The field of dynamical systems studies how systems evolve in time according to deterministic, probabilistic, or hybrid rule sets. Embedding theorems can be used to describe how observations of these systems can be used to reconstruct their dynamics. However, these theorems do not provide a backmapping to the full-dimensional descriptions of these dynamics. The recovery of these full-dimensional descriptions from time series observations, such as those furnished by experiments, is central to the study of dynamical systems. In this work we propose and validate a pipeline that combines embedding theorems and statistical learning to represent dynamics from time series in a mathematically rigorous way and learn backmappings to full dimensional descriptions with universal function approximators in the context of molecular dynamics. We demonstrate that this framework is robust under noise and extend it for use with arbitrary dynamical systems. We introduce the TAkens Reconstruction (TAR) software package to perform univariate, multivariate and multi-temporal Takens' reconstructions of arbitrary time series and apply the work beyond physics, in the context of economic systems. Lastly, we investigate optimization of observable choice to maximize reconstruction quality. This work provides a theoretical and computational framework with which we can reconstruct and analyze the dynamics of arbitrary dynamical systems. It constitutes a contribution to a broader class of techniques bridging the gap between experimental observation and theoretical understanding of dynamics.