Machine learning and data assimilation enables more realistic forecasting of multi-scale systems

Forecasting dynamical systems, like weather, is frequently accomplished using numerical, grid-based simulations. However, these can become inaccurate across long periods for systems where sub-grid-scale activity is nonnegligible. Gottwald et al. use machine learning and data assimilation to create surrogate models that can replicate dynamic systems, even when using noisy partial data.

Numerical models are only as accurate as their grid resolution, but creating simulations with ultra-fine grids comes at a great computational cost. The researchers bypass this need by extrapolating from observational data, where multi-scale interactions are inherent.

“We lose the power of interpretable equations, but we gain a fast computational model, which allows for a huge acceleration of computing time,” co-author Georg Gottwald said. “This makes long-time simulations feasible. Once such a machine-learning surrogate model is trained, it is very cheap to simulate.”

The data used to develop the surrogate model is drawn from noisy partial observations, indicative of a realistic dataset. To account for the noise, the researchers embedded the estimation of the model parameters in a data assimilation framework. Takens’ embedding theorem solves the issue of partial observation by embedding the dynamics in a higher-dimensional space of delay vectors.

This development may be potentially applicable to atmospheric, oceanic, and other similar systems, whose large-scale behavior is impacted by small-scale activity and vice-versa. Systems whose determining equations are too complex to deduce, such as those dependent on human behavior, may also benefit from this method.

Source: “Combining machine learning and data assimilation to forecast dynamical systems from noisy partial observations,” by Georg A. Gottwald and Sebastian Reich, Chaos (2021). The article can be accessed at https://doi.org/10.1063/5.0066080 .