  We demonstrate when and how an entire left-infinite orbit of an underlying
dynamical system or observations from such left-infinite orbits can be uniquely
represented by a pair of elements in a different space, a phenomenon which we
call \textit{causal embedding}. The collection of such pairs is derived from a
driven dynamical system and is used to learn a function which together with the
driven system would: (i). determine a system that is topologically conjugate to
the underlying system (ii). enable forecasting the underlying system's dynamics
since the conjugacy is computable and universal, i.e., it does not depend on
the underlying system (iii). guarantee an attractor containing the image of the
causally embedded object even if there is an error made in learning the
function. By accomplishing these we herald a new forecasting scheme that beats
the existing reservoir computing schemes that often lead to poor long-term
consistency as there is no guarantee of the existence of a learnable function,
and overcomes the challenges of stability in Takens delay embedding. We
illustrate accurate modeling of underlying systems where previously known
techniques have failed.
