Data-driven geophysical forecasting: Simple, low-cost, and accurate baselines with kernel methods
This provides a low-cost, interpretable forecasting method for geophysical processes, though it is incremental as it builds on existing kernel methods with learned kernels.
The paper tackles geophysical forecasting by learning kernel-based emulators from data, achieving faster and more accurate predictions than both equation-based models and neural networks like LSTM, with significant gains in computational cost and accuracy on sea-surface temperature and daily temperature datasets.
Modeling geophysical processes as low-dimensional dynamical systems and regressing their vector field from data is a promising approach for learning emulators of such systems. We show that when the kernel of these emulators is also learned from data (using kernel flows, a variant of cross-validation), then the resulting data-driven models are not only faster than equation-based models but are easier to train than neural networks such as the long short-term memory neural network. In addition, they are also more accurate and predictive than the latter. When trained on geophysical observational data, for example, the weekly averaged global sea-surface temperature, considerable gains are also observed by the proposed technique in comparison to classical partial differential equation-based models in terms of forecast computational cost and accuracy. When trained on publicly available re-analysis data for the daily temperature of the North-American continent, we see significant improvements over classical baselines such as climatology and persistence-based forecast techniques. Although our experiments concern specific examples, the proposed approach is general, and our results support the viability of kernel methods (with learned kernels) for interpretable and computationally efficient geophysical forecasting for a large diversity of processes.