder a few times can further enhance image quality. Across several datasets, the sphere encoder approach yields performance competitive with state of the art diffusions, but with a small fraction of the inference cost. Project page is available at https://sphere-encoder.github.io .

As 360{\deg} cameras become prevalent in many autonomous systems (e.g., self-driving cars and drones), efficient 360{\deg} perception becomes more and more important. We propose a novel self-supervised learning approach for predicting the omnidirectional depth and camera motion from a 360{\deg} video. In particular, starting from the SfMLearner, which is designed for cameras with normal field-of-view, we introduce three key features to process 360{\deg} images efficiently. Firstly, we convert each image from equirectangular projection to cubic projection in order to avoid image distortion. In each network layer, we use Cube Padding (CP), which pads intermediate features from adjacent faces, to avoid image boundaries. Secondly, we propose a novel "spherical" photometric consistency constraint on the whole viewing sphere. In this way, no pixel will be projected outside the image boundary which typically happens in images with normal field-of-view. Finally, rather than naively estimating six independent camera motions (i.e., naively applying SfM-Learner to each face on a cube), we propose a novel camera pose consistency loss to ensure the estimated camera motions reaching consensus. To train and evaluate our approach, we collect a new PanoSUNCG dataset containing a large amount of 360{\deg} videos with groundtruth depth and camera motion. Our approach achieves state-of-the-art depth prediction and camera motion estimation on PanoSUNCG with faster inference speed comparing to equirectangular. In real-world indoor videos, our approach can also achieve qualitatively reasonable depth prediction by acquiring model pre-trained on PanoSUNCG.

Volumetric rendering based methods, like NeRF, excel in HDR view synthesis from RAWimages, especially for nighttime scenes. While, they suffer from long training times and cannot perform real-time rendering due to dense sampling requirements. The advent of 3D Gaussian Splatting (3DGS) enables real-time rendering and faster training. However, implementing RAW image-based view synthesis directly using 3DGS is challenging due to its inherent drawbacks: 1) in nighttime scenes, extremely low SNR leads to poor structure-from-motion (SfM) estimation in distant views; 2) the limited representation capacity of spherical harmonics (SH) function is unsuitable for RAW linear color space; and 3) inaccurate scene structure hampers downstream tasks such as refocusing. To address these issues, we propose LE3D (Lighting Every darkness with 3DGS). Our method proposes Cone Scatter Initialization to enrich the estimation of SfM, and replaces SH with a Color MLP to represent the RAW linear color space. Additionally, we introduce depth distortion and near-far regularizations to improve the accuracy of scene structure for downstream tasks. These designs enable LE3D to perform real-time novel view synthesis, HDR rendering, refocusing, and tone-mapping changes. Compared to previous volumetric rendering based methods, LE3D reduces training time to 1% and improves rendering speed by up to 4,000 times for 2K resolution images in terms of FPS. Code and viewer can be found in https://github.com/Srameo/LE3D .

Few-step image generation has seen rapid progress, with consistency and meanflow-based methods significantly reducing the number of sampling steps. Despite their low inference cost, these approaches often suffer from training instability and limited scalability. Sphere Encoder is a recent alternative that produces high-quality images in only a few steps; however, it requires repeated transitions between the pixel space and latent space during inference while jointly optimizing reconstruction and generation within a single architecture. This design leads to computational inefficiency and objective conflict between reconstruction and generation. To address these limitations, we decouple the framework into a fixed pretrained image encoder and a separate latent denoising model trained entirely in a spherical latent space. Our approach eliminates repeated pixel-space operations during training and inference, improving efficiency and allowing reconstruction and generation to specialize independently. On Animal-Faces, Oxford-Flowers and ImageNet-1K datasets, our method significantly outperforms Sphere Encoder in both generation quality and inference speed, while achieving competitive results against strong few-step and multi-step baselines.

Autoregressive (AR) models are promising for image generation, yet continuous-token AR variants often trail latent diffusion and masked-generation models. The core issue is heterogeneous variance in VAE latents, which is amplified during AR decoding, especially under classifier-free guidance (CFG), and can cause variance collapse. We propose SphereAR to address this issue. Its core design is to constrain all AR inputs and outputs -- including after CFG -- to lie on a fixed-radius hypersphere (constant ell_2 norm), leveraging hyperspherical VAEs. Our theoretical analysis shows that hyperspherical constraint removes the scale component (the primary cause of variance collapse), thereby stabilizing AR decoding. Empirically, on ImageNet generation, SphereAR-H (943M) sets a new state of the art for AR models, achieving FID 1.34. Even at smaller scales, SphereAR-L (479M) reaches FID 1.54 and SphereAR-B (208M) reaches 1.92, matching or surpassing much larger baselines such as MAR-H (943M, 1.55) and VAR-d30 (2B, 1.92). To our knowledge, this is the first time a pure next-token AR image generator with raster order surpasses diffusion and masked-generation models at comparable parameter scales.

Non-line-of-sight (NLOS) imaging is conducted to infer invisible scenes from indirect light on visible objects. The neural transient field (NeTF) was proposed for representing scenes as neural radiance fields in NLOS scenes. We propose NLOS neural implicit surface (NLOS-NeuS), which extends the NeTF to neural implicit surfaces with a signed distance function (SDF) for reconstructing three-dimensional surfaces in NLOS scenes. We introduce two constraints as loss functions for correctly learning an SDF to avoid non-zero level-set surfaces. We also introduce a lower bound constraint of an SDF based on the geometry of the first-returning photons. The experimental results indicate that these constraints are essential for learning a correct SDF in NLOS scenes. Compared with previous methods with discretized representation, NLOS-NeuS with the neural continuous representation enables us to reconstruct smooth surfaces while preserving fine details in NLOS scenes. To the best of our knowledge, this is the first study on neural implicit surfaces with volume rendering in NLOS scenes.

We investigate asymptotic Schwarzschild exterior solutions in the context of modified gravity theories, specifically within the framework of f(R) gravity, where the asymptotic behavior recovers the standard Schwarzschild solution of General Relativity. Unlike previous studies that rely mainly on analytical approximations, our approach combines asymptotic analysis with numerical integration of the underlying differential equations. Using these solutions, we analyze strong lensing effects to obtain the photon sphere radius and the corresponding capture parameter. Considering rings produced by total reflection, we define the photon sphere width as the difference between the first total reflection and the capture parameter; and study how it is modified in the f(R) scenario. Our results show that the photon sphere width increases in the presence of f(R)-type modifications, indicating deviations from GR that could be observable in the strong-field regime.

A rational spherical triangle is a triangle on the unit sphere such that the lengths of its three sides and its area are rational multiples of π. Little and Coxeter have given examples of rational spherical triangles in 1980s. In this work, we are interested in determining all the rational spherical triangles. We introduce a conjecture on the solutions to a trigonometric Diophantine equation. An implication of the conjecture is that the only rational spherical triangles are the ones given by Little and Coxeter. We prove some partial results towards the conjecture.

The stellar structures of star-forming galaxies (SFGs) undergo significant size growth during their mass assembly and must pass through a compaction phase as they evolve into quiescent galaxies (QGs). To shed light on the mechanisms behind this structural evolution, we study the morphology of the star-forming components of 665 SFGs at 0<z<2.5 measured using JWST/MIRI observation and compare them with the morphology of their stellar components taken from the literature. The stellar and star-forming components of most SFGs (66%) have extended disk-like structures that are aligned with each other and are of the same size. The star-forming components of these galaxies follow a mass-size relation, similar to that followed by their stellar components. At the highest mass, the optical S\'ersic index of these SFGs increases to 2.5, suggesting the presence of a dominant stellar bulge. Because their star-forming components remain disk-like, these bulges cannot have formed by secular in-situ growth. We identify a second population of galaxies lying below the MIR mass-size relation, with compact star-forming components embedded in extended stellar components (EC galaxy). These galaxies are overall rare (15%) but become more dominant (30%) at high mass (>10^{10.5}M_odot). The compact star-forming components of these galaxies are also concentrated and slightly spheroidal, suggesting that this compaction phase can build dense bulge in-situ. Finally, we identify a third population of SFGs (19%), with both compact stellar and star-forming components. The density of their stellar cores resemble those of QGs and are compatible with being the descendants of EC galaxy. Overall, the structural evolution of SFGs is mainly dominated by a secular inside-out growth, which can, however, be interrupted by violent compaction phase(s) that can build dominant stellar bulges like those in massive SFGs or QGs.

Neural rendering techniques have made substantial progress in generating photo-realistic 3D scenes. The latest 3D Gaussian Splatting technique has achieved high quality novel view synthesis as well as fast rendering speed. However, 3D Gaussians lack proficiency in defining accurate 3D geometric structures despite their explicit primitive representations. This is due to the fact that Gaussian's attributes are primarily tailored and fine-tuned for rendering diverse 2D images by their anisotropic nature. To pave the way for efficient 3D reconstruction, we present Spherical Gaussians, a simple and effective representation for 3D geometric boundaries, from which we can directly reconstruct 3D feature curves from a set of calibrated multi-view images. Spherical Gaussians is optimized from grid initialization with a view-based rendering loss, where a 2D edge map is rendered at a specific view and then compared to the ground-truth edge map extracted from the corresponding image, without the need for any 3D guidance or supervision. Given Spherical Gaussians serve as intermedia for the robust edge representation, we further introduce a novel optimization-based algorithm called SGCR to directly extract accurate parametric curves from aligned Spherical Gaussians. We demonstrate that SGCR outperforms existing state-of-the-art methods in 3D edge reconstruction while enjoying great efficiency.