We introduce Mosaic, a probabilistic weather forecasting model that addresses two sources of spectral degradation in ML-based weather prediction: (1) training to predict the ensemble mean deterministically and (2) compressive encoding creating an information bottleneck. Mosaic combines learned functional perturbations for ensemble forecasting with block-sparse attention, a hardware-aligned formulation that shares keys and values across spatially adjacent queries, enabling each block to dynamically attend to the most relevant regions. By capturing arbitrarily long-range dependencies at linear cost, Mosaic processes high-resolution weather data without compression. Mosaic at 1.5° resolution matches or outperforms models trained on 0.25° data, with individual ensemble members exhibiting near-perfect spectral alignment across all resolved frequencies.

A key scalability challenge in neural solvers for industrial-scale physics simulations is efficiently capturing both fine-grained local interactions and long-range global dependencies across millions of spatial elements. We introduce the Multi-Scale Patch Transformer (MSPT), an architecture that combines local point attention within patches with global attention to coarse patch-level representations. To partition the input domain into spatially-coherent patches, we employ ball trees, which handle irregular geometries efficiently. This dual-scale design enables MSPT to scale to millions of points on a single GPU. We validate our method on standard PDE benchmarks (elasticity, plasticity, fluid dynamics, porous flow) and large-scale aerodynamic datasets (ShapeNet-Car, Ahmed-ML), achieving state-of-the-art accuracy with substantially lower memory footprint and computational cost.

Large-scale physical systems defined on irregular grids pose significant scalability challenges for deep learning methods, especially in the presence of long-range interactions and multi-scale coupling. Traditional approaches that compute all pairwise interactions, such as attention, become computationally prohibitive as they scale quadratically with the number of nodes. We present Erwin, a hierarchical transformer inspired by methods from computational many-body physics, which combines the efficiency of tree-based algorithms with the expressivity of attention mechanisms. Erwin employs ball tree partitioning to organize computation, which enables linear-time attention by processing nodes in parallel within local neighborhoods of fixed size. Through progressive coarsening and refinement of the ball tree structure, complemented by a novel cross-ball interaction mechanism, it captures both fine-grained local details and global features. We demonstrate Erwin’s effectiveness across multiple domains, including cosmology, molecular dynamics, and particle fluid dynamics, where it consistently outperforms baseline methods both in accuracy and computational efficiency.