Speaker: Boris Bonev (NVIDIA Zurich, École Polytechnique Paris) Title: Geometric Neural Operators for Machine Learning Probabilistic Weather Prediction Abstract: Machine learning has recently enabled fast and accurate surrogate models for numerical weather and climate prediction. However, many current architectures struggle on extreme events, introduce spurious artifacts or instabilities when they ignore the spherical geometry of the Earth, and are often tightly coupled to a particular input grid or resolution, limiting flexibility for downstream applications. These shortcomings highlight a mismatch between black‑box models and more traditional numerical methods, which encode underlying physical and geometric properties. Neural operators address part of this gap by learning solution operators of partial differential equations in a grid‑agnostic manner, yet standard Fourier Neural Operators (FNOs) break down on the sphere, where the flat‑geometry Fourier transform induces artifacts and excessive dissipation. This talk presents geometric neural operators that respect the symmetries and topology of the sphere, in the spirit of the geometric deep learning blueprint,  with a particular focus on applications to the chaotic dynamics of Earth’s atmosphere. The Spherical Fourier Neural Operator (SFNO) is formulated via Driscoll–Healy’s convolution theorem, linking spherical harmonic transforms to group convolutions on the sphere and yielding rotationally equivariant, grid-invariant models capable of stable, year‑long autoregressive rollouts with physically plausible dynamics. Building on insights from hyperbolic PDE solvers, a principled framework is introduced for incorporating localized integral and differential operators into neural operator architectures, using provably convergent differential layers and quadrature‑based discrete–continuous convolutions on both Euclidean and spherical geometries to capture sharp fronts and local extremes. To complement convolutional appr

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