Efficient Probabilistic Surrogate Modeling Techniques for Partially-Observed Large-Scale Dynamical Systems
Please login to view abstract download link
Forecasting the evolution of a dynamical system requires access to an accurate model. When only data is available, one must instead learn a predictive rule mapping past states to future ones, as studied extensively in the literature. Such approaches typically assume deterministic dynamics. However, many systems of practical interest, for example in weather and climate, are only partially observed, leading to effective non-determinism from the perspective of the observed variables. Deterministic models perform poorly in this regime. A more appropriate approach is to model unresolved degrees of freedom through stochasticity, an idea underlying modern probabilistic forecasting systems such as GenCast. These generative models are commonly trained via denoising diffusion or flow matching objectives. While training is straightforward, sampling generally requires the numerical solution of an ordinary differential equation, which can be computationally expensive. We present methods for accelerating the sampling process, including distillation-based techniques, adversarial diffusion, and rectified flows. We evaluate these methods on partially-observed dynamical systems, including two-dimensional slices of the three-dimensional Rayleigh-Taylor instability and downsampled Navier-Stokes simulations.
