BEGIN:VCALENDAR VERSION:2.0 PRODID:-//Memento EPFL// BEGIN:VEVENT SUMMARY:Geometric Neural Operators for Machine Learning Probabilistic Weat her Prediction DTSTART:20260925T131500 DTEND:20260925T141500 DTSTAMP:20260923T072912Z UID:9927e044a7b615d4057a8ddc0ba9702a965d7dd6388cb17517bba58a CATEGORIES:Conferences - Seminars DESCRIPTION:Boris Bonev\, NVIDIA\nMachine learning has recently enabled fa st and accurate surrogate models for numerical weather and climate predict ion. However\, many current architectures struggle on extreme events\, int roduce spurious artifacts or instabilities when they ignore the spherical geometry of the Earth\, and are often tightly coupled to a particular inpu t grid or resolution\, limiting flexibility for downstream applications. T hese shortcomings highlight a mismatch between black‑box models and more traditional numerical methods\, which encode underlying physical and geom etric properties. Neural operators address part of this gap by learning so lution operators of partial differential equations in a grid‑agnostic ma nner\, yet standard Fourier Neural Operators (FNOs) break down on the sphe re\, where the flat‑geometry Fourier transform induces artifacts and exc essive dissipation.\n\nThis talk presents geometric neural operators that respect the symmetries and topology of the sphere\, in the spirit of the g eometric deep learning\, with a particular focus on applications to the ch aotic dynamics of Earth's atmosphere. The Spherical Fourier Neural Operato r (SFNO) is formulated via Driscoll–Healy's convolution theorem\, linkin g spherical harmonic transforms to group convolutions on the sphere and yi elding 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 operat ors into neural operator architectures\, using provably convergent differe ntial layers and quadrature‑based discrete–continuous convolutions on both Euclidean and spherical geometries to capture sharp fronts and local extremes. To complement convolutional approaches\, a generalized attention mechanism for spherical domains is developed\, allowing Transformer‑sty le architectures to natively process data on the two‑dimensional sphere. This discretization‑agnostic spherical attention incorporates numerical quadrature weights into a continuous spherical formulation\, producing ge ometrically faithful attention that is approximately rotationally equivari ant.\n\nThe practical impact of these ideas is demonstrated with FourCastN et 3\, a scalable probabilistic weather forecasting system cast as a hidde n Markov model built from spherical signal‑processing primitives. FourCa stNet 3 is trained on 1000+ GPUs using flexible domain-parallelism paradig ms inspired from traditional HPC methods. The resulting method matches or exceeds leading conventional ensemble systems and state‑of‑the‑art d iffusion models while delivering 8–60× faster forecasts\, positioning i t as a robust foundation for next‑generation weather and climate modelin g and downscaling systems. LOCATION:CM 1 517 https://plan.epfl.ch/?room==CM%201%20517 STATUS:CONFIRMED END:VEVENT END:VCALENDAR