  Approximating functions by a linear span of truncated basis sets is a
standard procedure for the numerical solution of differential and integral
equations. Commonly used concepts of approximation methods are well-posed and
convergent, by provable approximation orders. On the down side, however, these
methods often suffer from the curse of dimensionality, which limits their
approximation behavior, especially in situations of highly oscillatory target
functions. Nonlinear approximation methods, such as neural networks, were shown
to be very efficient in approximating high-dimensional functions. We
investigate nonlinear approximation methods that are constructed by composing
standard basis sets with normalizing flows. Such models yield richer
approximation spaces while maintaining the density properties of the initial
basis set, as we show. Simulations to approximate eigenfunctions of a perturbed
quantum harmonic oscillator indicate convergence with respect to the size of
the basis set.
