From Fourier to Neural ODEs: Flow matching for modeling complex systems

arXiv:2405.11542v1 Announce Type: new
Abstract: Modeling complex systems using standard neural ordinary differential equations (NODEs) often faces some essential challenges, including high computational costs and susceptibility to local optima. To address these challenges, we propose a simulation-free framework, called Fourier NODEs (FNODEs), that effectively trains NODEs by directly matching the target vector field based on Fourier analysis. Specifically, we employ the Fourier analysis to estimate temporal and potential high-order spatial gradients from noisy observational data. We then incorporate the estimated …

abstract arxiv challenges complex systems computational costs cs.lg differential flow fourier framework free modeling nodes ordinary physics.ed-ph simulation standard systems trains type