Online model learning with data-assimilated reservoir computers

We propose an online learning framework for forecasting nonlinear spatio-temporal signals (fields). The method integrates (i) dimensionality reduction, here, a simple proper orthogonal decomposition (POD) projection; (ii) a generalized autoregressive model to forecast reduced dynamics, here, a reservoir computer; (iii) online adaptation to update the reservoir computer (the model), here, ensemble sequential data assimilation.We demonstrate the framework on a wake past a cylinder governed by the Navier-Stokes equations, exploring the assimilation of full flow fields (projected onto POD modes) and sparse sensors. Three scenarios are examined: a na\"ive physical state estimation; a two-fold estimation of physical and reservoir states; and a three-fold estimation that also adjusts the model parameters. The two-fold strategy significantly improves ensemble convergence and reduces reconstruction error compared to the na\"ive approach. The three-fold approach enables robust online training of partially-trained reservoir computers, overcoming limitations of a priori training. By unifying data-driven reduced order modelling with Bayesian data assimilation, this work opens new opportunities for scalable online model learning for nonlinear time series forecasting.

Data-Assimilated Model-Based Reinforcement Learning for Partially Observed Chaotic Flows

The goal of many applications in energy and transport sectors is to control turbulent flows. However, because of chaotic dynamics and high dimensionality, the control of turbulent flows is exceedingly difficult. Model-free reinforcement learning (RL) methods can discover optimal control policies by interacting with the environment, but they require full state information, which is often unavailable in experimental settings. We propose a data-assimilated model-based RL (DA-MBRL) framework for systems with partial observability and noisy measurements. Our framework employs a control-aware Echo State Network for data-driven prediction of the dynamics, and integrates data assimilation with an Ensemble Kalman Filter for real-time state estimation. An off-policy actor-critic algorithm is employed to learn optimal control strategies from state estimates. The framework is tested on the Kuramoto-Sivashinsky equation, demonstrating its effectiveness in stabilizing a spatiotemporally chaotic flow from noisy and partial measurements.