Sequential Reservoir Computing for Efficient High-Dimensional Spatiotemporal Forecasting

TL;DR

This paper introduces Sequential Reservoir Computing, a scalable architecture that efficiently forecasts high-dimensional spatiotemporal systems, outperforming traditional RNNs and LSTMs in accuracy and computational cost.

Contribution

The paper proposes a novel Sequential RC architecture that decomposes large reservoirs into smaller interconnected units, enhancing scalability and efficiency for high-dimensional forecasting tasks.

Findings

Achieves 15-25% longer forecast horizons

Reduces error metrics by 20-30% (SSIM, RMSE)

Up to three orders of magnitude lower training cost

Abstract

Forecasting high-dimensional spatiotemporal systems remains computationally challenging for recurrent neural networks (RNNs) and long short-term memory (LSTM) models due to gradient-based training and memory bottlenecks. Reservoir Computing (RC) mitigates these challenges by replacing backpropagation with fixed recurrent layers and a convex readout optimization, yet conventional RC architectures still scale poorly with input dimensionality. We introduce a Sequential Reservoir Computing (Sequential RC) architecture that decomposes a large reservoir into a series of smaller, interconnected reservoirs. This design reduces memory and computational costs while preserving long-term temporal dependencies. Using both low-dimensional chaotic systems (Lorenz63) and high-dimensional physical simulations (2D vorticity and shallow-water equations), Sequential RC achieves 15-25% longer valid forecast horizons, 20-30% lower error metrics (SSIM, RMSE), and up to three orders of magnitude lower training cost compared to LSTM and standard RNN baselines. The results demonstrate that Sequential RC maintains the simplicity and efficiency of conventional RC while achieving superior scalability for high-dimensional dynamical systems. This approach provides a practical path toward real-time, energy-efficient forecasting in scientific and engineering applications.