Augmenting Basis Sets by Normalizing Flows

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