Test preservation of dynamical invariants by OPTN walks

Determine whether an ordinal-pattern transition network-based symbolic walk preserves invariant geometric and statistical properties of the source dynamics, such as correlation dimension and multiscale entropy, when one-step prediction accuracy declines as the delay increases.

Background

The paper evaluates the OPTN construction primarily through one-step-ahead ordinal-pattern prediction and notes that such local accuracy may deteriorate with increasing delay. Conventional trained continuous reservoirs can nevertheless reproduce longer-term invariant properties of chaotic systems even when pointwise trajectory prediction degrades. Whether the symbolic OPTN walk has an analogous ability to preserve dynamical invariants is explicitly identified as untested and would provide a stronger validation of the proposed reservoir correspondence.

References

Whether an OPTN-based symbolic walk analogously preserves such invariants as one-step accuracy falls with increasing delay $\tau$ (Section~\ref{sec:results}) is untested here and would provide a more stringent assessment of the correspondence developed in Section~\ref{sec:central_correspondence} than one-step prediction accuracy alone.

— Ordinal-pattern transition networks as a symbolic substrate for reservoir computing  (2610.21973 - Potratzki et al., 15 Oct 2026) in Section Discussion