  Isostable reduction is a powerful technique that can be used to characterize
behaviors of nonlinear dynamical systems in a basis of slowly decaying
eigenfunctions of the Koopman operator. When the underlying dynamical equations
are known, previously developed numerical techniques allow for high-order
accuracy computation of isostable reduced models. However, in situations where
the dynamical equations are unknown, few general techniques are available that
provide reliable estimates of the isostable reduced equations, especially in
applications where large magnitude inputs are considered. In this work, a
purely data-driven inference strategy yielding high-accuracy isostable reduced
models is developed for dynamical systems with a fixed point attractor. By
analyzing steady state outputs of nonlinear systems in response to sinusoidal
forcing, both isostable response functions and isostable-to-output
relationships can be estimated to arbitrary accuracy in an expansion performed
in the isostable coordinates. Detailed examples are considered for a population
of synaptically coupled neurons and for the one-dimensional Burgers' equation.
While linear estimates of the isostable response functions are sufficient to
characterize the dynamical behavior when small magnitude inputs are considered,
the high-accuracy reduced order model inference strategy proposed here is
essential when considering large magnitude inputs.
