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.

Neural fields have revolutionized the area of 3D reconstruction and novel view synthesis of rigid scenes. A key challenge in making such methods applicable to articulated objects, such as the human body, is to model the deformation of 3D locations between the rest pose (a canonical space) and the deformed space. We propose a new articulation module for neural fields, Fast-SNARF, which finds accurate correspondences between canonical space and posed space via iterative root finding. Fast-SNARF is a drop-in replacement in functionality to our previous work, SNARF, while significantly improving its computational efficiency. We contribute several algorithmic and implementation improvements over SNARF, yielding a speed-up of 150×. These improvements include voxel-based correspondence search, pre-computing the linear blend skinning function, and an efficient software implementation with CUDA kernels. Fast-SNARF enables efficient and simultaneous optimization of shape and skinning weights given deformed observations without correspondences (e.g. 3D meshes). Because learning of deformation maps is a crucial component in many 3D human avatar methods and since Fast-SNARF provides a computationally efficient solution, we believe that this work represents a significant step towards the practical creation of 3D virtual humans.

In complex acoustic or elastic media, finite element meshes often require regions of refinement to honour external or internal topography, or small-scale features. These localized smaller elements create a bottleneck for explicit time-stepping schemes due to the Courant-Friedrichs-Lewy stability condition. Recently developed local time stepping (LTS) algorithms reduce the impact of these small elements by locally adapting the time-step size to the size of the element. The recursive, multi-level nature of our LTS scheme introduces an additional challenge, as standard partitioning schemes create a strong load imbalance across processors. We examine the use of multi-constraint graph and hypergraph partitioning tools to achieve effective, load-balanced parallelization. We implement LTS-Newmark in the seismology code SPECFEM3D and compare performance and scalability between different partitioning tools on CPU and GPU clusters using examples from computational seismology.

Computational seismology is an area of wide sociological and economic impact, ranging from earthquake risk assessment to subsurface imaging and oil and gas exploration. At the core of these simulations is the modeling of wave propagation in a complex medium. Here we report on the extension of the high-order finite-element seismic wave simulation package SPECFEM3D to support the largest scale hybrid and homogeneous supercomputers. Starting from an existing highly tuned MPI code, we migrated to a CUDA version. In order to be of immediate impact to the science mission of computational seismologists, we had to port the entire production package, rather than just individual kernels. One of the challenges in parallelizing finite element codes is the potential for race conditions during the assembly phase. We therefore investigated different methods such as mesh coloring or atomic updates on the GPU. In order to achieve strong scaling, we needed to ensure good overlap of data motion at all levels, including internode and host-accelerator transfers. Finally we carefully tuned the GPU implementation. The new MPI/CUDA solver exhibits excellent scalability and achieves speedup on a node-to-node basis over the carefully tuned equivalent multi-core MPI solver. To demonstrate the performance of both the forward and adjoint functionality, we present two case studies run on the Cray XE6 CPU and Cray XK6 GPU architectures up to 896 nodes: (1) focusing on most commonly used forward simulations, we simulate seismic wave propagation generated by earthquakes in Turkey, and (2) testing the most complex seismic inversion type of the package, we use ambient seismic noise to image 3-D crust and mantle structure beneath western Europe.