Reservoir computing for learned latent state propagation of fluid flows

Reservoir computing (RC) approaches have shown strong performance in forecasting complex and chaotic dynamical systems. However, their application to fluid dynamics remains limited due to the high dimensionality of fluid flows, which demand impractically large reservoirs or the instantiation of many parallel reservoirs. Moreover, trained RC models frequently suffer from instabilities, making them unreliable for use with noisy or imperfect data. We propose a hybrid shallow recurrent decoder architecture that combines a learned latent representation of fluid states with an ensemble of echo state networks to achieve stable, long-horizon predictions. By operating in a reduced latent space, our method mitigates the need for excessively large reservoirs. Moreover, ensembling echo state networks helps reduce instability in extended forecasts. We demonstrate that this architecture produces stable long-horizon forecasts on canonical fluid dynamics systems such as a lid driven cavity and closely reproduces the statistical properties of the true dynamics. These results establish a practical and scalable framework for applying reservoir computing to high-dimensional fluid dynamics, enabling accurate and stable long-horizon forecasting.