Cross-scale reservoir computing for large spatio-temporal forecasting and modeling

We propose a new reservoir computing method for forecasting high-resolution spatiotemporal datasets. While many machine learning methods suffer from limited interpretability and computational intractability in high-dimensional settings, reservoir computing offers inherent advantages through its lightweight linear training. Our hierarchical architecture combines multi-resolution inputs from coarser to finer layers, enabling the capture of both local dynamics and long-range dependencies. Applied to Sea Surface Temperature data, it outperforms standard parallel reservoir models in long-term forecasting, demonstrating the effectiveness of cross-layer coupling in improving predictive accuracy. We find that the optimal network dynamics in each layer become increasingly linear, revealing the slow modes propagated to subsequent layers. Finally, we evaluate the method on a chaotic system, where a strongly coupled two-layer configuration achieves accurate forecasts and offers favorable accuracy-cost tradeoffs compared with established reservoir baselines.