  Large scale dynamical systems (e.g. many nonlinear coupled differential
equations) can often be summarized in terms of only a few state variables (a
few equations), a trait that reduces complexity and facilitates exploration of
behavioral aspects of otherwise intractable models. High model dimensionality
and complexity makes symbolic, pen--and--paper model reduction tedious and
impractical, a difficulty addressed by recently developed frameworks that
computerize reduction. Symbolic work has the benefit, however, of identifying
both reduced state variables and parameter combinations that matter most
(effective parameters, "inputs"); whereas current computational reduction
schemes leave the parameter reduction aspect mostly unaddressed. As the
interest in mapping out and optimizing complex input--output relations keeps
growing, it becomes clear that combating the curse of dimensionality also
requires efficient schemes for input space exploration and reduction. Here, we
explore systematic, data-driven parameter reduction by means of effective
parameter identification, starting from current nonlinear manifold-learning
techniques enabling state space reduction. Our approach aspires to extend the
data-driven determination of effective state variables with the data-driven
discovery of effective model parameters, and thus to accelerate the exploration
of high-dimensional parameter spaces associated with complex models.
