Omer Rochman

Gérôme Andry, Sacha Lewin, François Rozet et al.

Deep learning has advanced weather forecasting, but accurate predictions first require identifying the current state of the atmosphere from observational data. In this work, we introduce Appa, a score-based data assimilation model generating global atmospheric trajectories at 0.25\si{\degree} resolution and 1-hour intervals. Powered by a 565M-parameter latent diffusion model trained on ERA5, Appa can be conditioned on arbitrary observations to infer plausible trajectories, without retraining. Our probabilistic framework handles reanalysis, filtering, and forecasting, within a single model, producing physically consistent reconstructions from various inputs. Results establish latent score-based data assimilation as a promising foundation for future global atmospheric modeling systems.

Omer Rochman, Gilles Louppe

Neural PDE solvers used for scientific simulation often violate governing equation constraints. While linear constraints can be projected cheaply, many constraints are nonlinear, complicating projection onto the feasible set. Dynamical PDEs are especially difficult because constraints induce long-range dependencies in time. In this work, we evaluate two training-free, post hoc projections of approximate solutions: a nonlinear optimization-based projection, and a local linearization-based projection using Jacobian-vector and vector-Jacobian products. We analyze constraints across representative PDEs and find that both projections substantially reduce violations and improve accuracy over physics-informed baselines.