We propose an online learning framework for forecasting nonlinear
spatio-temporal signals (fields). The method integrates (io) dimensionality
reduction, here, a simple proper orthogonal decomposition (POD) projection;
(ii) a generalized autoregressive model to forecast reduced dynamics, here, UN
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) E
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.

Questo articolo esplora i giri e le loro implicazioni.

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