The success of machine learning algorithms generally depends on **data** representation, and it is often hypothesized that this is because different representations can entangle and hide more or less the different explanatory factors of variations behind the **data** [1]. To be reasonably addressed, the problem of finding relevant data-adaptive basis functions for a successful inverse modeling, must be considered within a specific domain of applications [2]. This article is concerned with addressing this problem for time-evolving datasets produced by a dynamical system either deterministic or stochastic.