Title: Flow-Distorted Plane Waves
Primary area: applications to physical sciences (physics, chemistry, biology, etc.)
Keywords: AI for science, Normalizing Flow, Fourier Transform, Density Functional Theory

Abstract: The plane wave basis is widely used in Galerkin approximation, due to its periodicity and computational advantage, where the fast Fourier transform (FFT) can be applied. However, since its spatial resolution is uniform, the number of basis functions required can be excessive for problems with rapidly varying local features. We propose an adaptive basis called flow-distorted plane wave (FDPW), where the bijection of a normalizing flow is used to distort the problem domain, hence achieving adaptive resolution. We apply FDPW to Kohn-Sham density functional theory (DFT) calculations to both molecular and solid-state systems, demonstrating improved speed and memory usage.