Flow map learning in nonlinear vector autoregressive models: influence of the feature-library structure on the training error
Time series forecasting often requires learning nonlinear and time-delayed dependencies. A paradigmatic class of forecasting models are nonlinear vector autoregressive processes (NVAR), also known as next-generation reservoir computers (NG-RCs). These models approximate the Koopman operator on the space spanned by their explicit feature library. We consider the identifiability problem for learning Markovian nonlinear dynamical systems and show that the training error as a function of time resolution follows characteristic (pre-)asymptotic scaling laws. These laws depend on whether the feature library can represent the early Lie-series coefficients of the flow map (propagator) exactly or m...
| Authors | Markus Gross |
|---|---|
| Primary category | cs.LG |
| Published | 29 May 2026 |
| Last updated at source | 29 May 2026 |
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